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(navazující magisterské studium)",[1153,1248,1250],{"id":1249},"cíl-předmětu","Cíl předmětu",[1252,1253,1254],"blockquote",{},[1110,1255,1256],{},"Cílem předmětu je naučit studenty pracovat s náhodnými veličinami, zpracovat a vyhodnotit statistický materiál, umět použít metody pro statistickou regulaci procesu a určit a vyhodnotit indexy způsobilosti.",[1153,1258,1260],{"id":1259},"hlavní-tematické-okruhy","Hlavní tematické okruhy",[1262,1263,1264,1278,1290,1302,1314,1326],"ol",{},[1265,1266,1267,1270,1271,1277],"li",{},[1136,1268,1269],{},"Pravděpodobnost a rozdělení"," — náhodná veličina a rozdělení pravděpodobnosti (",[1127,1272,1276],{"href":1273,"className":1274,"dataFsResolvedFilePath":1275},"\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni",[1131],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","náhodné veličiny a rozdělení",").",[1265,1279,1280,1283,1284,1277],{},[1136,1281,1282],{},"Zpracování dat"," — empirické charakteristiky, kvantily a třídění dat do tříd (",[1127,1285,1289],{"href":1286,"className":1287,"dataFsResolvedFilePath":1288},"\u002Fwiki\u002Fpopisna-statistika",[1131],"topics\u002Fpopisna-statistika.md","popisná statistika a datové soubory",[1265,1291,1292,1295,1296,1277],{},[1136,1293,1294],{},"Testování hypotéz"," — parametrické a neparametrické testy o střední hodnotě, rozptylu a shodě s rozdělením (",[1127,1297,1301],{"href":1298,"className":1299,"dataFsResolvedFilePath":1300},"\u002Fwiki\u002Ftestovani-hypotez",[1131],"topics\u002Ftestovani-hypotez.md","testování statistických hypotéz",[1265,1303,1304,1307,1308,1277],{},[1136,1305,1306],{},"Regresní a korelační analýza"," — lineární, nelineární a vícenásobná regrese, diagnostika modelu (",[1127,1309,1313],{"href":1310,"className":1311,"dataFsResolvedFilePath":1312},"\u002Fwiki\u002Fregresni-a-korelacni-analyza",[1131],"topics\u002Fregresni-a-korelacni-analyza.md","regresní a korelační analýza",[1265,1315,1316,1319,1320,1277],{},[1136,1317,1318],{},"Kontingenční tabulky"," — test nezávislosti kvalitativních znaků (",[1127,1321,1325],{"href":1322,"className":1323,"dataFsResolvedFilePath":1324},"\u002Fwiki\u002Fkontingencni-tabulky",[1131],"topics\u002Fkontingencni-tabulky.md","kontingenční tabulky",[1265,1327,1328,1331,1332,1277],{},[1136,1329,1330],{},"Statistická regulace procesu"," — Shewhartovy regulační diagramy a indexy způsobilosti (",[1127,1333,1337],{"href":1334,"className":1335,"dataFsResolvedFilePath":1336},"\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[1131],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","regulační diagramy a indexy způsobilosti",[1153,1339,1341],{"id":1340},"hodnocení","Hodnocení",[1110,1343,1344],{},"Zkouškový test trvá přibližně 45 minut a probíhá v počítačové učebně; student v něm řeší 2 až 3 příklady v programu R. Pro úspěšné složení je nutné získat alespoň 50 bodů ze 100.",[1158,1346,1347,1357],{},[1161,1348,1349],{},[1164,1350,1351,1354],{},[1167,1352,1353],{},"Známka",[1167,1355,1356],{},"Body",[1174,1358,1359,1367,1375,1383,1391,1399],{},[1164,1360,1361,1364],{},[1179,1362,1363],{},"A",[1179,1365,1366],{},"90–100",[1164,1368,1369,1372],{},[1179,1370,1371],{},"B",[1179,1373,1374],{},"80–89",[1164,1376,1377,1380],{},[1179,1378,1379],{},"C",[1179,1381,1382],{},"70–79",[1164,1384,1385,1388],{},[1179,1386,1387],{},"D",[1179,1389,1390],{},"60–69",[1164,1392,1393,1396],{},[1179,1394,1395],{},"E",[1179,1397,1398],{},"50–59",[1164,1400,1401,1404],{},[1179,1402,1403],{},"F",[1179,1405,1406],{},"méně než 50",[1153,1408,1410],{"id":1409},"doporučená-literatura","Doporučená literatura",[1262,1412,1413,1424,1432,1440,1449,1458,1467],{},[1265,1414,1415,1418,1419,1423],{},[1136,1416,1417],{},"KROPÁČ, J."," ",[1420,1421,1422],"em",{},"Statistika A."," 4. vyd. Brno: Fakulta podnikatelská VUT, 2011. ISBN 978-80-214-4226-9.",[1265,1425,1426,1418,1428,1431],{},[1136,1427,1417],{},[1420,1429,1430],{},"Statistika B."," 2. vyd. Brno: Fakulta podnikatelská VUT, 2009. ISBN 978-80-214-3295-6.",[1265,1433,1434,1418,1436,1439],{},[1136,1435,1417],{},[1420,1437,1438],{},"Statistika C."," 2. vyd. Brno: Akademické nakladatelství CERM, 2012. ISBN 978-80-7204-789-5.",[1265,1441,1442,1418,1445,1448],{},[1136,1443,1444],{},"KUPKA, K.",[1420,1446,1447],{},"Statistické řízení jakosti."," Pardubice: TriloByte Statistical Software, 1997. ISBN 80-238-1818-X.",[1265,1450,1451,1418,1454,1457],{},[1136,1452,1453],{},"ČSN ISO 8258.",[1420,1455,1456],{},"Shewhartovy regulační diagramy."," Praha: Český normalizační institut, 1994.",[1265,1459,1460,1418,1463,1466],{},[1136,1461,1462],{},"MONTGOMERY, D. C.",[1420,1464,1465],{},"Introduction to Statistical Quality Control."," 6. vyd. John Wiley & Sons, 2005. ISBN 978-0-470-16992-6.",[1265,1468,1469,1418,1472,1475],{},[1136,1470,1471],{},"TOŠENOVSKÝ, J., NOSKIEVIČOVÁ, D.",[1420,1473,1474],{},"Statistické metody pro zlepšování jakosti."," 1. vyd. Ostrava: Montanex, 2000. ISBN 80-7225-040-X.",[1153,1477,1479],{"id":1478},"prerekvizity","Prerekvizity",[1252,1481,1482],{},[1110,1483,1484],{},"Pro úspěšné zvládnutí jsou požadovány základní znalosti teorie pravděpodobnosti, popisné statistiky a matematické statistiky.",[1153,1486,1488],{"id":1487},"elearning","eLearning",[1110,1490,1491,1492,1497],{},"Aktuální otevřený kurz na Moodle VUT: ",[1127,1493,1494],{"href":1494,"rel":1495},"https:\u002F\u002Fmoodle.vut.cz\u002Fcourse\u002Fview.php?id=305692",[1496],"nofollow",".",[1153,1499,1501],{"id":1500},"související-stránky","Související stránky",[1503,1504,1505,1510,1516,1522,1528,1533,1538,1544],"ul",{},[1265,1506,1507],{},[1127,1508,1133],{"href":1129,"className":1509,"dataFsResolvedFilePath":1132},[1131],[1265,1511,1512],{},[1127,1513,1515],{"href":1273,"className":1514,"dataFsResolvedFilePath":1275},[1131],"Náhodné veličiny a rozdělení pravděpodobnosti",[1265,1517,1518],{},[1127,1519,1521],{"href":1286,"className":1520,"dataFsResolvedFilePath":1288},[1131],"Popisná statistika a datové soubory",[1265,1523,1524],{},[1127,1525,1527],{"href":1298,"className":1526,"dataFsResolvedFilePath":1300},[1131],"Testování statistických hypotéz",[1265,1529,1530],{},[1127,1531,1306],{"href":1310,"className":1532,"dataFsResolvedFilePath":1312},[1131],[1265,1534,1535],{},[1127,1536,1318],{"href":1322,"className":1537,"dataFsResolvedFilePath":1324},[1131],[1265,1539,1540],{},[1127,1541,1543],{"href":1334,"className":1542,"dataFsResolvedFilePath":1336},[1131],"Regulační diagramy a indexy způsobilosti",[1265,1545,1546],{},[1127,1547,1551],{"href":1548,"className":1549,"dataFsResolvedFilePath":1550},"\u002Fwiki\u002Fmask-r-tahak",[1131],"outputs\u002Fmask-r-tahak.md","masK — Tahák pro R",[1153,1553,1554],{"id":934},"Reference",[1110,1556,1557,1558,1561],{},"KROPÁČ, J. ",[1420,1559,1560],{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[1110,1563,1557,1564,1567],{},[1420,1565,1566],{},"Statistika B",". 2. vyd. Brno: Fakulta podnikatelská VUT, 2009.",[1110,1569,1557,1570,1573],{},[1420,1571,1572],{},"Statistika C",". 2. vyd. Brno: Akademické nakladatelství CERM, 2012.",[1110,1575,1576,1577,1580],{},"KUPKA, K. ",[1420,1578,1579],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[1110,1582,1583,1584,1587],{},"ČSN ISO 8258. ",[1420,1585,1586],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,1589,1590,1591,1594],{},"MONTGOMERY, D. C. ",[1420,1592,1593],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,1596,1597,1598,1601],{},"TOŠENOVSKÝ, J., NOSKIEVIČOVÁ, D. ",[1420,1599,1600],{},"Statistické metody pro zlepšování jakosti",". Ostrava: Montanex, 2000.",{"title":1603,"searchDepth":27,"depth":27,"links":1604},"",[1605,1606,1607,1608,1609,1610,1611,1612,1613],{"id":1155,"depth":27,"text":1156},{"id":1249,"depth":27,"text":1250},{"id":1259,"depth":27,"text":1260},{"id":1340,"depth":27,"text":1341},{"id":1409,"depth":27,"text":1410},{"id":1478,"depth":27,"text":1479},{"id":1487,"depth":27,"text":1488},{"id":1500,"depth":27,"text":1501},{"id":934,"depth":27,"text":1554},null,"2026-10-02","md",{},true,"\u002Fsummaries\u002Fmask-detail-predmetu",{"title":1094,"description":1603},[1622,1623],"raw\u002Fmask\u002FDetail předmětu.md","raw\u002Fmask\u002Finformace k předmětu.docx","summaries\u002Fmask-detail-predmetu",[23,67,192,232],"summary","IK2lDajIb6EhLzCvO1rJ3Vfhdbd16tTPaZcmiSHNH-c","summaries",[1630,6784,11247,16013,20714,26158],{"id":1631,"title":1318,"body":1632,"course":23,"courses":1614,"created":1615,"description":1603,"extension":1616,"meta":6774,"navigation":1618,"path":6775,"seo":6776,"sources":6777,"stem":6780,"tags":6781,"type":6782,"updated":1615,"__hash__":6783},"topics\u002Ftopics\u002Fkontingencni-tabulky.md",{"type":1096,"value":1633,"toc":6764},[1634,1637,1831,1835,1850,1868,2078,2219,2814,2831,2944,2948,2979,2984,3586,3593,3813,4039,4047,4128,4240,4393,4399,4480,4501,4510,4544,4551,4554,4560,4626,4685,4838,4844,4851,4929,4932,4988,5326,5347,5451,5560,5563,5584,5587,5842,5924,5931,5935,6165,6179,6328,6462,6468,6526,6530,6549,6564,6570,6615,6634,6649,6655,6714,6716,6754,6756,6760],[1099,1635,1318],{"id":1636},"kontingenční-tabulky",[1103,1638,1642,1650],{"className":1639,"dataCallout":1641},[1106,1640],"callout-default","tldr",[1110,1643,1645,1649],{"className":1644},[1113],[1115,1646],{"className":1647,"ariaHidden":1121},[1118,1648,1120],"i-lucide:info","V kostce",[1503,1651,1652,1659,1733,1754,1792,1820],{},[1265,1653,1654,1655,1658],{},"Kontingenční tabulka zaznamenává ",[1136,1656,1657],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1265,1660,1661,1664,1665,1695,1696,1717,1718,1732],{},[1136,1662,1663],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,1666,1669],{"className":1667},[1668],"katex",[1670,1671,1673],"math",{"xmlns":1672},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1674,1675,1676,1690],"semantics",{},[1677,1678,1679],"mrow",{},[1680,1681,1682,1686],"msub",{},[1683,1684,1685],"mi",{},"H",[1687,1688,1689],"mn",{},"0",[1691,1692,1694],"annotation",{"encoding":1693},"application\u002Fx-tex","H_0"," pomocí statistiky ",[1115,1697,1699],{"className":1698},[1668],[1670,1700,1701],{"xmlns":1672},[1674,1702,1703,1714],{},[1677,1704,1705],{},[1706,1707,1708,1711],"msup",{},[1683,1709,1710],{},"χ",[1687,1712,1713],{},"2",[1691,1715,1716],{"encoding":1693},"\\chi^2","; rozhoduje kritický obor ",[1115,1719,1721],{"className":1720},[1668],[1670,1722,1723],{"xmlns":1672},[1674,1724,1725,1730],{},[1677,1726,1727],{},[1683,1728,1729],{},"W",[1691,1731,1729],{"encoding":1693},", prakticky p-hodnota.",[1265,1734,1735,1736,1753],{},"Aproximace ",[1115,1737,1739],{"className":1738},[1668],[1670,1740,1741],{"xmlns":1672},[1674,1742,1743,1751],{},[1677,1744,1745],{},[1706,1746,1747,1749],{},[1683,1748,1710],{},[1687,1750,1713],{},[1691,1752,1716],{"encoding":1693}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1265,1755,1756,1757,1774,1775,1418,1778,1497],{},"Zamítnutí ",[1115,1758,1760],{"className":1759},[1668],[1670,1761,1762],{"xmlns":1672},[1674,1763,1764,1772],{},[1677,1765,1766],{},[1680,1767,1768,1770],{},[1683,1769,1685],{},[1687,1771,1689],{},[1691,1773,1694],{"encoding":1693}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1136,1776,1777],{},"Cramérův koeficient kontingence",[1115,1779,1781],{"className":1780},[1668],[1670,1782,1783],{"xmlns":1672},[1674,1784,1785,1790],{},[1677,1786,1787],{},[1683,1788,1789],{},"V",[1691,1791,1789],{"encoding":1693},[1265,1793,1794,1797,1798,1497],{},[1136,1795,1796],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,1799,1801],{"className":1800},[1668],[1670,1802,1803],{"xmlns":1672},[1674,1804,1805,1817],{},[1677,1806,1807,1810,1814],{},[1683,1808,1809],{},"n",[1811,1812,1813],"mo",{},">",[1687,1815,1816],{},"40",[1691,1818,1819],{"encoding":1693},"n>40",[1265,1821,1822,1823,1826,1827,1830],{},"Pro ",[1136,1824,1825],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1136,1828,1829],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1153,1832,1834],{"id":1833},"kontingenční-tabulka","Kontingenční tabulka",[1110,1836,1837,1838,1841,1842,1845,1846,1849],{},"V rámci ",[1127,1839,1133],{"className":1840,"dataFsResolvedFilePath":1132,"href":1129},[1131]," navazují kontingenční tabulky na\n",[1127,1843,1301],{"className":1844,"dataFsResolvedFilePath":1300,"href":1298},[1131],": místo jedné náhodné veličiny teď sledujeme dva\n",[1136,1847,1848],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,1851,1852,1853,1856,1857,1859,1860,1863,1864,1867],{},"Znak je ",[1136,1854,1855],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1136,1858,1848],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1136,1861,1862],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1136,1865,1866],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,1869,1870,1871,1884,1885,1898,1899,1932,1933,1946,1947,1978,1979,1981,1982,2009,2010,1418,2013,2035,2036,2054,2055,2073,2074,2077],{},"Mějme ",[1115,1872,1874],{"className":1873},[1668],[1670,1875,1876],{"xmlns":1672},[1674,1877,1878,1882],{},[1677,1879,1880],{},[1683,1881,1809],{},[1691,1883,1809],{"encoding":1693}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,1886,1888],{"className":1887},[1668],[1670,1889,1890],{"xmlns":1672},[1674,1891,1892,1896],{},[1677,1893,1894],{},[1683,1895,1363],{},[1691,1897,1363],{"encoding":1693}," (varianty ",[1115,1900,1902],{"className":1901},[1668],[1670,1903,1904],{"xmlns":1672},[1674,1905,1906,1929],{},[1677,1907,1908,1915,1918,1921,1923],{},[1680,1909,1910,1912],{},[1683,1911,1363],{},[1687,1913,1914],{},"1",[1811,1916,1917],{"separator":1121},",",[1811,1919,1920],{},"…",[1811,1922,1917],{"separator":1121},[1680,1924,1925,1927],{},[1683,1926,1363],{},[1683,1928,71],{},[1691,1930,1931],{"encoding":1693},"A_1,\\dots,A_r",") a ",[1115,1934,1936],{"className":1935},[1668],[1670,1937,1938],{"xmlns":1672},[1674,1939,1940,1944],{},[1677,1941,1942],{},[1683,1943,1371],{},[1691,1945,1371],{"encoding":1693},"\n(varianty ",[1115,1948,1950],{"className":1949},[1668],[1670,1951,1952],{"xmlns":1672},[1674,1953,1954,1975],{},[1677,1955,1956,1962,1964,1966,1968],{},[1680,1957,1958,1960],{},[1683,1959,1371],{},[1687,1961,1914],{},[1811,1963,1917],{"separator":1121},[1811,1965,1920],{},[1811,1967,1917],{"separator":1121},[1680,1969,1970,1972],{},[1683,1971,1371],{},[1683,1973,1974],{},"s",[1691,1976,1977],{"encoding":1693},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1136,1980,1325],{},": v políčku ",[1115,1983,1985],{"className":1984},[1668],[1670,1986,1987],{"xmlns":1672},[1674,1988,1989,2006],{},[1677,1990,1991,1995,1998,2000,2003],{},[1811,1992,1994],{"stretchy":1993},"false","(",[1683,1996,1997],{},"i",[1811,1999,1917],{"separator":1121},[1683,2001,2002],{},"j",[1811,2004,2005],{"stretchy":1993},")",[1691,2007,2008],{"encoding":1693},"(i,j)"," je ",[1136,2011,2012],{},"simultánní\nčetnost",[1115,2014,2016],{"className":2015},[1668],[1670,2017,2018],{"xmlns":1672},[1674,2019,2020,2032],{},[1677,2021,2022],{},[1680,2023,2024,2026],{},[1683,2025,1809],{},[1677,2027,2028,2030],{},[1683,2029,1997],{},[1683,2031,2002],{},[1691,2033,2034],{"encoding":1693},"n_{ij}",", tedy počet pokusů s variantou ",[1115,2037,2039],{"className":2038},[1668],[1670,2040,2041],{"xmlns":1672},[1674,2042,2043,2051],{},[1677,2044,2045],{},[1680,2046,2047,2049],{},[1683,2048,1363],{},[1683,2050,1997],{},[1691,2052,2053],{"encoding":1693},"A_i"," zároveň s variantou ",[1115,2056,2058],{"className":2057},[1668],[1670,2059,2060],{"xmlns":1672},[1674,2061,2062,2070],{},[1677,2063,2064],{},[1680,2065,2066,2068],{},[1683,2067,1371],{},[1683,2069,2002],{},[1691,2071,2072],{"encoding":1693},"B_j",". Řádkové a sloupcové součty\njsou ",[1136,2075,2076],{},"marginální četnosti",":",[1115,2079,2081],{"className":2080},[1668],[1670,2082,2084],{"xmlns":1672,"display":2083},"block",[1674,2085,2086,2216],{},[1677,2087,2088,2099,2102,2118,2128,2130,2134,2144,2146,2160,2170,2172,2174,2176,2178,2192,2206],{},[1680,2089,2090,2092],{},[1683,2091,1809],{},[1677,2093,2094,2096],{},[1683,2095,1997],{},[1811,2097,2098],{},"∙",[1811,2100,2101],{},"=",[2103,2104,2105,2108,2116],"munderover",{},[1811,2106,2107],{},"∑",[1677,2109,2110,2112,2114],{},[1683,2111,2002],{},[1811,2113,2101],{},[1687,2115,1914],{},[1683,2117,1974],{},[1680,2119,2120,2122],{},[1683,2121,1809],{},[1677,2123,2124,2126],{},[1683,2125,1997],{},[1683,2127,2002],{},[1811,2129,1917],{"separator":1121},[2131,2132],"mspace",{"width":2133},"2em",[1680,2135,2136,2138],{},[1683,2137,1809],{},[1677,2139,2140,2142],{},[1811,2141,2098],{},[1683,2143,2002],{},[1811,2145,2101],{},[2103,2147,2148,2150,2158],{},[1811,2149,2107],{},[1677,2151,2152,2154,2156],{},[1683,2153,1997],{},[1811,2155,2101],{},[1687,2157,1914],{},[1683,2159,71],{},[1680,2161,2162,2164],{},[1683,2163,1809],{},[1677,2165,2166,2168],{},[1683,2167,1997],{},[1683,2169,2002],{},[1811,2171,1917],{"separator":1121},[2131,2173],{"width":2133},[1683,2175,1809],{},[1811,2177,2101],{},[2103,2179,2180,2182,2190],{},[1811,2181,2107],{},[1677,2183,2184,2186,2188],{},[1683,2185,1997],{},[1811,2187,2101],{},[1687,2189,1914],{},[1683,2191,71],{},[2103,2193,2194,2196,2204],{},[1811,2195,2107],{},[1677,2197,2198,2200,2202],{},[1683,2199,2002],{},[1811,2201,2101],{},[1687,2203,1914],{},[1683,2205,1974],{},[1680,2207,2208,2210],{},[1683,2209,1809],{},[1677,2211,2212,2214],{},[1683,2213,1997],{},[1683,2215,2002],{},[1691,2217,2218],{"encoding":1693},"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}",[1158,2220,2221,2333],{},[1161,2222,2223],{},[1164,2224,2225,2247,2267,2287,2289,2309],{},[1167,2226,2227],{},[1115,2228,2230],{"className":2229},[1668],[1670,2231,2232],{"xmlns":1672},[1674,2233,2234,2244],{},[1677,2235,2236,2238,2242],{},[1683,2237,1363],{},[1683,2239,2241],{"mathvariant":2240},"normal","\\",[1683,2243,1371],{},[1691,2245,2246],{"encoding":1693},"A \\backslash B",[1167,2248,2249],{},[1115,2250,2252],{"className":2251},[1668],[1670,2253,2254],{"xmlns":1672},[1674,2255,2256,2264],{},[1677,2257,2258],{},[1680,2259,2260,2262],{},[1683,2261,1371],{},[1687,2263,1914],{},[1691,2265,2266],{"encoding":1693},"B_1",[1167,2268,2269],{},[1115,2270,2272],{"className":2271},[1668],[1670,2273,2274],{"xmlns":1672},[1674,2275,2276,2284],{},[1677,2277,2278],{},[1680,2279,2280,2282],{},[1683,2281,1371],{},[1687,2283,1713],{},[1691,2285,2286],{"encoding":1693},"B_2",[1167,2288,1920],{},[1167,2290,2291],{},[1115,2292,2294],{"className":2293},[1668],[1670,2295,2296],{"xmlns":1672},[1674,2297,2298,2306],{},[1677,2299,2300],{},[1680,2301,2302,2304],{},[1683,2303,1371],{},[1683,2305,1974],{},[1691,2307,2308],{"encoding":1693},"B_s",[1167,2310,2311],{},[1115,2312,2314],{"className":2313},[1668],[1670,2315,2316],{"xmlns":1672},[1674,2317,2318,2330],{},[1677,2319,2320],{},[1680,2321,2322,2324],{},[1683,2323,1809],{},[1677,2325,2326,2328],{},[1683,2327,1997],{},[1811,2329,2098],{},[1691,2331,2332],{"encoding":1693},"n_{i\\bullet}",[1174,2334,2335,2449,2563,2579,2699],{},[1164,2336,2337,2357,2378,2399,2401,2425],{},[1179,2338,2339],{},[1115,2340,2342],{"className":2341},[1668],[1670,2343,2344],{"xmlns":1672},[1674,2345,2346,2354],{},[1677,2347,2348],{},[1680,2349,2350,2352],{},[1683,2351,1363],{},[1687,2353,1914],{},[1691,2355,2356],{"encoding":1693},"A_1",[1179,2358,2359],{},[1115,2360,2362],{"className":2361},[1668],[1670,2363,2364],{"xmlns":1672},[1674,2365,2366,2375],{},[1677,2367,2368],{},[1680,2369,2370,2372],{},[1683,2371,1809],{},[1687,2373,2374],{},"11",[1691,2376,2377],{"encoding":1693},"n_{11}",[1179,2379,2380],{},[1115,2381,2383],{"className":2382},[1668],[1670,2384,2385],{"xmlns":1672},[1674,2386,2387,2396],{},[1677,2388,2389],{},[1680,2390,2391,2393],{},[1683,2392,1809],{},[1687,2394,2395],{},"12",[1691,2397,2398],{"encoding":1693},"n_{12}",[1179,2400,1920],{},[1179,2402,2403],{},[1115,2404,2406],{"className":2405},[1668],[1670,2407,2408],{"xmlns":1672},[1674,2409,2410,2422],{},[1677,2411,2412],{},[1680,2413,2414,2416],{},[1683,2415,1809],{},[1677,2417,2418,2420],{},[1687,2419,1914],{},[1683,2421,1974],{},[1691,2423,2424],{"encoding":1693},"n_{1s}",[1179,2426,2427],{},[1115,2428,2430],{"className":2429},[1668],[1670,2431,2432],{"xmlns":1672},[1674,2433,2434,2446],{},[1677,2435,2436],{},[1680,2437,2438,2440],{},[1683,2439,1809],{},[1677,2441,2442,2444],{},[1687,2443,1914],{},[1811,2445,2098],{},[1691,2447,2448],{"encoding":1693},"n_{1\\bullet}",[1164,2450,2451,2471,2492,2513,2515,2539],{},[1179,2452,2453],{},[1115,2454,2456],{"className":2455},[1668],[1670,2457,2458],{"xmlns":1672},[1674,2459,2460,2468],{},[1677,2461,2462],{},[1680,2463,2464,2466],{},[1683,2465,1363],{},[1687,2467,1713],{},[1691,2469,2470],{"encoding":1693},"A_2",[1179,2472,2473],{},[1115,2474,2476],{"className":2475},[1668],[1670,2477,2478],{"xmlns":1672},[1674,2479,2480,2489],{},[1677,2481,2482],{},[1680,2483,2484,2486],{},[1683,2485,1809],{},[1687,2487,2488],{},"21",[1691,2490,2491],{"encoding":1693},"n_{21}",[1179,2493,2494],{},[1115,2495,2497],{"className":2496},[1668],[1670,2498,2499],{"xmlns":1672},[1674,2500,2501,2510],{},[1677,2502,2503],{},[1680,2504,2505,2507],{},[1683,2506,1809],{},[1687,2508,2509],{},"22",[1691,2511,2512],{"encoding":1693},"n_{22}",[1179,2514,1920],{},[1179,2516,2517],{},[1115,2518,2520],{"className":2519},[1668],[1670,2521,2522],{"xmlns":1672},[1674,2523,2524,2536],{},[1677,2525,2526],{},[1680,2527,2528,2530],{},[1683,2529,1809],{},[1677,2531,2532,2534],{},[1687,2533,1713],{},[1683,2535,1974],{},[1691,2537,2538],{"encoding":1693},"n_{2s}",[1179,2540,2541],{},[1115,2542,2544],{"className":2543},[1668],[1670,2545,2546],{"xmlns":1672},[1674,2547,2548,2560],{},[1677,2549,2550],{},[1680,2551,2552,2554],{},[1683,2553,1809],{},[1677,2555,2556,2558],{},[1687,2557,1713],{},[1811,2559,2098],{},[1691,2561,2562],{"encoding":1693},"n_{2\\bullet}",[1164,2564,2565,2568,2570,2572,2575,2577],{},[1179,2566,2567],{},"⋮",[1179,2569,2567],{},[1179,2571,2567],{},[1179,2573,2574],{},"⋱",[1179,2576,2567],{},[1179,2578,2567],{},[1164,2580,2581,2601,2625,2649,2651,2675],{},[1179,2582,2583],{},[1115,2584,2586],{"className":2585},[1668],[1670,2587,2588],{"xmlns":1672},[1674,2589,2590,2598],{},[1677,2591,2592],{},[1680,2593,2594,2596],{},[1683,2595,1363],{},[1683,2597,71],{},[1691,2599,2600],{"encoding":1693},"A_r",[1179,2602,2603],{},[1115,2604,2606],{"className":2605},[1668],[1670,2607,2608],{"xmlns":1672},[1674,2609,2610,2622],{},[1677,2611,2612],{},[1680,2613,2614,2616],{},[1683,2615,1809],{},[1677,2617,2618,2620],{},[1683,2619,71],{},[1687,2621,1914],{},[1691,2623,2624],{"encoding":1693},"n_{r1}",[1179,2626,2627],{},[1115,2628,2630],{"className":2629},[1668],[1670,2631,2632],{"xmlns":1672},[1674,2633,2634,2646],{},[1677,2635,2636],{},[1680,2637,2638,2640],{},[1683,2639,1809],{},[1677,2641,2642,2644],{},[1683,2643,71],{},[1687,2645,1713],{},[1691,2647,2648],{"encoding":1693},"n_{r2}",[1179,2650,1920],{},[1179,2652,2653],{},[1115,2654,2656],{"className":2655},[1668],[1670,2657,2658],{"xmlns":1672},[1674,2659,2660,2672],{},[1677,2661,2662],{},[1680,2663,2664,2666],{},[1683,2665,1809],{},[1677,2667,2668,2670],{},[1683,2669,71],{},[1683,2671,1974],{},[1691,2673,2674],{"encoding":1693},"n_{rs}",[1179,2676,2677],{},[1115,2678,2680],{"className":2679},[1668],[1670,2681,2682],{"xmlns":1672},[1674,2683,2684,2696],{},[1677,2685,2686],{},[1680,2687,2688,2690],{},[1683,2689,1809],{},[1677,2691,2692,2694],{},[1683,2693,71],{},[1811,2695,2098],{},[1691,2697,2698],{"encoding":1693},"n_{r\\bullet}",[1164,2700,2701,2725,2749,2773,2775,2799],{},[1179,2702,2703],{},[1115,2704,2706],{"className":2705},[1668],[1670,2707,2708],{"xmlns":1672},[1674,2709,2710,2722],{},[1677,2711,2712],{},[1680,2713,2714,2716],{},[1683,2715,1809],{},[1677,2717,2718,2720],{},[1811,2719,2098],{},[1683,2721,2002],{},[1691,2723,2724],{"encoding":1693},"n_{\\bullet j}",[1179,2726,2727],{},[1115,2728,2730],{"className":2729},[1668],[1670,2731,2732],{"xmlns":1672},[1674,2733,2734,2746],{},[1677,2735,2736],{},[1680,2737,2738,2740],{},[1683,2739,1809],{},[1677,2741,2742,2744],{},[1811,2743,2098],{},[1687,2745,1914],{},[1691,2747,2748],{"encoding":1693},"n_{\\bullet 1}",[1179,2750,2751],{},[1115,2752,2754],{"className":2753},[1668],[1670,2755,2756],{"xmlns":1672},[1674,2757,2758,2770],{},[1677,2759,2760],{},[1680,2761,2762,2764],{},[1683,2763,1809],{},[1677,2765,2766,2768],{},[1811,2767,2098],{},[1687,2769,1713],{},[1691,2771,2772],{"encoding":1693},"n_{\\bullet 2}",[1179,2774,1920],{},[1179,2776,2777],{},[1115,2778,2780],{"className":2779},[1668],[1670,2781,2782],{"xmlns":1672},[1674,2783,2784,2796],{},[1677,2785,2786],{},[1680,2787,2788,2790],{},[1683,2789,1809],{},[1677,2791,2792,2794],{},[1811,2793,2098],{},[1683,2795,1974],{},[1691,2797,2798],{"encoding":1693},"n_{\\bullet s}",[1179,2800,2801],{},[1115,2802,2804],{"className":2803},[1668],[1670,2805,2806],{"xmlns":1672},[1674,2807,2808,2812],{},[1677,2809,2810],{},[1683,2811,1809],{},[1691,2813,1809],{"encoding":1693},[1110,2815,2816,2817,2830],{},"Vydělením četností počtem opakování ",[1115,2818,2820],{"className":2819},[1668],[1670,2821,2822],{"xmlns":1672},[1674,2823,2824,2828],{},[1677,2825,2826],{},[1683,2827,1809],{},[1691,2829,1809],{"encoding":1693}," dostaneme odhady pravděpodobností:",[1115,2832,2834],{"className":2833},[1668],[1670,2835,2836],{"xmlns":1672,"display":2083},[1674,2837,2838,2941],{},[1677,2839,2840,2856,2858,2873,2875,2877,2891,2893,2907,2909,2911,2925,2927],{},[1680,2841,2842,2850],{},[2843,2844,2845,2847],"mover",{"accent":1121},[1683,2846,1110],{},[1811,2848,2849],{},"^",[1677,2851,2852,2854],{},[1683,2853,1997],{},[1683,2855,2002],{},[1811,2857,2101],{},[2859,2860,2861,2871],"mfrac",{},[1680,2862,2863,2865],{},[1683,2864,1809],{},[1677,2866,2867,2869],{},[1683,2868,1997],{},[1683,2870,2002],{},[1683,2872,1809],{},[1811,2874,1917],{"separator":1121},[2131,2876],{"width":2133},[1680,2878,2879,2885],{},[2843,2880,2881,2883],{"accent":1121},[1683,2882,1110],{},[1811,2884,2849],{},[1677,2886,2887,2889],{},[1683,2888,1997],{},[1811,2890,2098],{},[1811,2892,2101],{},[2859,2894,2895,2905],{},[1680,2896,2897,2899],{},[1683,2898,1809],{},[1677,2900,2901,2903],{},[1683,2902,1997],{},[1811,2904,2098],{},[1683,2906,1809],{},[1811,2908,1917],{"separator":1121},[2131,2910],{"width":2133},[1680,2912,2913,2919],{},[2843,2914,2915,2917],{"accent":1121},[1683,2916,1110],{},[1811,2918,2849],{},[1677,2920,2921,2923],{},[1811,2922,2098],{},[1683,2924,2002],{},[1811,2926,2101],{},[2859,2928,2929,2939],{},[1680,2930,2931,2933],{},[1683,2932,1809],{},[1677,2934,2935,2937],{},[1811,2936,2098],{},[1683,2938,2002],{},[1683,2940,1809],{},[1691,2942,2943],{"encoding":1693},"\\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}",[1153,2945,2947],{"id":2946},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,2949,2950,2951,2964,2965,2978],{},"Test ověřuje, zda varianty znaku ",[1115,2952,2954],{"className":2953},[1668],[1670,2955,2956],{"xmlns":1672},[1674,2957,2958,2962],{},[1677,2959,2960],{},[1683,2961,1363],{},[1691,2963,1363],{"encoding":1693}," a varianty znaku ",[1115,2966,2968],{"className":2967},[1668],[1670,2969,2970],{"xmlns":1672},[1674,2971,2972,2976],{},[1677,2973,2974],{},[1683,2975,1371],{},[1691,2977,1371],{"encoding":1693}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,2980,2981],{},[1136,2982,2983],{},"Postup testu:",[1262,2985,2986,3118,3436,3518],{},[1265,2987,2988,3044,3045,3071,3072,3098,3099,3117],{},[1115,2989,2991],{"className":2990},[1668],[1670,2992,2993],{"xmlns":1672},[1674,2994,2995,3041],{},[1677,2996,2997,3003,3005,3015,3017,3027,3031],{},[1680,2998,2999,3001],{},[1683,3000,1685],{},[1687,3002,1689],{},[1811,3004,2077],{},[1680,3006,3007,3009],{},[1683,3008,1110],{},[1677,3010,3011,3013],{},[1683,3012,1997],{},[1683,3014,2002],{},[1811,3016,2101],{},[1680,3018,3019,3021],{},[1683,3020,1110],{},[1677,3022,3023,3025],{},[1683,3024,1997],{},[1811,3026,2098],{},[3028,3029,3030],"mtext",{}," ",[1680,3032,3033,3035],{},[1683,3034,1110],{},[1677,3036,3037,3039],{},[1811,3038,2098],{},[1683,3040,2002],{},[1691,3042,3043],{"encoding":1693},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,3046,3048],{"className":3047},[1668],[1670,3049,3050],{"xmlns":1672},[1674,3051,3052,3068],{},[1677,3053,3054,3056,3058,3060,3062,3064,3066],{},[1683,3055,1997],{},[1811,3057,2101],{},[1687,3059,1914],{},[1811,3061,1917],{"separator":1121},[1811,3063,1920],{},[1811,3065,1917],{"separator":1121},[1683,3067,71],{},[1691,3069,3070],{"encoding":1693},"i = 1,\\dots,r",", ",[1115,3073,3075],{"className":3074},[1668],[1670,3076,3077],{"xmlns":1672},[1674,3078,3079,3095],{},[1677,3080,3081,3083,3085,3087,3089,3091,3093],{},[1683,3082,2002],{},[1811,3084,2101],{},[1687,3086,1914],{},[1811,3088,1917],{"separator":1121},[1811,3090,1920],{},[1811,3092,1917],{"separator":1121},[1683,3094,1974],{},[1691,3096,3097],{"encoding":1693},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,3100,3102],{"className":3101},[1668],[1670,3103,3104],{"xmlns":1672},[1674,3105,3106,3114],{},[1677,3107,3108],{},[1680,3109,3110,3112],{},[1683,3111,1685],{},[1687,3113,1914],{},[1691,3115,3116],{"encoding":1693},"H_1",": znaky jsou závislé.",[1265,3119,3120,3121,3278,3281,3282,3299,3300,3332,3333,2009,3392,3395,3396,3417,3418,3435],{},"Testové kritérium",[1115,3122,3124],{"className":3123},[1668],[1670,3125,3126],{"xmlns":1672,"display":2083},[1674,3127,3128,3275],{},[1677,3129,3130,3136,3138,3152,3166,3225,3227,3229,3243,3245,3259,3261],{},[1706,3131,3132,3134],{},[1683,3133,1710],{},[1687,3135,1713],{},[1811,3137,2101],{},[2103,3139,3140,3142,3150],{},[1811,3141,2107],{},[1677,3143,3144,3146,3148],{},[1683,3145,1997],{},[1811,3147,2101],{},[1687,3149,1914],{},[1683,3151,71],{},[2103,3153,3154,3156,3164],{},[1811,3155,2107],{},[1677,3157,3158,3160,3162],{},[1683,3159,2002],{},[1811,3161,2101],{},[1687,3163,1914],{},[1683,3165,1974],{},[2859,3167,3168,3207],{},[1677,3169,3170,3172,3182,3185,3187,3201],{},[1811,3171,1994],{"stretchy":1993},[1680,3173,3174,3176],{},[1683,3175,1809],{},[1677,3177,3178,3180],{},[1683,3179,1997],{},[1683,3181,2002],{},[1811,3183,3184],{},"−",[1683,3186,1809],{},[1680,3188,3189,3195],{},[2843,3190,3191,3193],{"accent":1121},[1683,3192,1110],{},[1811,3194,2849],{},[1677,3196,3197,3199],{},[1683,3198,1997],{},[1683,3200,2002],{},[1706,3202,3203,3205],{},[1811,3204,2005],{"stretchy":1993},[1687,3206,1713],{},[1677,3208,3209,3211],{},[1683,3210,1809],{},[1680,3212,3213,3219],{},[2843,3214,3215,3217],{"accent":1121},[1683,3216,1110],{},[1811,3218,2849],{},[1677,3220,3221,3223],{},[1683,3222,1997],{},[1683,3224,2002],{},[1811,3226,1917],{"separator":1121},[2131,3228],{"width":2133},[1680,3230,3231,3237],{},[2843,3232,3233,3235],{"accent":1121},[1683,3234,1110],{},[1811,3236,2849],{},[1677,3238,3239,3241],{},[1683,3240,1997],{},[1683,3242,2002],{},[1811,3244,2101],{},[1680,3246,3247,3253],{},[2843,3248,3249,3251],{"accent":1121},[1683,3250,1110],{},[1811,3252,2849],{},[1677,3254,3255,3257],{},[1683,3256,1997],{},[1811,3258,2098],{},[3028,3260,3030],{},[1680,3262,3263,3269],{},[2843,3264,3265,3267],{"accent":1121},[1683,3266,1110],{},[1811,3268,2849],{},[1677,3270,3271,3273],{},[1811,3272,2098],{},[1683,3274,2002],{},[1691,3276,3277],{"encoding":1693},"\\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}",[3279,3280],"br",{},"má asymptoticky Pearsonovo (",[1115,3283,3285],{"className":3284},[1668],[1670,3286,3287],{"xmlns":1672},[1674,3288,3289,3297],{},[1677,3290,3291],{},[1706,3292,3293,3295],{},[1683,3294,1710],{},[1687,3296,1713],{},[1691,3298,1716],{"encoding":1693},") rozdělení o ",[1115,3301,3303],{"className":3302},[1668],[1670,3304,3305],{"xmlns":1672},[1674,3306,3307,3329],{},[1677,3308,3309,3311,3313,3315,3317,3319,3321,3323,3325,3327],{},[1811,3310,1994],{"stretchy":1993},[1683,3312,71],{},[1811,3314,3184],{},[1687,3316,1914],{},[1811,3318,2005],{"stretchy":1993},[1811,3320,1994],{"stretchy":1993},[1683,3322,1974],{},[1811,3324,3184],{},[1687,3326,1914],{},[1811,3328,2005],{"stretchy":1993},[1691,3330,3331],{"encoding":1693},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,3334,3336],{"className":3335},[1668],[1670,3337,3338],{"xmlns":1672},[1674,3339,3340,3389],{},[1677,3341,3342,3344,3358,3360],{},[1683,3343,1809],{},[1680,3345,3346,3352],{},[2843,3347,3348,3350],{"accent":1121},[1683,3349,1110],{},[1811,3351,2849],{},[1677,3353,3354,3356],{},[1683,3355,1997],{},[1683,3357,2002],{},[1811,3359,2101],{},[3361,3362,3363],"mstyle",{"scriptlevel":1689,"displaystyle":1121},[2859,3364,3365,3387],{},[1677,3366,3367,3377],{},[1680,3368,3369,3371],{},[1683,3370,1809],{},[1677,3372,3373,3375],{},[1683,3374,1997],{},[1811,3376,2098],{},[1680,3378,3379,3381],{},[1683,3380,1809],{},[1677,3382,3383,3385],{},[1811,3384,2098],{},[1683,3386,2002],{},[1683,3388,1809],{},[1691,3390,3391],{"encoding":1693},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1136,3393,3394],{},"očekávaná četnost"," políčka ",[1115,3397,3399],{"className":3398},[1668],[1670,3400,3401],{"xmlns":1672},[1674,3402,3403,3415],{},[1677,3404,3405,3407,3409,3411,3413],{},[1811,3406,1994],{"stretchy":1993},[1683,3408,1997],{},[1811,3410,1917],{"separator":1121},[1683,3412,2002],{},[1811,3414,2005],{"stretchy":1993},[1691,3416,2008],{"encoding":1693}," — četnost, kterou bychom čekali, kdyby ",[1115,3419,3421],{"className":3420},[1668],[1670,3422,3423],{"xmlns":1672},[1674,3424,3425,3433],{},[1677,3426,3427],{},[1680,3428,3429,3431],{},[1683,3430,1685],{},[1687,3432,1689],{},[1691,3434,1694],{"encoding":1693}," platila.",[1265,3437,3438,3439,1497],{},"Kritický obor: ",[1115,3440,3442],{"className":3441},[1668],[1670,3443,3444],{"xmlns":1672},[1674,3445,3446,3515],{},[1677,3447,3448,3450,3452,3455,3461,3463,3469,3472,3488,3490,3492,3494,3496,3498,3500,3502,3504,3506,3508,3510,3512],{},[1683,3449,1729],{},[1811,3451,2101],{},[1811,3453,3454],{"stretchy":1993},"{",[1706,3456,3457,3459],{},[1683,3458,1710],{},[1687,3460,1713],{},[1811,3462,2077],{},[1706,3464,3465,3467],{},[1683,3466,1710],{},[1687,3468,1713],{},[1811,3470,3471],{},"≥",[3473,3474,3475,3477,3486],"msubsup",{},[1683,3476,1710],{},[1677,3478,3479,3481,3483],{},[1687,3480,1914],{},[1811,3482,3184],{},[1683,3484,3485],{},"α",[1687,3487,1713],{},[1811,3489,1994],{"stretchy":1993},[1811,3491,1994],{"stretchy":1993},[1683,3493,71],{},[1811,3495,3184],{},[1687,3497,1914],{},[1811,3499,2005],{"stretchy":1993},[1811,3501,1994],{"stretchy":1993},[1683,3503,1974],{},[1811,3505,3184],{},[1687,3507,1914],{},[1811,3509,2005],{"stretchy":1993},[1811,3511,2005],{"stretchy":1993},[1811,3513,3514],{"stretchy":1993},"}",[1691,3516,3517],{"encoding":1693},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1265,3519,3520,3521,3534,3535,3549,3550,3567,3568,3585],{},"Padne-li testové kritérium do ",[1115,3522,3524],{"className":3523},[1668],[1670,3525,3526],{"xmlns":1672},[1674,3527,3528,3532],{},[1677,3529,3530],{},[1683,3531,1729],{},[1691,3533,1729],{"encoding":1693},", zamítáme na hladině ",[1115,3536,3538],{"className":3537},[1668],[1670,3539,3540],{"xmlns":1672},[1674,3541,3542,3546],{},[1677,3543,3544],{},[1683,3545,3485],{},[1691,3547,3548],{"encoding":1693},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,3551,3553],{"className":3552},[1668],[1670,3554,3555],{"xmlns":1672},[1674,3556,3557,3565],{},[1677,3558,3559],{},[1680,3560,3561,3563],{},[1683,3562,1685],{},[1687,3564,1914],{},[1691,3566,3116],{"encoding":1693},"; jinak nemáme důvod ",[1115,3569,3571],{"className":3570},[1668],[1670,3572,3573],{"xmlns":1672},[1674,3574,3575,3583],{},[1677,3576,3577],{},[1680,3578,3579,3581],{},[1683,3580,1685],{},[1687,3582,1689],{},[1691,3584,1694],{"encoding":1693}," zamítnout.",[1110,3587,3588,3589,1497],{},"V R počítá test i očekávané četnosti funkce ",[3590,3591,3592],"code",{},"chisq.test()",[1103,3594,3598,3606,3609,3612,3758],{"className":3595,"dataCallout":3597},[1106,3596],"callout-example","example",[1110,3599,3601,3605],{"className":3600},[1113],[1115,3602],{"className":3603,"ariaHidden":1121},[1118,3604,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,3607,3608],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,3610,3611],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1158,3613,3614,3653],{},[1161,3615,3616],{},[1164,3617,3618,3621,3624,3627,3630],{},[1167,3619,3620],{},"vzdělání \\ nákup",[1167,3622,3623],{},"ano",[1167,3625,3626],{},"ne, ale plánuji",[1167,3628,3629],{},"ne, neplánuji",[1167,3631,3632],{},[1115,3633,3635],{"className":3634},[1668],[1670,3636,3637],{"xmlns":1672},[1674,3638,3639,3651],{},[1677,3640,3641],{},[1680,3642,3643,3645],{},[1683,3644,1809],{},[1677,3646,3647,3649],{},[1683,3648,1997],{},[1811,3650,2098],{},[1691,3652,2332],{"encoding":1693},[1174,3654,3655,3671,3688,3705,3721],{},[1164,3656,3657,3660,3663,3666,3668],{},[1179,3658,3659],{},"SŠ bez maturity",[1179,3661,3662],{},"4",[1179,3664,3665],{},"13",[1179,3667,2395],{},[1179,3669,3670],{},"29",[1164,3672,3673,3676,3679,3682,3685],{},[1179,3674,3675],{},"SŠ s maturitou, VOŠ",[1179,3677,3678],{},"31",[1179,3680,3681],{},"62",[1179,3683,3684],{},"71",[1179,3686,3687],{},"164",[1164,3689,3690,3693,3696,3699,3702],{},[1179,3691,3692],{},"VŠ",[1179,3694,3695],{},"44",[1179,3697,3698],{},"58",[1179,3700,3701],{},"66",[1179,3703,3704],{},"168",[1164,3706,3707,3710,3713,3716,3718],{},[1179,3708,3709],{},"ZŠ",[1179,3711,3712],{},"3",[1179,3714,3715],{},"9",[1179,3717,2395],{},[1179,3719,3720],{},"24",[1164,3722,3723,3746,3749,3752,3755],{},[1179,3724,3725],{},[1115,3726,3728],{"className":3727},[1668],[1670,3729,3730],{"xmlns":1672},[1674,3731,3732,3744],{},[1677,3733,3734],{},[1680,3735,3736,3738],{},[1683,3737,1809],{},[1677,3739,3740,3742],{},[1811,3741,2098],{},[1683,3743,2002],{},[1691,3745,2724],{"encoding":1693},[1179,3747,3748],{},"82",[1179,3750,3751],{},"142",[1179,3753,3754],{},"161",[1179,3756,3757],{},"385",[1110,3759,3760,3812],{},[1115,3761,3763],{"className":3762},[1668],[1670,3764,3765],{"xmlns":1672},[1674,3766,3767,3809],{},[1677,3768,3769,3775,3777,3787,3789,3799],{},[1680,3770,3771,3773],{},[1683,3772,1685],{},[1687,3774,1689],{},[1811,3776,2077],{},[1680,3778,3779,3781],{},[1683,3780,1110],{},[1677,3782,3783,3785],{},[1683,3784,1997],{},[1683,3786,2002],{},[1811,3788,2101],{},[1680,3790,3791,3793],{},[1683,3792,1110],{},[1677,3794,3795,3797],{},[1683,3796,1997],{},[1811,3798,2098],{},[1680,3800,3801,3803],{},[1683,3802,1110],{},[1677,3804,3805,3807],{},[1811,3806,2098],{},[1683,3808,2002],{},[1691,3810,3811],{"encoding":1693},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3814,3815,3818],"pre",{"className":3816,"code":3817,"language":71,"meta":1603,"style":1603},"language-r shiki shiki-themes github-light github-light github-dark","tab1 \u003C- matrix(c(4, 13, 12,\n                 31, 62, 71,\n                 44, 58, 66,\n                 3,  9, 12),\n               nrow = 4, byrow = TRUE,\n               dimnames = list(\n                 vzdelani = c(\"SS bez maturity\", \"SS s maturitou nebo VOS\", \"VS\", \"ZS\"),\n                 nakup    = c(\"ano\", \"ne, ale planuji\", \"ne, neplanuji\")))\nchisq.test(tab1)\nchisq.test(tab1)$expected\n",[3590,3819,3820,3859,3876,3893,3911,3934,3947,3982,4010,4023],{"__ignoreMap":1603},[1115,3821,3823,3827,3831,3835,3838,3841,3843,3846,3848,3851,3853,3856],{"class":3822,"line":10},"line",[1115,3824,3826],{"class":3825},"sP4rz","tab1",[1115,3828,3830],{"class":3829},"s8jYJ"," \u003C-",[1115,3832,3834],{"class":3833},"snPdu"," matrix",[1115,3836,1994],{"class":3837},"sxrX7",[1115,3839,3840],{"class":3833},"c",[1115,3842,1994],{"class":3837},[1115,3844,3662],{"class":3845},"sBjJW",[1115,3847,1917],{"class":3829},[1115,3849,3850],{"class":3845}," 13",[1115,3852,1917],{"class":3829},[1115,3854,3855],{"class":3845}," 12",[1115,3857,3858],{"class":3829},",\n",[1115,3860,3861,3864,3866,3869,3871,3874],{"class":3822,"line":27},[1115,3862,3863],{"class":3845},"                 31",[1115,3865,1917],{"class":3829},[1115,3867,3868],{"class":3845}," 62",[1115,3870,1917],{"class":3829},[1115,3872,3873],{"class":3845}," 71",[1115,3875,3858],{"class":3829},[1115,3877,3878,3881,3883,3886,3888,3891],{"class":3822,"line":148},[1115,3879,3880],{"class":3845},"                 44",[1115,3882,1917],{"class":3829},[1115,3884,3885],{"class":3845}," 58",[1115,3887,1917],{"class":3829},[1115,3889,3890],{"class":3845}," 66",[1115,3892,3858],{"class":3829},[1115,3894,3895,3898,3900,3903,3905,3907,3909],{"class":3822,"line":111},[1115,3896,3897],{"class":3845},"                 3",[1115,3899,1917],{"class":3829},[1115,3901,3902],{"class":3845},"  9",[1115,3904,1917],{"class":3829},[1115,3906,3855],{"class":3845},[1115,3908,2005],{"class":3837},[1115,3910,3858],{"class":3829},[1115,3912,3913,3916,3919,3922,3924,3927,3929,3932],{"class":3822,"line":96},[1115,3914,3915],{"class":3825},"               nrow",[1115,3917,3918],{"class":3829}," =",[1115,3920,3921],{"class":3845}," 4",[1115,3923,1917],{"class":3829},[1115,3925,3926],{"class":3825}," byrow",[1115,3928,3918],{"class":3829},[1115,3930,3931],{"class":3845}," TRUE",[1115,3933,3858],{"class":3829},[1115,3935,3936,3939,3941,3944],{"class":3822,"line":89},[1115,3937,3938],{"class":3825},"               dimnames",[1115,3940,3918],{"class":3829},[1115,3942,3943],{"class":3833}," list",[1115,3945,3946],{"class":3837},"(\n",[1115,3948,3949,3952,3954,3957,3959,3963,3965,3968,3970,3973,3975,3978,3980],{"class":3822,"line":82},[1115,3950,3951],{"class":3825},"                 vzdelani",[1115,3953,3918],{"class":3829},[1115,3955,3956],{"class":3833}," c",[1115,3958,1994],{"class":3837},[1115,3960,3962],{"class":3961},"sIIMD","\"SS bez maturity\"",[1115,3964,1917],{"class":3829},[1115,3966,3967],{"class":3961}," \"SS s maturitou nebo VOS\"",[1115,3969,1917],{"class":3829},[1115,3971,3972],{"class":3961}," \"VS\"",[1115,3974,1917],{"class":3829},[1115,3976,3977],{"class":3961}," \"ZS\"",[1115,3979,2005],{"class":3837},[1115,3981,3858],{"class":3829},[1115,3983,3984,3987,3990,3992,3994,3997,3999,4002,4004,4007],{"class":3822,"line":75},[1115,3985,3986],{"class":3825},"                 nakup",[1115,3988,3989],{"class":3829},"    =",[1115,3991,3956],{"class":3833},[1115,3993,1994],{"class":3837},[1115,3995,3996],{"class":3961},"\"ano\"",[1115,3998,1917],{"class":3829},[1115,4000,4001],{"class":3961}," \"ne, ale planuji\"",[1115,4003,1917],{"class":3829},[1115,4005,4006],{"class":3961}," \"ne, neplanuji\"",[1115,4008,4009],{"class":3837},")))\n",[1115,4011,4013,4016,4018,4020],{"class":3822,"line":4012},9,[1115,4014,4015],{"class":3833},"chisq.test",[1115,4017,1994],{"class":3837},[1115,4019,3826],{"class":3825},[1115,4021,4022],{"class":3837},")\n",[1115,4024,4025,4027,4029,4031,4033,4036],{"class":3822,"line":72},[1115,4026,4015],{"class":3833},[1115,4028,1994],{"class":3837},[1115,4030,3826],{"class":3825},[1115,4032,2005],{"class":3837},[1115,4034,4035],{"class":3829},"$",[1115,4037,4038],{"class":3825},"expected\n",[3814,4040,4045],{"className":4041,"code":4043,"language":4044,"meta":1603},[4042],"language-text","    Pearson's Chi-squared test\n\ndata:  tab1\nX-squared = 5.4875, df = 6, p-value = 0.483\n\n                         nakup\nvzdelani                        ano ne, ale planuji ne, neplanuji\n  SS bez maturity          6.176623       10.696104      12.12727\n  SS s maturitou nebo VOS 34.929870       60.488312      68.58182\n  VS                      35.781818       61.963636      70.25455\n  ZS                       5.111688        8.851948      10.03636\n","text",[3590,4046,4043],{"__ignoreMap":1603},[1110,4048,4049,4050,4073,4074,4088,4089,4109,4110,4127],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,4051,4053],{"className":4052},[1668],[1670,4054,4055],{"xmlns":1672},[1674,4056,4057,4070],{},[1677,4058,4059,4065,4067],{},[1706,4060,4061,4063],{},[1683,4062,1710],{},[1687,4064,1713],{},[1811,4066,2101],{},[1687,4068,4069],{},"5,49",[1691,4071,4072],{"encoding":1693},"\\chi^2 = 5{,}49"," s ",[1115,4075,4077],{"className":4076},[1668],[1670,4078,4079],{"xmlns":1672},[1674,4080,4081,4086],{},[1677,4082,4083],{},[1687,4084,4085],{},"6",[1691,4087,4085],{"encoding":1693}," stupni\nvolnosti dává p-hodnotu ",[1115,4090,4092],{"className":4091},[1668],[1670,4093,4094],{"xmlns":1672},[1674,4095,4096,4106],{},[1677,4097,4098,4101,4103],{},[1687,4099,4100],{},"0,483",[1811,4102,1813],{},[1687,4104,4105],{},"0,05",[1691,4107,4108],{"encoding":1693},"0{,}483 > 0{,}05",": ",[1115,4111,4113],{"className":4112},[1668],[1670,4114,4115],{"xmlns":1672},[1674,4116,4117,4125],{},[1677,4118,4119],{},[1680,4120,4121,4123],{},[1683,4122,1685],{},[1687,4124,1689],{},[1691,4126,1694],{"encoding":1693}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,4129,4131,4138,4141,4186],{"className":4130,"dataCallout":3597},[1106,3596],[1110,4132,4134,4137],{"className":4133},[1113],[1115,4135],{"className":4136,"ariaHidden":1121},[1118,3604,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,4139,4140],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1158,4142,4143,4157],{},[1161,4144,4145],{},[1164,4146,4147,4150,4153,4155],{},[1167,4148,4149],{},"zveřejňuje \\ vzdělání",[1167,4151,4152],{},"SŠ",[1167,4154,3692],{},[1167,4156,3709],{},[1174,4158,4159,4173],{},[1164,4160,4161,4164,4167,4170],{},[1179,4162,4163],{},"ne",[1179,4165,4166],{},"20",[1179,4168,4169],{},"33",[1179,4171,4172],{},"39",[1164,4174,4175,4177,4180,4183],{},[1179,4176,3623],{},[1179,4178,4179],{},"25",[1179,4181,4182],{},"28",[1179,4184,4185],{},"76",[1110,4187,4188,4239],{},[1115,4189,4191],{"className":4190},[1668],[1670,4192,4193],{"xmlns":1672},[1674,4194,4195,4237],{},[1677,4196,4197,4203,4205,4215,4217,4227],{},[1680,4198,4199,4201],{},[1683,4200,1685],{},[1687,4202,1689],{},[1811,4204,2077],{},[1680,4206,4207,4209],{},[1683,4208,1110],{},[1677,4210,4211,4213],{},[1683,4212,1997],{},[1683,4214,2002],{},[1811,4216,2101],{},[1680,4218,4219,4221],{},[1683,4220,1110],{},[1677,4222,4223,4225],{},[1683,4224,1997],{},[1811,4226,2098],{},[1680,4228,4229,4231],{},[1683,4230,1110],{},[1677,4232,4233,4235],{},[1811,4234,2098],{},[1683,4236,2002],{},[1691,4238,3811],{"encoding":1693}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3814,4241,4243],{"className":3816,"code":4242,"language":71,"meta":1603,"style":1603},"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",[3590,4244,4245,4274,4293,4312,4322,4345,4369,4379],{"__ignoreMap":1603},[1115,4246,4247,4250,4252,4254,4256,4258,4260,4262,4264,4267,4269,4272],{"class":3822,"line":10},[1115,4248,4249],{"class":3825},"tab2",[1115,4251,3830],{"class":3829},[1115,4253,3834],{"class":3833},[1115,4255,1994],{"class":3837},[1115,4257,3840],{"class":3833},[1115,4259,1994],{"class":3837},[1115,4261,4166],{"class":3845},[1115,4263,1917],{"class":3829},[1115,4265,4266],{"class":3845}," 33",[1115,4268,1917],{"class":3829},[1115,4270,4271],{"class":3845}," 39",[1115,4273,3858],{"class":3829},[1115,4275,4276,4279,4281,4284,4286,4289,4291],{"class":3822,"line":27},[1115,4277,4278],{"class":3845},"                 25",[1115,4280,1917],{"class":3829},[1115,4282,4283],{"class":3845}," 28",[1115,4285,1917],{"class":3829},[1115,4287,4288],{"class":3845}," 76",[1115,4290,2005],{"class":3837},[1115,4292,3858],{"class":3829},[1115,4294,4295,4297,4299,4302,4304,4306,4308,4310],{"class":3822,"line":148},[1115,4296,3915],{"class":3825},[1115,4298,3918],{"class":3829},[1115,4300,4301],{"class":3845}," 2",[1115,4303,1917],{"class":3829},[1115,4305,3926],{"class":3825},[1115,4307,3918],{"class":3829},[1115,4309,3931],{"class":3845},[1115,4311,3858],{"class":3829},[1115,4313,4314,4316,4318,4320],{"class":3822,"line":111},[1115,4315,3938],{"class":3825},[1115,4317,3918],{"class":3829},[1115,4319,3943],{"class":3833},[1115,4321,3946],{"class":3837},[1115,4323,4324,4327,4329,4331,4333,4336,4338,4341,4343],{"class":3822,"line":96},[1115,4325,4326],{"class":3825},"                 zverejnuje",[1115,4328,3918],{"class":3829},[1115,4330,3956],{"class":3833},[1115,4332,1994],{"class":3837},[1115,4334,4335],{"class":3961},"\"ne\"",[1115,4337,1917],{"class":3829},[1115,4339,4340],{"class":3961}," \"ano\"",[1115,4342,2005],{"class":3837},[1115,4344,3858],{"class":3829},[1115,4346,4347,4349,4352,4354,4356,4359,4361,4363,4365,4367],{"class":3822,"line":89},[1115,4348,3951],{"class":3825},[1115,4350,4351],{"class":3829},"   =",[1115,4353,3956],{"class":3833},[1115,4355,1994],{"class":3837},[1115,4357,4358],{"class":3961},"\"SS\"",[1115,4360,1917],{"class":3829},[1115,4362,3972],{"class":3961},[1115,4364,1917],{"class":3829},[1115,4366,3977],{"class":3961},[1115,4368,4009],{"class":3837},[1115,4370,4371,4373,4375,4377],{"class":3822,"line":82},[1115,4372,4015],{"class":3833},[1115,4374,1994],{"class":3837},[1115,4376,4249],{"class":3825},[1115,4378,4022],{"class":3837},[1115,4380,4381,4383,4385,4387,4389,4391],{"class":3822,"line":75},[1115,4382,4015],{"class":3833},[1115,4384,1994],{"class":3837},[1115,4386,4249],{"class":3825},[1115,4388,2005],{"class":3837},[1115,4390,4035],{"class":3829},[1115,4392,4038],{"class":3825},[3814,4394,4397],{"className":4395,"code":4396,"language":4044,"meta":1603},[4042],"    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",[3590,4398,4396],{"__ignoreMap":1603},[1110,4400,4401,4402,4073,4425,4438,4439,4109,4459,4476,4477,1497],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,4403,4405],{"className":4404},[1668],[1670,4406,4407],{"xmlns":1672},[1674,4408,4409,4422],{},[1677,4410,4411,4417,4419],{},[1706,4412,4413,4415],{},[1683,4414,1710],{},[1687,4416,1713],{},[1811,4418,2101],{},[1687,4420,4421],{},"6,87",[1691,4423,4424],{"encoding":1693},"\\chi^2 = 6{,}87",[1115,4426,4428],{"className":4427},[1668],[1670,4429,4430],{"xmlns":1672},[1674,4431,4432,4436],{},[1677,4433,4434],{},[1687,4435,1713],{},[1691,4437,1713],{"encoding":1693}," stupni volnosti dává\np-hodnotu ",[1115,4440,4442],{"className":4441},[1668],[1670,4443,4444],{"xmlns":1672},[1674,4445,4446,4456],{},[1677,4447,4448,4451,4454],{},[1687,4449,4450],{},"0,032",[1811,4452,4453],{},"\u003C",[1687,4455,4105],{},[1691,4457,4458],{"encoding":1693},"0{,}032 \u003C 0{,}05",[1115,4460,4462],{"className":4461},[1668],[1670,4463,4464],{"xmlns":1672},[1674,4465,4466,4474],{},[1677,4467,4468],{},[1680,4469,4470,4472],{},[1683,4471,1685],{},[1687,4473,1689],{},[1691,4475,1694],{"encoding":1693}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1136,4478,4479],{},"závisí",[1110,4481,4482,4483,4500],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,4484,4486],{"className":4485},[1668],[1670,4487,4488],{"xmlns":1672},[1674,4489,4490,4498],{},[1677,4491,4492],{},[1680,4493,4494,4496],{},[1683,4495,1685],{},[1687,4497,1689],{},[1691,4499,1694],{"encoding":1693}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,4502,4503],{},[4504,4505],"img",{"alt":4506,"className":4507,"src":4509},"mask-kt-observed-expected",[1131,4508],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,4511,4512,4513,4530,4531,2077],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,4514,4516],{"className":4515},[1668],[1670,4517,4518],{"xmlns":1672},[1674,4519,4520,4528],{},[1677,4521,4522],{},[1706,4523,4524,4526],{},[1683,4525,1710],{},[1687,4527,1713],{},[1691,4529,1716],{"encoding":1693}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,4532,4534],{"className":4533},[1668],[1670,4535,4536],{"xmlns":1672},[1674,4537,4538,4542],{},[1677,4539,4540],{},[1683,4541,1729],{},[1691,4543,1729],{"encoding":1693},[1110,4545,4546],{},[4504,4547],{"alt":4548,"className":4549,"src":4550},"mask-kt-chi2-kriticky-obor",[1131,4508],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1153,4552,1777],{"id":4553},"cramérův-koeficient-kontingence",[1110,4555,4556,4557,2077],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1136,4558,4559],{},"Cramérův koeficient\nkontingence",[1115,4561,4563],{"className":4562},[1668],[1670,4564,4565],{"xmlns":1672,"display":2083},[1674,4566,4567,4623],{},[1677,4568,4569,4571,4573,4599,4601,4603,4605,4607,4610,4613,4615,4617,4619,4621],{},[1683,4570,1789],{},[1811,4572,2101],{},[4574,4575,4576],"msqrt",{},[2859,4577,4578,4584],{},[1706,4579,4580,4582],{},[1683,4581,1710],{},[1687,4583,1713],{},[1677,4585,4586,4588,4590,4593,4595,4597],{},[1683,4587,1809],{},[1811,4589,1994],{"stretchy":1993},[1683,4591,4592],{},"m",[1811,4594,3184],{},[1687,4596,1914],{},[1811,4598,2005],{"stretchy":1993},[1811,4600,1917],{"separator":1121},[2131,4602],{"width":2133},[1683,4604,4592],{},[1811,4606,2101],{},[1683,4608,4609],{},"min",[1811,4611,4612],{},"⁡",[1811,4614,1994],{"stretchy":1993},[1683,4616,71],{},[1811,4618,1917],{"separator":1121},[1683,4620,1974],{},[1811,4622,2005],{"stretchy":1993},[1691,4624,4625],{"encoding":1693},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,4627,4628,4629,4646,4647,4665,4666,4684],{},"kde ",[1115,4630,4632],{"className":4631},[1668],[1670,4633,4634],{"xmlns":1672},[1674,4635,4636,4644],{},[1677,4637,4638],{},[1706,4639,4640,4642],{},[1683,4641,1710],{},[1687,4643,1713],{},[1691,4645,1716],{"encoding":1693}," je hodnota testového kritéria z testu nezávislosti. ",[1115,4648,4650],{"className":4649},[1668],[1670,4651,4652],{"xmlns":1672},[1674,4653,4654,4662],{},[1677,4655,4656,4658,4660],{},[1683,4657,1789],{},[1811,4659,2101],{},[1687,4661,1689],{},[1691,4663,4664],{"encoding":1693},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,4667,4669],{"className":4668},[1668],[1670,4670,4671],{"xmlns":1672},[1674,4672,4673,4681],{},[1677,4674,4675,4677,4679],{},[1683,4676,1789],{},[1811,4678,2101],{},[1687,4680,1914],{},[1691,4682,4683],{"encoding":1693},"V = 1"," jejich úplné závislosti.",[3814,4686,4688],{"className":3816,"code":4687,"language":71,"meta":1603,"style":1603},"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",[3590,4689,4690,4765,4828,4833],{"__ignoreMap":1603},[1115,4691,4692,4695,4697,4700,4702,4705,4707,4709,4711,4713,4715,4717,4720,4723,4726,4729,4732,4734,4736,4738,4741,4743,4745,4747,4750,4752,4754,4757,4760,4763],{"class":3822,"line":10},[1115,4693,4694],{"class":3825},"V1",[1115,4696,3830],{"class":3829},[1115,4698,4699],{"class":3833}," sqrt",[1115,4701,1994],{"class":3837},[1115,4703,4704],{"class":3833},"as.numeric",[1115,4706,1994],{"class":3837},[1115,4708,4015],{"class":3833},[1115,4710,1994],{"class":3837},[1115,4712,3826],{"class":3825},[1115,4714,2005],{"class":3837},[1115,4716,4035],{"class":3829},[1115,4718,4719],{"class":3825},"statistic",[1115,4721,4722],{"class":3837},") ",[1115,4724,4725],{"class":3829},"\u002F",[1115,4727,4728],{"class":3837}," (",[1115,4730,4731],{"class":3833},"sum",[1115,4733,1994],{"class":3837},[1115,4735,3826],{"class":3825},[1115,4737,4722],{"class":3837},[1115,4739,4740],{"class":3829},"*",[1115,4742,4728],{"class":3837},[1115,4744,4609],{"class":3833},[1115,4746,1994],{"class":3837},[1115,4748,4749],{"class":3833},"dim",[1115,4751,1994],{"class":3837},[1115,4753,3826],{"class":3825},[1115,4755,4756],{"class":3837},")) ",[1115,4758,4759],{"class":3829},"-",[1115,4761,4762],{"class":3845}," 1",[1115,4764,4009],{"class":3837},[1115,4766,4767,4770,4772,4774,4776,4778,4780,4782,4784,4786,4788,4790,4792,4794,4796,4798,4800,4802,4804,4806,4808,4810,4812,4814,4816,4818,4820,4822,4824,4826],{"class":3822,"line":27},[1115,4768,4769],{"class":3825},"V2",[1115,4771,3830],{"class":3829},[1115,4773,4699],{"class":3833},[1115,4775,1994],{"class":3837},[1115,4777,4704],{"class":3833},[1115,4779,1994],{"class":3837},[1115,4781,4015],{"class":3833},[1115,4783,1994],{"class":3837},[1115,4785,4249],{"class":3825},[1115,4787,2005],{"class":3837},[1115,4789,4035],{"class":3829},[1115,4791,4719],{"class":3825},[1115,4793,4722],{"class":3837},[1115,4795,4725],{"class":3829},[1115,4797,4728],{"class":3837},[1115,4799,4731],{"class":3833},[1115,4801,1994],{"class":3837},[1115,4803,4249],{"class":3825},[1115,4805,4722],{"class":3837},[1115,4807,4740],{"class":3829},[1115,4809,4728],{"class":3837},[1115,4811,4609],{"class":3833},[1115,4813,1994],{"class":3837},[1115,4815,4749],{"class":3833},[1115,4817,1994],{"class":3837},[1115,4819,4249],{"class":3825},[1115,4821,4756],{"class":3837},[1115,4823,4759],{"class":3829},[1115,4825,4762],{"class":3845},[1115,4827,4009],{"class":3837},[1115,4829,4830],{"class":3822,"line":148},[1115,4831,4832],{"class":3825},"V1\n",[1115,4834,4835],{"class":3822,"line":111},[1115,4836,4837],{"class":3825},"V2\n",[3814,4839,4842],{"className":4840,"code":4841,"language":4044,"meta":1603},[4042],"[1] 0.08441958\n[1] 0.1762822\n",[3590,4843,4841],{"__ignoreMap":1603},[1110,4845,4846],{},[4504,4847],{"alt":4848,"className":4849,"src":4850},"mask-kt-cramerovo-v",[1131,4508],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,4852,4853,4854,4873,4874,4891,4892,4109,4911,4928],{},"U nákupu potravin je ",[1115,4855,4857],{"className":4856},[1668],[1670,4858,4859],{"xmlns":1672},[1674,4860,4861,4870],{},[1677,4862,4863,4865,4867],{},[1683,4864,1789],{},[1811,4866,2101],{},[1687,4868,4869],{},"0,084",[1691,4871,4872],{"encoding":1693},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,4875,4877],{"className":4876},[1668],[1670,4878,4879],{"xmlns":1672},[1674,4880,4881,4889],{},[1677,4882,4883],{},[1680,4884,4885,4887],{},[1683,4886,1685],{},[1687,4888,1689],{},[1691,4890,1694],{"encoding":1693}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,4893,4895],{"className":4894},[1668],[1670,4896,4897],{"xmlns":1672},[1674,4898,4899,4908],{},[1677,4900,4901,4903,4905],{},[1683,4902,1789],{},[1811,4904,2101],{},[1687,4906,4907],{},"0,176",[1691,4909,4910],{"encoding":1693},"V = 0{,}176",[1115,4912,4914],{"className":4913},[1668],[1670,4915,4916],{"xmlns":1672},[1674,4917,4918,4926],{},[1677,4919,4920],{},[1680,4921,4922,4924],{},[1683,4923,1685],{},[1687,4925,1689],{},[1691,4927,1694],{"encoding":1693},"\njsme zamítli, ale samotná závislost je stále slabá.",[1153,4930,1796],{"id":4931},"čtyřpolní-tabulka",[1110,4933,4934,4936,4937,4950,4951,4964,4965,4987],{},[1136,4935,1796],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,4938,4940],{"className":4939},[1668],[1670,4941,4942],{"xmlns":1672},[1674,4943,4944,4948],{},[1677,4945,4946],{},[1683,4947,1363],{},[1691,4949,1363],{"encoding":1693}," i ",[1115,4952,4954],{"className":4953},[1668],[1670,4955,4956],{"xmlns":1672},[1674,4957,4958,4962],{},[1677,4959,4960],{},[1683,4961,1371],{},[1691,4963,1371],{"encoding":1693}," mají jen dvě varianty\n(",[1115,4966,4968],{"className":4967},[1668],[1670,4969,4970],{"xmlns":1672},[1674,4971,4972,4984],{},[1677,4973,4974,4976,4978,4980,4982],{},[1683,4975,71],{},[1811,4977,2101],{},[1683,4979,1974],{},[1811,4981,2101],{},[1687,4983,1713],{},[1691,4985,4986],{"encoding":1693},"r = s = 2","):",[1158,4989,4990,5074],{},[1161,4991,4992],{},[1164,4993,4994,5013,5032,5051],{},[1167,4995,4996],{},[1115,4997,4999],{"className":4998},[1668],[1670,5000,5001],{"xmlns":1672},[1674,5002,5003,5011],{},[1677,5004,5005,5007,5009],{},[1683,5006,1363],{},[1683,5008,2241],{"mathvariant":2240},[1683,5010,1371],{},[1691,5012,2246],{"encoding":1693},[1167,5014,5015],{},[1115,5016,5018],{"className":5017},[1668],[1670,5019,5020],{"xmlns":1672},[1674,5021,5022,5030],{},[1677,5023,5024],{},[1680,5025,5026,5028],{},[1683,5027,1371],{},[1687,5029,1914],{},[1691,5031,2266],{"encoding":1693},[1167,5033,5034],{},[1115,5035,5037],{"className":5036},[1668],[1670,5038,5039],{"xmlns":1672},[1674,5040,5041,5049],{},[1677,5042,5043],{},[1680,5044,5045,5047],{},[1683,5046,1371],{},[1687,5048,1713],{},[1691,5050,2286],{"encoding":1693},[1167,5052,5053],{},[1115,5054,5056],{"className":5055},[1668],[1670,5057,5058],{"xmlns":1672},[1674,5059,5060,5072],{},[1677,5061,5062],{},[1680,5063,5064,5066],{},[1683,5065,1809],{},[1677,5067,5068,5070],{},[1683,5069,1997],{},[1811,5071,2098],{},[1691,5073,2332],{"encoding":1693},[1174,5075,5076,5158,5240],{},[1164,5077,5078,5097,5116,5135],{},[1179,5079,5080],{},[1115,5081,5083],{"className":5082},[1668],[1670,5084,5085],{"xmlns":1672},[1674,5086,5087,5095],{},[1677,5088,5089],{},[1680,5090,5091,5093],{},[1683,5092,1363],{},[1687,5094,1914],{},[1691,5096,2356],{"encoding":1693},[1179,5098,5099],{},[1115,5100,5102],{"className":5101},[1668],[1670,5103,5104],{"xmlns":1672},[1674,5105,5106,5114],{},[1677,5107,5108],{},[1680,5109,5110,5112],{},[1683,5111,1809],{},[1687,5113,2374],{},[1691,5115,2377],{"encoding":1693},[1179,5117,5118],{},[1115,5119,5121],{"className":5120},[1668],[1670,5122,5123],{"xmlns":1672},[1674,5124,5125,5133],{},[1677,5126,5127],{},[1680,5128,5129,5131],{},[1683,5130,1809],{},[1687,5132,2395],{},[1691,5134,2398],{"encoding":1693},[1179,5136,5137],{},[1115,5138,5140],{"className":5139},[1668],[1670,5141,5142],{"xmlns":1672},[1674,5143,5144,5156],{},[1677,5145,5146],{},[1680,5147,5148,5150],{},[1683,5149,1809],{},[1677,5151,5152,5154],{},[1687,5153,1914],{},[1811,5155,2098],{},[1691,5157,2448],{"encoding":1693},[1164,5159,5160,5179,5198,5217],{},[1179,5161,5162],{},[1115,5163,5165],{"className":5164},[1668],[1670,5166,5167],{"xmlns":1672},[1674,5168,5169,5177],{},[1677,5170,5171],{},[1680,5172,5173,5175],{},[1683,5174,1363],{},[1687,5176,1713],{},[1691,5178,2470],{"encoding":1693},[1179,5180,5181],{},[1115,5182,5184],{"className":5183},[1668],[1670,5185,5186],{"xmlns":1672},[1674,5187,5188,5196],{},[1677,5189,5190],{},[1680,5191,5192,5194],{},[1683,5193,1809],{},[1687,5195,2488],{},[1691,5197,2491],{"encoding":1693},[1179,5199,5200],{},[1115,5201,5203],{"className":5202},[1668],[1670,5204,5205],{"xmlns":1672},[1674,5206,5207,5215],{},[1677,5208,5209],{},[1680,5210,5211,5213],{},[1683,5212,1809],{},[1687,5214,2509],{},[1691,5216,2512],{"encoding":1693},[1179,5218,5219],{},[1115,5220,5222],{"className":5221},[1668],[1670,5223,5224],{"xmlns":1672},[1674,5225,5226,5238],{},[1677,5227,5228],{},[1680,5229,5230,5232],{},[1683,5231,1809],{},[1677,5233,5234,5236],{},[1687,5235,1713],{},[1811,5237,2098],{},[1691,5239,2562],{"encoding":1693},[1164,5241,5242,5265,5288,5311],{},[1179,5243,5244],{},[1115,5245,5247],{"className":5246},[1668],[1670,5248,5249],{"xmlns":1672},[1674,5250,5251,5263],{},[1677,5252,5253],{},[1680,5254,5255,5257],{},[1683,5256,1809],{},[1677,5258,5259,5261],{},[1811,5260,2098],{},[1683,5262,2002],{},[1691,5264,2724],{"encoding":1693},[1179,5266,5267],{},[1115,5268,5270],{"className":5269},[1668],[1670,5271,5272],{"xmlns":1672},[1674,5273,5274,5286],{},[1677,5275,5276],{},[1680,5277,5278,5280],{},[1683,5279,1809],{},[1677,5281,5282,5284],{},[1811,5283,2098],{},[1687,5285,1914],{},[1691,5287,2748],{"encoding":1693},[1179,5289,5290],{},[1115,5291,5293],{"className":5292},[1668],[1670,5294,5295],{"xmlns":1672},[1674,5296,5297,5309],{},[1677,5298,5299],{},[1680,5300,5301,5303],{},[1683,5302,1809],{},[1677,5304,5305,5307],{},[1811,5306,2098],{},[1687,5308,1713],{},[1691,5310,2772],{"encoding":1693},[1179,5312,5313],{},[1115,5314,5316],{"className":5315},[1668],[1670,5317,5318],{"xmlns":1672},[1674,5319,5320,5324],{},[1677,5321,5322],{},[1683,5323,1809],{},[1691,5325,1809],{"encoding":1693},[1110,5327,1822,5328,5346],{},[1115,5329,5331],{"className":5330},[1668],[1670,5332,5333],{"xmlns":1672},[1674,5334,5335,5343],{},[1677,5336,5337,5339,5341],{},[1683,5338,1809],{},[1811,5340,1813],{},[1687,5342,1816],{},[1691,5344,5345],{"encoding":1693},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,5348,5350],{"className":5349},[1668],[1670,5351,5352],{"xmlns":1672,"display":2083},[1674,5353,5354,5448],{},[1677,5355,5356,5362,5364,5366,5368],{},[1706,5357,5358,5360],{},[1683,5359,1710],{},[1687,5361,1713],{},[1811,5363,2101],{},[1683,5365,1809],{},[3028,5367,3030],{},[2859,5369,5370,5406],{},[1677,5371,5372,5374,5380,5386,5388,5394,5400],{},[1811,5373,1994],{"stretchy":1993},[1680,5375,5376,5378],{},[1683,5377,1809],{},[1687,5379,2374],{},[1680,5381,5382,5384],{},[1683,5383,1809],{},[1687,5385,2509],{},[1811,5387,3184],{},[1680,5389,5390,5392],{},[1683,5391,1809],{},[1687,5393,2395],{},[1680,5395,5396,5398],{},[1683,5397,1809],{},[1687,5399,2488],{},[1706,5401,5402,5404],{},[1811,5403,2005],{"stretchy":1993},[1687,5405,1713],{},[1677,5407,5408,5418,5428,5438],{},[1680,5409,5410,5412],{},[1683,5411,1809],{},[1677,5413,5414,5416],{},[1687,5415,1914],{},[1811,5417,2098],{},[1680,5419,5420,5422],{},[1683,5421,1809],{},[1677,5423,5424,5426],{},[1687,5425,1713],{},[1811,5427,2098],{},[1680,5429,5430,5432],{},[1683,5431,1809],{},[1677,5433,5434,5436],{},[1811,5435,2098],{},[1687,5437,1914],{},[1680,5439,5440,5442],{},[1683,5441,1809],{},[1677,5443,5444,5446],{},[1811,5445,2098],{},[1687,5447,1713],{},[1691,5449,5450],{"encoding":1693},"\\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}}",[1110,5452,5453,5454,5514,5515,5551,5552,5555,5556,5559],{},"s kritickým oborem ",[1115,5455,5457],{"className":5456},[1668],[1670,5458,5459],{"xmlns":1672},[1674,5460,5461,5511],{},[1677,5462,5463,5469,5471,5473,5479,5481,5487,5489,5503,5505,5507,5509],{},[1680,5464,5465,5467],{},[1683,5466,1729],{},[1683,5468,3485],{},[1811,5470,2101],{},[1811,5472,3454],{"stretchy":1993},[1706,5474,5475,5477],{},[1683,5476,1710],{},[1687,5478,1713],{},[1811,5480,2077],{},[1706,5482,5483,5485],{},[1683,5484,1710],{},[1687,5486,1713],{},[1811,5488,3471],{},[3473,5490,5491,5493,5501],{},[1683,5492,1710],{},[1677,5494,5495,5497,5499],{},[1687,5496,1914],{},[1811,5498,3184],{},[1683,5500,3485],{},[1687,5502,1713],{},[1811,5504,1994],{"stretchy":1993},[1687,5506,1914],{},[1811,5508,2005],{"stretchy":1993},[1811,5510,3514],{"stretchy":1993},[1691,5512,5513],{"encoding":1693},"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 ",[1115,5516,5518],{"className":5517},[1668],[1670,5519,5520],{"xmlns":1672},[1674,5521,5522,5548],{},[1677,5523,5524,5526,5528,5530,5532,5534,5536,5538,5540,5542,5544,5546],{},[1811,5525,1994],{"stretchy":1993},[1683,5527,71],{},[1811,5529,3184],{},[1687,5531,1914],{},[1811,5533,2005],{"stretchy":1993},[1811,5535,1994],{"stretchy":1993},[1683,5537,1974],{},[1811,5539,3184],{},[1687,5541,1914],{},[1811,5543,2005],{"stretchy":1993},[1811,5545,2101],{},[1687,5547,1914],{},[1691,5549,5550],{"encoding":1693},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3590,5553,5554],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3590,5557,5558],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1153,5561,1829],{"id":5562},"mcnemarův-test",[1110,5564,5565,5566,5569,5570,5572,5573,5576,5577,5580,5581,5583],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1136,5567,5568],{},"různé"," znaky na stejném souboru. ",[1136,5571,1829],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1136,5574,5575],{},"jeden"," alternativní znak, a to ",[1136,5578,5579],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1136,5582,1825],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,5585,5586],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1158,5588,5589,5624],{},[1161,5590,5591],{},[1164,5592,5593,5596,5599,5601],{},[1167,5594,5595],{},"před \\ po",[1167,5597,5598],{},"+",[1167,5600,3184],{},[1167,5602,5603],{},[1115,5604,5606],{"className":5605},[1668],[1670,5607,5608],{"xmlns":1672},[1674,5609,5610,5622],{},[1677,5611,5612],{},[1680,5613,5614,5616],{},[1683,5615,1809],{},[1677,5617,5618,5620],{},[1683,5619,1997],{},[1811,5621,2098],{},[1691,5623,2332],{"encoding":1693},[1174,5625,5626,5691,5756],{},[1164,5627,5628,5630,5649,5668],{},[1179,5629,5598],{},[1179,5631,5632],{},[1115,5633,5635],{"className":5634},[1668],[1670,5636,5637],{"xmlns":1672},[1674,5638,5639,5647],{},[1677,5640,5641],{},[1680,5642,5643,5645],{},[1683,5644,1809],{},[1687,5646,2374],{},[1691,5648,2377],{"encoding":1693},[1179,5650,5651],{},[1115,5652,5654],{"className":5653},[1668],[1670,5655,5656],{"xmlns":1672},[1674,5657,5658,5666],{},[1677,5659,5660],{},[1680,5661,5662,5664],{},[1683,5663,1809],{},[1687,5665,2395],{},[1691,5667,2398],{"encoding":1693},[1179,5669,5670],{},[1115,5671,5673],{"className":5672},[1668],[1670,5674,5675],{"xmlns":1672},[1674,5676,5677,5689],{},[1677,5678,5679],{},[1680,5680,5681,5683],{},[1683,5682,1809],{},[1677,5684,5685,5687],{},[1687,5686,1914],{},[1811,5688,2098],{},[1691,5690,2448],{"encoding":1693},[1164,5692,5693,5695,5714,5733],{},[1179,5694,3184],{},[1179,5696,5697],{},[1115,5698,5700],{"className":5699},[1668],[1670,5701,5702],{"xmlns":1672},[1674,5703,5704,5712],{},[1677,5705,5706],{},[1680,5707,5708,5710],{},[1683,5709,1809],{},[1687,5711,2488],{},[1691,5713,2491],{"encoding":1693},[1179,5715,5716],{},[1115,5717,5719],{"className":5718},[1668],[1670,5720,5721],{"xmlns":1672},[1674,5722,5723,5731],{},[1677,5724,5725],{},[1680,5726,5727,5729],{},[1683,5728,1809],{},[1687,5730,2509],{},[1691,5732,2512],{"encoding":1693},[1179,5734,5735],{},[1115,5736,5738],{"className":5737},[1668],[1670,5739,5740],{"xmlns":1672},[1674,5741,5742,5754],{},[1677,5743,5744],{},[1680,5745,5746,5748],{},[1683,5747,1809],{},[1677,5749,5750,5752],{},[1687,5751,1713],{},[1811,5753,2098],{},[1691,5755,2562],{"encoding":1693},[1164,5757,5758,5781,5804,5827],{},[1179,5759,5760],{},[1115,5761,5763],{"className":5762},[1668],[1670,5764,5765],{"xmlns":1672},[1674,5766,5767,5779],{},[1677,5768,5769],{},[1680,5770,5771,5773],{},[1683,5772,1809],{},[1677,5774,5775,5777],{},[1811,5776,2098],{},[1683,5778,2002],{},[1691,5780,2724],{"encoding":1693},[1179,5782,5783],{},[1115,5784,5786],{"className":5785},[1668],[1670,5787,5788],{"xmlns":1672},[1674,5789,5790,5802],{},[1677,5791,5792],{},[1680,5793,5794,5796],{},[1683,5795,1809],{},[1677,5797,5798,5800],{},[1811,5799,2098],{},[1687,5801,1914],{},[1691,5803,2748],{"encoding":1693},[1179,5805,5806],{},[1115,5807,5809],{"className":5808},[1668],[1670,5810,5811],{"xmlns":1672},[1674,5812,5813,5825],{},[1677,5814,5815],{},[1680,5816,5817,5819],{},[1683,5818,1809],{},[1677,5820,5821,5823],{},[1811,5822,2098],{},[1687,5824,1713],{},[1691,5826,2772],{"encoding":1693},[1179,5828,5829],{},[1115,5830,5832],{"className":5831},[1668],[1670,5833,5834],{"xmlns":1672},[1674,5835,5836,5840],{},[1677,5837,5838],{},[1683,5839,1809],{},[1691,5841,1809],{"encoding":1693},[1110,5843,5844,5845,5862,5863,5880,5881,5884,5885,5862,5902,5919,5920,5923],{},"Pole ",[1115,5846,5848],{"className":5847},[1668],[1670,5849,5850],{"xmlns":1672},[1674,5851,5852,5860],{},[1677,5853,5854],{},[1680,5855,5856,5858],{},[1683,5857,1809],{},[1687,5859,2374],{},[1691,5861,2377],{"encoding":1693}," a ",[1115,5864,5866],{"className":5865},[1668],[1670,5867,5868],{"xmlns":1672},[1674,5869,5870,5878],{},[1677,5871,5872],{},[1680,5873,5874,5876],{},[1683,5875,1809],{},[1687,5877,2509],{},[1691,5879,2512],{"encoding":1693}," jsou ",[1136,5882,5883],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,5886,5888],{"className":5887},[1668],[1670,5889,5890],{"xmlns":1672},[1674,5891,5892,5900],{},[1677,5893,5894],{},[1680,5895,5896,5898],{},[1683,5897,1809],{},[1687,5899,2395],{},[1691,5901,2398],{"encoding":1693},[1115,5903,5905],{"className":5904},[1668],[1670,5906,5907],{"xmlns":1672},[1674,5908,5909,5917],{},[1677,5910,5911],{},[1680,5912,5913,5915],{},[1683,5914,1809],{},[1687,5916,2488],{},[1691,5918,2491],{"encoding":1693}," jsou\n",[1136,5921,5922],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,5925,5926],{},[4504,5927],{"alt":5928,"className":5929,"src":5930},"mask-kt-mcnemar-tabulka",[1131,4508],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,5932,5933],{},[1136,5934,2983],{},[1262,5936,5937,5974,6055,6113],{},[1265,5938,5939,5973],{},[1115,5940,5942],{"className":5941},[1668],[1670,5943,5944],{"xmlns":1672},[1674,5945,5946,5970],{},[1677,5947,5948,5954,5956,5962,5964],{},[1680,5949,5950,5952],{},[1683,5951,1685],{},[1687,5953,1689],{},[1811,5955,2077],{},[1680,5957,5958,5960],{},[1683,5959,1110],{},[1687,5961,2395],{},[1811,5963,2101],{},[1680,5965,5966,5968],{},[1683,5967,1110],{},[1687,5969,2488],{},[1691,5971,5972],{"encoding":1693},"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.",[1265,5975,3120,5976,6038,6040,6041,6054],{},[1115,5977,5979],{"className":5978},[1668],[1670,5980,5981],{"xmlns":1672,"display":2083},[1674,5982,5983,6035],{},[1677,5984,5985,5991,5993],{},[1706,5986,5987,5989],{},[1683,5988,1710],{},[1687,5990,1713],{},[1811,5992,2101],{},[2859,5994,5995,6019],{},[1677,5996,5997,5999,6005,6007,6013],{},[1811,5998,1994],{"stretchy":1993},[1680,6000,6001,6003],{},[1683,6002,1809],{},[1687,6004,2395],{},[1811,6006,3184],{},[1680,6008,6009,6011],{},[1683,6010,1809],{},[1687,6012,2488],{},[1706,6014,6015,6017],{},[1811,6016,2005],{"stretchy":1993},[1687,6018,1713],{},[1677,6020,6021,6027,6029],{},[1680,6022,6023,6025],{},[1683,6024,1809],{},[1687,6026,2395],{},[1811,6028,5598],{},[1680,6030,6031,6033],{},[1683,6032,1809],{},[1687,6034,2488],{},[1691,6036,6037],{"encoding":1693},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[3279,6039],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,6042,6044],{"className":6043},[1668],[1670,6045,6046],{"xmlns":1672},[1674,6047,6048,6052],{},[1677,6049,6050],{},[1687,6051,1914],{},[1691,6053,1914],{"encoding":1693}," stupni volnosti.",[1265,6056,3438,6057,1497],{},[1115,6058,6060],{"className":6059},[1668],[1670,6061,6062],{"xmlns":1672},[1674,6063,6064,6110],{},[1677,6065,6066,6068,6070,6072,6078,6080,6086,6088,6102,6104,6106,6108],{},[1683,6067,1729],{},[1811,6069,2101],{},[1811,6071,3454],{"stretchy":1993},[1706,6073,6074,6076],{},[1683,6075,1710],{},[1687,6077,1713],{},[1811,6079,2077],{},[1706,6081,6082,6084],{},[1683,6083,1710],{},[1687,6085,1713],{},[1811,6087,3471],{},[3473,6089,6090,6092,6100],{},[1683,6091,1710],{},[1677,6093,6094,6096,6098],{},[1687,6095,1914],{},[1811,6097,3184],{},[1683,6099,3485],{},[1687,6101,1713],{},[1811,6103,1994],{"stretchy":1993},[1687,6105,1914],{},[1811,6107,2005],{"stretchy":1993},[1811,6109,3514],{"stretchy":1993},[1691,6111,6112],{"encoding":1693},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1265,6114,3520,6115,6128,6129,6146,6147,6164],{},[1115,6116,6118],{"className":6117},[1668],[1670,6119,6120],{"xmlns":1672},[1674,6121,6122,6126],{},[1677,6123,6124],{},[1683,6125,1729],{},[1691,6127,1729],{"encoding":1693},", zamítáme ",[1115,6130,6132],{"className":6131},[1668],[1670,6133,6134],{"xmlns":1672},[1674,6135,6136,6144],{},[1677,6137,6138],{},[1680,6139,6140,6142],{},[1683,6141,1685],{},[1687,6143,1689],{},[1691,6145,1694],{"encoding":1693}," a přijímáme ",[1115,6148,6150],{"className":6149},[1668],[1670,6151,6152],{"xmlns":1672},[1674,6153,6154,6162],{},[1677,6155,6156],{},[1680,6157,6158,6160],{},[1683,6159,1685],{},[1687,6161,1914],{},[1691,6163,3116],{"encoding":1693},": zásah rozdělení variant změnil.",[1110,6166,6167,6168,6171,6172,6175,6176,6178],{},"V R počítá tento test funkce ",[3590,6169,6170],{},"mcnemar.test()",". Vzorec výše ",[1136,6173,6174],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3590,6177,5558],{}," (viz Časté chyby níže).",[1103,6180,6182,6189,6192,6195,6292],{"className":6181,"dataCallout":3597},[1106,3596],[1110,6183,6185,6188],{"className":6184},[1113],[1115,6186],{"className":6187,"ariaHidden":1121},[1118,3604,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,6190,6191],{},"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.",[1110,6193,6194],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1158,6196,6197,6232],{},[1161,6198,6199],{},[1164,6200,6201,6203,6206,6209],{},[1167,6202,5595],{},[1167,6204,6205],{},"nezveřejňuje",[1167,6207,6208],{},"zveřejňuje",[1167,6210,6211],{},[1115,6212,6214],{"className":6213},[1668],[1670,6215,6216],{"xmlns":1672},[1674,6217,6218,6230],{},[1677,6219,6220],{},[1680,6221,6222,6224],{},[1683,6223,1809],{},[1677,6225,6226,6228],{},[1683,6227,1997],{},[1811,6229,2098],{},[1691,6231,2332],{"encoding":1693},[1174,6233,6234,6246,6258],{},[1164,6235,6236,6238,6240,6243],{},[1179,6237,6205],{},[1179,6239,3720],{},[1179,6241,6242],{},"68",[1179,6244,6245],{},"92",[1164,6247,6248,6250,6252,6255],{},[1179,6249,6208],{},[1179,6251,4182],{},[1179,6253,6254],{},"50",[1179,6256,6257],{},"78",[1164,6259,6260,6283,6286,6289],{},[1179,6261,6262],{},[1115,6263,6265],{"className":6264},[1668],[1670,6266,6267],{"xmlns":1672},[1674,6268,6269,6281],{},[1677,6270,6271],{},[1680,6272,6273,6275],{},[1683,6274,1809],{},[1677,6276,6277,6279],{},[1811,6278,2098],{},[1683,6280,2002],{},[1691,6282,2724],{"encoding":1693},[1179,6284,6285],{},"52",[1179,6287,6288],{},"118",[1179,6290,6291],{},"170",[1110,6293,6294,6327],{},[1115,6295,6297],{"className":6296},[1668],[1670,6298,6299],{"xmlns":1672},[1674,6300,6301,6325],{},[1677,6302,6303,6309,6311,6317,6319],{},[1680,6304,6305,6307],{},[1683,6306,1685],{},[1687,6308,1689],{},[1811,6310,2077],{},[1680,6312,6313,6315],{},[1683,6314,1110],{},[1687,6316,2395],{},[1811,6318,2101],{},[1680,6320,6321,6323],{},[1683,6322,1110],{},[1687,6324,2488],{},[1691,6326,5972],{"encoding":1693}," — informační kampaň nemá na chování vliv.",[3814,6329,6331],{"className":3816,"code":6330,"language":71,"meta":1603,"style":1603},"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",[3590,6332,6333,6357,6371,6389,6399,6422,6441],{"__ignoreMap":1603},[1115,6334,6335,6338,6340,6342,6344,6346,6348,6350,6352,6355],{"class":3822,"line":10},[1115,6336,6337],{"class":3825},"tab3",[1115,6339,3830],{"class":3829},[1115,6341,3834],{"class":3833},[1115,6343,1994],{"class":3837},[1115,6345,3840],{"class":3833},[1115,6347,1994],{"class":3837},[1115,6349,3720],{"class":3845},[1115,6351,1917],{"class":3829},[1115,6353,6354],{"class":3845}," 68",[1115,6356,3858],{"class":3829},[1115,6358,6359,6362,6364,6367,6369],{"class":3822,"line":27},[1115,6360,6361],{"class":3845},"                 28",[1115,6363,1917],{"class":3829},[1115,6365,6366],{"class":3845}," 50",[1115,6368,2005],{"class":3837},[1115,6370,3858],{"class":3829},[1115,6372,6373,6375,6377,6379,6381,6383,6385,6387],{"class":3822,"line":148},[1115,6374,3915],{"class":3825},[1115,6376,3918],{"class":3829},[1115,6378,4301],{"class":3845},[1115,6380,1917],{"class":3829},[1115,6382,3926],{"class":3825},[1115,6384,3918],{"class":3829},[1115,6386,3931],{"class":3845},[1115,6388,3858],{"class":3829},[1115,6390,6391,6393,6395,6397],{"class":3822,"line":111},[1115,6392,3938],{"class":3825},[1115,6394,3918],{"class":3829},[1115,6396,3943],{"class":3833},[1115,6398,3946],{"class":3837},[1115,6400,6401,6404,6406,6408,6410,6413,6415,6418,6420],{"class":3822,"line":96},[1115,6402,6403],{"class":3825},"                 pred",[1115,6405,3918],{"class":3829},[1115,6407,3956],{"class":3833},[1115,6409,1994],{"class":3837},[1115,6411,6412],{"class":3961},"\"nezverejnuje\"",[1115,6414,1917],{"class":3829},[1115,6416,6417],{"class":3961}," \"zverejnuje\"",[1115,6419,2005],{"class":3837},[1115,6421,3858],{"class":3829},[1115,6423,6424,6427,6429,6431,6433,6435,6437,6439],{"class":3822,"line":89},[1115,6425,6426],{"class":3825},"                 po",[1115,6428,4351],{"class":3829},[1115,6430,3956],{"class":3833},[1115,6432,1994],{"class":3837},[1115,6434,6412],{"class":3961},[1115,6436,1917],{"class":3829},[1115,6438,6417],{"class":3961},[1115,6440,4009],{"class":3837},[1115,6442,6443,6446,6448,6450,6452,6455,6457,6460],{"class":3822,"line":82},[1115,6444,6445],{"class":3833},"mcnemar.test",[1115,6447,1994],{"class":3837},[1115,6449,6337],{"class":3825},[1115,6451,1917],{"class":3829},[1115,6453,6454],{"class":3825}," correct",[1115,6456,3918],{"class":3829},[1115,6458,6459],{"class":3845}," FALSE",[1115,6461,4022],{"class":3837},[3814,6463,6466],{"className":6464,"code":6465,"language":4044,"meta":1603},[4042],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3590,6467,6465],{"__ignoreMap":1603},[1110,6469,6470,6471,4109,6490,6507,6508,6525],{},"P-hodnota ",[1115,6472,6474],{"className":6473},[1668],[1670,6475,6476],{"xmlns":1672},[1674,6477,6478,6487],{},[1677,6479,6480,6483,6485],{},[1687,6481,6482],{},"0,00004456",[1811,6484,4453],{},[1687,6486,4105],{},[1691,6488,6489],{"encoding":1693},"0{,}00004456 \u003C 0{,}05",[1115,6491,6493],{"className":6492},[1668],[1670,6494,6495],{"xmlns":1672},[1674,6496,6497,6505],{},[1677,6498,6499],{},[1680,6500,6501,6503],{},[1683,6502,1685],{},[1687,6504,1689],{},[1691,6506,1694],{"encoding":1693}," zamítáme, přijímáme ",[1115,6509,6511],{"className":6510},[1668],[1670,6512,6513],{"xmlns":1672},[1674,6514,6515,6523],{},[1677,6516,6517],{},[1680,6518,6519,6521],{},[1683,6520,1685],{},[1687,6522,1914],{},[1691,6524,3116],{"encoding":1693}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1153,6527,6529],{"id":6528},"časté-chyby","Časté chyby",[1103,6531,6535,6543],{"className":6532,"dataCallout":6534},[1106,6533],"callout-warning","warning",[1110,6536,6538,6542],{"className":6537},[1113],[1115,6539],{"className":6540,"ariaHidden":1121},[1118,6541,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,6544,6545,6546,6548],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3590,6547,3592],{}," 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.",[3814,6550,6552],{"className":3816,"code":6551,"language":71,"meta":1603,"style":1603},"chisq.test(tab3)\n",[3590,6553,6554],{"__ignoreMap":1603},[1115,6555,6556,6558,6560,6562],{"class":3822,"line":10},[1115,6557,4015],{"class":3833},[1115,6559,1994],{"class":3837},[1115,6561,6337],{"class":3825},[1115,6563,4022],{"class":3837},[3814,6565,6568],{"className":6566,"code":6567,"language":4044,"meta":1603},[4042],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3590,6569,6567],{"__ignoreMap":1603},[1110,6571,6470,6572,6591,6592,6609,6610,6612,6613,1497],{},[1115,6573,6575],{"className":6574},[1668],[1670,6576,6577],{"xmlns":1672},[1674,6578,6579,6588],{},[1677,6580,6581,6584,6586],{},[1687,6582,6583],{},"0,224",[1811,6585,1813],{},[1687,6587,4105],{},[1691,6589,6590],{"encoding":1693},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,6593,6595],{"className":6594},[1668],[1670,6596,6597],{"xmlns":1672},[1674,6598,6599,6607],{},[1677,6600,6601],{},[1680,6602,6603,6605],{},[1683,6604,1685],{},[1687,6606,1689],{},[1691,6608,1694],{"encoding":1693}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3590,6611,6170],{},", nikdy ",[3590,6614,3592],{},[1103,6616,6618,6627],{"className":6617,"dataCallout":6534},[1106,6533],[1110,6619,6621,6624,6625],{"className":6620},[1113],[1115,6622],{"className":6623,"ariaHidden":1121},[1118,6541,1120],"Výchozí korekce na kontinuitu v ",[3590,6626,6170],{},[1110,6628,6629,6630,6633],{},"Bez argumentu ",[3590,6631,6632],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3814,6635,6637],{"className":3816,"code":6636,"language":71,"meta":1603,"style":1603},"mcnemar.test(tab3)\n",[3590,6638,6639],{"__ignoreMap":1603},[1115,6640,6641,6643,6645,6647],{"class":3822,"line":10},[1115,6642,6445],{"class":3833},[1115,6644,1994],{"class":3837},[1115,6646,6337],{"class":3825},[1115,6648,4022],{"class":3837},[3814,6650,6653],{"className":6651,"code":6652,"language":4044,"meta":1603},[4042],"    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",[3590,6654,6652],{"__ignoreMap":1603},[1110,6656,6657,6658,6676,6677,6696,6697,6710,6711,1497],{},"Oproti nekorigované hodnotě ",[1115,6659,6661],{"className":6660},[1668],[1670,6662,6663],{"xmlns":1672},[1674,6664,6665,6673],{},[1677,6666,6667,6669,6671],{},[1683,6668,1110],{},[1811,6670,2101],{},[1687,6672,6482],{},[1691,6674,6675],{"encoding":1693},"p = 0{,}00004456"," vyjde ",[1115,6678,6680],{"className":6679},[1668],[1670,6681,6682],{"xmlns":1672},[1674,6683,6684,6693],{},[1677,6685,6686,6688,6690],{},[1683,6687,1110],{},[1811,6689,2101],{},[1687,6691,6692],{},"0,00006879",[1691,6694,6695],{"encoding":1693},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,6698,6700],{"className":6699},[1668],[1670,6701,6702],{"xmlns":1672},[1674,6703,6704,6708],{},[1677,6705,6706],{},[1683,6707,3485],{},[1691,6709,3548],{"encoding":1693}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3590,6712,6713],{},"mcnemar.test(x, correct = FALSE)",[1153,6715,1501],{"id":1500},[1503,6717,6718,6723,6728,6733,6738,6743,6748],{},[1265,6719,6720],{},[1127,6721,1133],{"className":6722,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,6724,6725],{},[1127,6726,1527],{"className":6727,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1265,6729,6730],{},[1127,6731,1521],{"className":6732,"dataFsResolvedFilePath":1288,"href":1286},[1131],[1265,6734,6735],{},[1127,6736,1515],{"className":6737,"dataFsResolvedFilePath":1275,"href":1273},[1131],[1265,6739,6740],{},[1127,6741,1306],{"className":6742,"dataFsResolvedFilePath":1312,"href":1310},[1131],[1265,6744,6745],{},[1127,6746,1543],{"className":6747,"dataFsResolvedFilePath":1336,"href":1334},[1131],[1265,6749,6750],{},[1127,6751,6753],{"className":6752,"dataFsResolvedFilePath":1550,"href":1548},[1131],"Tahák pro R",[1153,6755,1554],{"id":934},[1110,6757,1557,6758,1561],{},[1420,6759,1560],{},[6761,6762,6763],"style",{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .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 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05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":6785,"title":1515,"body":6786,"course":23,"courses":1614,"created":1615,"description":1603,"extension":1616,"meta":11237,"navigation":1618,"path":11238,"seo":11239,"sources":11240,"stem":11244,"tags":11245,"type":6782,"updated":1615,"__hash__":11246},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":6787,"toc":11225},[6788,6791,7077,7081,7314,7317,7385,7389,7396,7403,7562,7601,7604,7838,7841,7919,7973,8071,8075,8177,8180,8184,8190,8245,8248,8256,8406,8413,8466,8496,8615,8618,8666,8828,8883,8890,8997,9059,9063,9166,9169,9206,9212,9271,9320,9327,9363,9369,9372,9420,9427,9489,9495,9498,9562,9569,9608,9614,9617,9621,9647,9978,10016,10071,10201,10207,10211,10218,10237,10343,10387,10406,10501,10518,10560,10735,10742,10745,10748,10902,10905,10981,10987,10989,11175,11177,11216,11218,11222],[1099,6789,1515],{"id":6790},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,6792,6794,6800],{"className":6793,"dataCallout":1641},[1106,1640],[1110,6795,6797,1649],{"className":6796},[1113],[1115,6798],{"className":6799,"ariaHidden":1121},[1118,1648,1120],[1503,6801,6802,6813,6917,6984,7065],{},[1265,6803,6804,6805,6808,6809,6812],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1136,6806,6807],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1136,6810,6811],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1265,6814,6815,6816,1418,6819,6857,6858,6895,6896,6916],{},"Každou náhodnou veličinu popisuje ",[1136,6817,6818],{},"distribuční funkce",[1115,6820,6822],{"className":6821},[1668],[1670,6823,6824],{"xmlns":1672},[1674,6825,6826,6854],{},[1677,6827,6828,6830,6832,6835,6837,6839,6842,6844,6847,6850,6852],{},[1683,6829,1403],{},[1811,6831,1994],{"stretchy":1993},[1683,6833,6834],{},"x",[1811,6836,2005],{"stretchy":1993},[1811,6838,2101],{},[1683,6840,6841],{},"P",[1811,6843,1994],{"stretchy":1993},[1683,6845,6846],{},"X",[1811,6848,6849],{},"≤",[1683,6851,6834],{},[1811,6853,2005],{"stretchy":1993},[1691,6855,6856],{"encoding":1693},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,6859,6861],{"className":6860},[1668],[1670,6862,6863],{"xmlns":1672},[1674,6864,6865,6892],{},[1677,6866,6867,6875,6877,6879,6881,6883,6886,6888,6890],{},[1706,6868,6869,6871],{},[1683,6870,1403],{},[1811,6872,6874],{"mathvariant":2240,"lspace":6873,"rspace":6873},"0em","′",[1811,6876,1994],{"stretchy":1993},[1683,6878,6834],{},[1811,6880,2005],{"stretchy":1993},[1811,6882,2101],{},[1683,6884,6885],{},"f",[1811,6887,1994],{"stretchy":1993},[1683,6889,6834],{},[1811,6891,2005],{"stretchy":1993},[1691,6893,6894],{"encoding":1693},"F'(x) = f(x)",", kde ",[1115,6897,6899],{"className":6898},[1668],[1670,6900,6901],{"xmlns":1672},[1674,6902,6903,6913],{},[1677,6904,6905,6907,6909,6911],{},[1683,6906,6885],{},[1811,6908,1994],{"stretchy":1993},[1683,6910,6834],{},[1811,6912,2005],{"stretchy":1993},[1691,6914,6915],{"encoding":1693},"f(x)"," je hustota pravděpodobnosti.",[1265,6918,6919,6920,1497],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,6921,6923],{"className":6922},[1668],[1670,6924,6925],{"xmlns":1672},[1674,6926,6927,6981],{},[1677,6928,6929,6931,6933,6939,6941,6943,6945,6951,6953,6955,6957,6959,6965,6967,6969,6971,6973,6979],{},[1683,6930,6841],{},[1811,6932,1994],{"stretchy":1993},[1680,6934,6935,6937],{},[1683,6936,6834],{},[1687,6938,1914],{},[1811,6940,4453],{},[1683,6942,6846],{},[1811,6944,4453],{},[1680,6946,6947,6949],{},[1683,6948,6834],{},[1687,6950,1713],{},[1811,6952,2005],{"stretchy":1993},[1811,6954,2101],{},[1683,6956,1403],{},[1811,6958,1994],{"stretchy":1993},[1680,6960,6961,6963],{},[1683,6962,6834],{},[1687,6964,1713],{},[1811,6966,2005],{"stretchy":1993},[1811,6968,3184],{},[1683,6970,1403],{},[1811,6972,1994],{"stretchy":1993},[1680,6974,6975,6977],{},[1683,6976,6834],{},[1687,6978,1914],{},[1811,6980,2005],{"stretchy":1993},[1691,6982,6983],{"encoding":1693},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1265,6985,6986,1418,6989,7021,7022,3071,7025,3071,7028,7031,7032,7046,7047,1497],{},[1136,6987,6988],{},"Normální rozdělení",[1115,6990,6992],{"className":6991},[1668],[1670,6993,6994],{"xmlns":1672},[1674,6995,6996,7018],{},[1677,6997,6998,7001,7003,7006,7009,7016],{},[1683,6999,7000],{},"N",[1811,7002,1994],{"stretchy":1993},[1683,7004,7005],{},"μ",[1811,7007,7008],{"separator":1121},";",[1706,7010,7011,7014],{},[1683,7012,7013],{},"σ",[1687,7015,1713],{},[1811,7017,2005],{"stretchy":1993},[1691,7019,7020],{"encoding":1693},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3590,7023,7024],{},"dnorm",[3590,7026,7027],{},"pnorm",[3590,7029,7030],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,7033,7035],{"className":7034},[1668],[1670,7036,7037],{"xmlns":1672},[1674,7038,7039,7043],{},[1677,7040,7041],{},[1683,7042,7013],{},[1691,7044,7045],{"encoding":1693},"\\sigma",", ne rozptyl ",[1115,7048,7050],{"className":7049},[1668],[1670,7051,7052],{"xmlns":1672},[1674,7053,7054,7062],{},[1677,7055,7056],{},[1706,7057,7058,7060],{},[1683,7059,7013],{},[1687,7061,1713],{},[1691,7063,7064],{"encoding":1693},"\\sigma^2",[1265,7066,7067,3071,7070,5862,7073,7076],{},[1136,7068,7069],{},"Studentovo",[1136,7071,7072],{},"Pearsonovo (χ²)",[1136,7074,7075],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1153,7078,7080],{"id":7079},"náhodná-veličina","Náhodná veličina",[1110,7082,7083,7086,7087,7102,7103,1418,7105,7118,7119,7139,7140,6895,7153,7177,7178,3071,7191,3071,7205,7219,7220,3071,7233,3071,7247,7261,7262,7275,7276,7289,7290,1497],{},[1127,7084,1133],{"className":7085,"dataFsResolvedFilePath":1132,"href":1129},[1131]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,7088,7090],{"className":7089},[1668],[1670,7091,7092],{"xmlns":1672},[1674,7093,7094,7099],{},[1677,7095,7096],{},[1683,7097,7098],{"mathvariant":2240},"Ω",[1691,7100,7101],{"encoding":1693},"\\Omega"," přiřazený výsledkům pokusu. ",[1136,7104,7080],{},[1115,7106,7108],{"className":7107},[1668],[1670,7109,7110],{"xmlns":1672},[1674,7111,7112,7116],{},[1677,7113,7114],{},[1683,7115,6846],{},[1691,7117,6846],{"encoding":1693}," je funkce, která prvkům ",[1115,7120,7122],{"className":7121},[1668],[1670,7123,7124],{"xmlns":1672},[1674,7125,7126,7136],{},[1677,7127,7128,7131,7134],{},[1683,7129,7130],{},"ω",[1811,7132,7133],{},"∈",[1683,7135,7098],{"mathvariant":2240},[1691,7137,7138],{"encoding":1693},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,7141,7143],{"className":7142},[1668],[1670,7144,7145],{"xmlns":1672},[1674,7146,7147,7151],{},[1677,7148,7149],{},[1683,7150,6834],{},[1691,7152,6834],{"encoding":1693},[1115,7154,7156],{"className":7155},[1668],[1670,7157,7158],{"xmlns":1672},[1674,7159,7160,7174],{},[1677,7161,7162,7164,7166,7168,7170,7172],{},[1683,7163,6834],{},[1811,7165,2101],{},[1683,7167,6846],{},[1811,7169,1994],{"stretchy":1993},[1683,7171,7130],{},[1811,7173,2005],{"stretchy":1993},[1691,7175,7176],{"encoding":1693},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,7179,7181],{"className":7180},[1668],[1670,7182,7183],{"xmlns":1672},[1674,7184,7185,7189],{},[1677,7186,7187],{},[1683,7188,6846],{},[1691,7190,6846],{"encoding":1693},[1115,7192,7194],{"className":7193},[1668],[1670,7195,7196],{"xmlns":1672},[1674,7197,7198,7203],{},[1677,7199,7200],{},[1683,7201,7202],{},"Y",[1691,7204,7202],{"encoding":1693},[1115,7206,7208],{"className":7207},[1668],[1670,7209,7210],{"xmlns":1672},[1674,7211,7212,7217],{},[1677,7213,7214],{},[1683,7215,7216],{},"T",[1691,7218,7216],{"encoding":1693},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,7221,7223],{"className":7222},[1668],[1670,7224,7225],{"xmlns":1672},[1674,7226,7227,7231],{},[1677,7228,7229],{},[1683,7230,6834],{},[1691,7232,6834],{"encoding":1693},[1115,7234,7236],{"className":7235},[1668],[1670,7237,7238],{"xmlns":1672},[1674,7239,7240,7245],{},[1677,7241,7242],{},[1683,7243,7244],{},"y",[1691,7246,7244],{"encoding":1693},[1115,7248,7250],{"className":7249},[1668],[1670,7251,7252],{"xmlns":1672},[1674,7253,7254,7259],{},[1677,7255,7256],{},[1683,7257,7258],{},"t",[1691,7260,7258],{"encoding":1693},"); pravděpodobnost, že ",[1115,7263,7265],{"className":7264},[1668],[1670,7266,7267],{"xmlns":1672},[1674,7268,7269,7273],{},[1677,7270,7271],{},[1683,7272,6846],{},[1691,7274,6846],{"encoding":1693}," nabyla hodnoty ",[1115,7277,7279],{"className":7278},[1668],[1670,7280,7281],{"xmlns":1672},[1674,7282,7283,7287],{},[1677,7284,7285],{},[1683,7286,6834],{},[1691,7288,6834],{"encoding":1693},", zapisujeme ",[1115,7291,7293],{"className":7292},[1668],[1670,7294,7295],{"xmlns":1672},[1674,7296,7297,7311],{},[1677,7298,7299,7301,7303,7305,7307,7309],{},[1683,7300,6841],{},[1811,7302,1994],{"stretchy":1993},[1683,7304,6846],{},[1811,7306,2101],{},[1683,7308,6834],{},[1811,7310,2005],{"stretchy":1993},[1691,7312,7313],{"encoding":1693},"P(X = x)",[1110,7315,7316],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1503,7318,7319,7379],{},[1265,7320,7321,7324,7325,7338,7339,7378],{},[1136,7322,7323],{},"Diskrétní náhodná veličina"," — prvky ",[1115,7326,7328],{"className":7327},[1668],[1670,7329,7330],{"xmlns":1672},[1674,7331,7332,7336],{},[1677,7333,7334],{},[1683,7335,7098],{"mathvariant":2240},[1691,7337,7101],{"encoding":1693}," se zobrazí na osu reálných čísel jako izolované body ",[1115,7340,7342],{"className":7341},[1668],[1670,7343,7344],{"xmlns":1672},[1674,7345,7346,7375],{},[1677,7347,7348,7354,7356,7362,7364,7366,7368],{},[1680,7349,7350,7352],{},[1683,7351,6834],{},[1687,7353,1914],{},[1811,7355,1917],{"separator":1121},[1680,7357,7358,7360],{},[1683,7359,6834],{},[1687,7361,1713],{},[1811,7363,1917],{"separator":1121},[1811,7365,1920],{},[1811,7367,1917],{"separator":1121},[1680,7369,7370,7372],{},[1683,7371,6834],{},[1683,7373,7374],{},"k",[1691,7376,7377],{"encoding":1693},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1265,7380,7381,7384],{},[1136,7382,7383],{},"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.",[1153,7386,7388],{"id":7387},"distribuční-funkce","Distribuční funkce",[1110,7390,7391,7392,7395],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1136,7393,7394],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,7397,7398],{},[4504,7399],{"alt":7400,"className":7401,"src":7402},"mask-nv-distribucni-funkce",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,7404,7407,7414],{"className":7405,"dataCallout":654},[1106,7406],"callout-info",[1110,7408,7410,7413],{"className":7409},[1113],[1115,7411],{"className":7412,"ariaHidden":1121},[1118,1648,1120],"Definice",[1110,7415,7416,7417,7430,7431,7451,7452,7465,7466,7502,7521,7522,7535,7536,1497],{},"Distribuční funkcí náhodné veličiny ",[1115,7418,7420],{"className":7419},[1668],[1670,7421,7422],{"xmlns":1672},[1674,7423,7424,7428],{},[1677,7425,7426],{},[1683,7427,6846],{},[1691,7429,6846],{"encoding":1693}," nazýváme reálnou funkci ",[1115,7432,7434],{"className":7433},[1668],[1670,7435,7436],{"xmlns":1672},[1674,7437,7438,7448],{},[1677,7439,7440,7442,7444,7446],{},[1683,7441,1403],{},[1811,7443,1994],{"stretchy":1993},[1683,7445,6834],{},[1811,7447,2005],{"stretchy":1993},[1691,7449,7450],{"encoding":1693},"F(x)"," definovanou pro každé reálné číslo ",[1115,7453,7455],{"className":7454},[1668],[1670,7456,7457],{"xmlns":1672},[1674,7458,7459,7463],{},[1677,7460,7461],{},[1683,7462,6834],{},[1691,7464,6834],{"encoding":1693}," jako\n",[1115,7467,7469],{"className":7468},[1668],[1670,7470,7471],{"xmlns":1672},[1674,7472,7473,7499],{},[1677,7474,7475,7477,7479,7481,7483,7485,7487,7489,7491,7493,7495,7497],{},[1683,7476,1403],{},[1811,7478,1994],{"stretchy":1993},[1683,7480,6834],{},[1811,7482,2005],{"stretchy":1993},[1811,7484,2101],{},[1683,7486,6841],{},[1811,7488,1994],{"stretchy":1993},[1683,7490,6846],{},[1811,7492,6849],{},[1683,7494,6834],{},[1811,7496,2005],{"stretchy":1993},[1683,7498,1497],{"mathvariant":2240},[1691,7500,7501],{"encoding":1693},"F(x) = P(X \\le x).",[1115,7503,7505],{"className":7504},[1668],[1670,7506,7507],{"xmlns":1672},[1674,7508,7509,7519],{},[1677,7510,7511,7513,7515,7517],{},[1683,7512,1403],{},[1811,7514,1994],{"stretchy":1993},[1683,7516,6834],{},[1811,7518,2005],{"stretchy":1993},[1691,7520,7450],{"encoding":1693}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,7523,7525],{"className":7524},[1668],[1670,7526,7527],{"xmlns":1672},[1674,7528,7529,7533],{},[1677,7530,7531],{},[1683,7532,6846],{},[1691,7534,6846],{"encoding":1693}," nabude hodnoty z intervalu ",[1115,7537,7539],{"className":7538},[1668],[1670,7540,7541],{"xmlns":1672},[1674,7542,7543,7559],{},[1677,7544,7545,7547,7549,7552,7554,7556],{},[1811,7546,1994],{"stretchy":1993},[1811,7548,3184],{},[1683,7550,7551],{"mathvariant":2240},"∞",[1811,7553,1917],{"separator":1121},[1683,7555,6834],{},[1811,7557,7558],{"stretchy":1993},"⟩",[1691,7560,7561],{"encoding":1693},"(-\\infty, x\\rangle",[1110,7563,7564,7565,7578,7579,7600],{},"Značí-li například ",[1115,7566,7568],{"className":7567},[1668],[1670,7569,7570],{"xmlns":1672},[1674,7571,7572,7576],{},[1677,7573,7574],{},[1683,7575,6846],{},[1691,7577,6846],{"encoding":1693}," výšku mužů v populaci, pak ",[1115,7580,7582],{"className":7581},[1668],[1670,7583,7584],{"xmlns":1672},[1674,7585,7586,7597],{},[1677,7587,7588,7590,7592,7595],{},[1683,7589,1403],{},[1811,7591,1994],{"stretchy":1993},[1687,7593,7594],{},"175",[1811,7596,2005],{"stretchy":1993},[1691,7598,7599],{"encoding":1693},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,7602,7603],{},"Pro distribuční funkci vždy platí:",[1503,7605,7606,7636,7694,7754],{},[1265,7607,7608,1917],{},[1115,7609,7611],{"className":7610},[1668],[1670,7612,7613],{"xmlns":1672},[1674,7614,7615,7633],{},[1677,7616,7617,7619,7621,7623,7625,7627,7629,7631],{},[1687,7618,1689],{},[1811,7620,6849],{},[1683,7622,1403],{},[1811,7624,1994],{"stretchy":1993},[1683,7626,6834],{},[1811,7628,2005],{"stretchy":1993},[1811,7630,6849],{},[1687,7632,1914],{},[1691,7634,7635],{"encoding":1693},"0 \\le F(x) \\le 1",[1265,7637,7638,7639,1917],{},"je neklesající: ",[1115,7640,7642],{"className":7641},[1668],[1670,7643,7644],{"xmlns":1672},[1674,7645,7646,7691],{},[1677,7647,7648,7654,7656,7662,7665,7667,7669,7675,7677,7679,7681,7683,7689],{},[1680,7649,7650,7652],{},[1683,7651,6834],{},[1687,7653,1914],{},[1811,7655,6849],{},[1680,7657,7658,7660],{},[1683,7659,6834],{},[1687,7661,1713],{},[1811,7663,7664],{},"⇒",[1683,7666,1403],{},[1811,7668,1994],{"stretchy":1993},[1680,7670,7671,7673],{},[1683,7672,6834],{},[1687,7674,1914],{},[1811,7676,2005],{"stretchy":1993},[1811,7678,6849],{},[1683,7680,1403],{},[1811,7682,1994],{"stretchy":1993},[1680,7684,7685,7687],{},[1683,7686,6834],{},[1687,7688,1713],{},[1811,7690,2005],{"stretchy":1993},[1691,7692,7693],{"encoding":1693},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1265,7695,7696,7697,1917],{},"je spojitá zprava: ",[1115,7698,7700],{"className":7699},[1668],[1670,7701,7702],{"xmlns":1672},[1674,7703,7704,7751],{},[1677,7705,7706,7729,7731,7733,7735,7737,7739,7741,7743,7745,7747,7749],{},[1680,7707,7708,7715],{},[1677,7709,7710,7713],{},[1683,7711,7712],{},"lim",[1811,7714,4612],{},[1677,7716,7717,7720,7723],{},[1683,7718,7719],{},"h",[1811,7721,7722],{},"→",[1706,7724,7725,7727],{},[1687,7726,1689],{},[1811,7728,5598],{},[1683,7730,1403],{},[1811,7732,1994],{"stretchy":1993},[1683,7734,6834],{},[1811,7736,5598],{},[1683,7738,7719],{},[1811,7740,2005],{"stretchy":1993},[1811,7742,2101],{},[1683,7744,1403],{},[1811,7746,1994],{"stretchy":1993},[1683,7748,6834],{},[1811,7750,2005],{"stretchy":1993},[1691,7752,7753],{"encoding":1693},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1265,7755,7756,3071,7798,1497],{},[1115,7757,7759],{"className":7758},[1668],[1670,7760,7761],{"xmlns":1672},[1674,7762,7763,7795],{},[1677,7764,7765,7783,7785,7787,7789,7791,7793],{},[1680,7766,7767,7773],{},[1677,7768,7769,7771],{},[1683,7770,7712],{},[1811,7772,4612],{},[1677,7774,7775,7777,7779,7781],{},[1683,7776,6834],{},[1811,7778,7722],{},[1811,7780,3184],{},[1683,7782,7551],{"mathvariant":2240},[1683,7784,1403],{},[1811,7786,1994],{"stretchy":1993},[1683,7788,6834],{},[1811,7790,2005],{"stretchy":1993},[1811,7792,2101],{},[1687,7794,1689],{},[1691,7796,7797],{"encoding":1693},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,7799,7801],{"className":7800},[1668],[1670,7802,7803],{"xmlns":1672},[1674,7804,7805,7835],{},[1677,7806,7807,7823,7825,7827,7829,7831,7833],{},[1680,7808,7809,7815],{},[1677,7810,7811,7813],{},[1683,7812,7712],{},[1811,7814,4612],{},[1677,7816,7817,7819,7821],{},[1683,7818,6834],{},[1811,7820,7722],{},[1683,7822,7551],{"mathvariant":2240},[1683,7824,1403],{},[1811,7826,1994],{"stretchy":1993},[1683,7828,6834],{},[1811,7830,2005],{"stretchy":1993},[1811,7832,2101],{},[1687,7834,1914],{},[1691,7836,7837],{"encoding":1693},"\\lim_{x \\to \\infty} F(x) = 1",[1110,7839,7840],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,7842,7844],{"className":7843},[1668],[1670,7845,7846],{"xmlns":1672,"display":2083},[1674,7847,7848,7916],{},[1677,7849,7850,7856,7858,7860,7862,7864,7866,7868,7870,7872,7874,7876,7878,7880,7882,7884,7886,7899,7901,7903,7905,7907,7909,7912,7914],{},[1706,7851,7852,7854],{},[1683,7853,1403],{},[1811,7855,6874],{"mathvariant":2240,"lspace":6873,"rspace":6873},[1811,7857,1994],{"stretchy":1993},[1683,7859,6834],{},[1811,7861,2005],{"stretchy":1993},[1811,7863,2101],{},[1683,7865,6885],{},[1811,7867,1994],{"stretchy":1993},[1683,7869,6834],{},[1811,7871,2005],{"stretchy":1993},[1811,7873,1917],{"separator":1121},[2131,7875],{"width":2133},[1683,7877,1403],{},[1811,7879,1994],{"stretchy":1993},[1683,7881,6834],{},[1811,7883,2005],{"stretchy":1993},[1811,7885,2101],{},[3473,7887,7888,7891,7897],{},[1811,7889,7890],{},"∫",[1677,7892,7893,7895],{},[1811,7894,3184],{},[1683,7896,7551],{"mathvariant":2240},[1683,7898,6834],{},[1683,7900,6885],{},[1811,7902,1994],{"stretchy":1993},[1683,7904,7258],{},[1811,7906,2005],{"stretchy":1993},[3028,7908,3030],{},[1683,7910,7911],{},"d",[1683,7913,7258],{},[1683,7915,1497],{"mathvariant":2240},[1691,7917,7918],{"encoding":1693},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,7920,7921,7922,7935,7936,5862,7954,7972],{},"Pravděpodobnost, že ",[1115,7923,7925],{"className":7924},[1668],[1670,7926,7927],{"xmlns":1672},[1674,7928,7929,7933],{},[1677,7930,7931],{},[1683,7932,6846],{},[1691,7934,6846],{"encoding":1693}," padne mezi body ",[1115,7937,7939],{"className":7938},[1668],[1670,7940,7941],{"xmlns":1672},[1674,7942,7943,7951],{},[1677,7944,7945],{},[1680,7946,7947,7949],{},[1683,7948,6834],{},[1687,7950,1914],{},[1691,7952,7953],{"encoding":1693},"x_1",[1115,7955,7957],{"className":7956},[1668],[1670,7958,7959],{"xmlns":1672},[1674,7960,7961,7969],{},[1677,7962,7963],{},[1680,7964,7965,7967],{},[1683,7966,6834],{},[1687,7968,1713],{},[1691,7970,7971],{"encoding":1693},"x_2",", se pak počítá jako",[1115,7974,7976],{"className":7975},[1668],[1670,7977,7978],{"xmlns":1672,"display":2083},[1674,7979,7980,8068],{},[1677,7981,7982,7984,7986,7992,7994,7996,7998,8004,8006,8008,8024,8026,8028,8030,8032,8034,8036,8038,8040,8042,8044,8050,8052,8054,8056,8058,8064,8066],{},[1683,7983,6841],{},[1811,7985,1994],{"stretchy":1993},[1680,7987,7988,7990],{},[1683,7989,6834],{},[1687,7991,1914],{},[1811,7993,4453],{},[1683,7995,6846],{},[1811,7997,4453],{},[1680,7999,8000,8002],{},[1683,8001,6834],{},[1687,8003,1713],{},[1811,8005,2005],{"stretchy":1993},[1811,8007,2101],{},[3473,8009,8010,8012,8018],{},[1811,8011,7890],{},[1680,8013,8014,8016],{},[1683,8015,6834],{},[1687,8017,1914],{},[1680,8019,8020,8022],{},[1683,8021,6834],{},[1687,8023,1713],{},[1683,8025,6885],{},[1811,8027,1994],{"stretchy":1993},[1683,8029,7258],{},[1811,8031,2005],{"stretchy":1993},[3028,8033,3030],{},[1683,8035,7911],{},[1683,8037,7258],{},[1811,8039,2101],{},[1683,8041,1403],{},[1811,8043,1994],{"stretchy":1993},[1680,8045,8046,8048],{},[1683,8047,6834],{},[1687,8049,1713],{},[1811,8051,2005],{"stretchy":1993},[1811,8053,3184],{},[1683,8055,1403],{},[1811,8057,1994],{"stretchy":1993},[1680,8059,8060,8062],{},[1683,8061,6834],{},[1687,8063,1914],{},[1811,8065,2005],{"stretchy":1993},[1683,8067,1497],{"mathvariant":2240},[1691,8069,8070],{"encoding":1693},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1153,8072,8074],{"id":8073},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,8076,8078,8084],{"className":8077,"dataCallout":654},[1106,7406],[1110,8079,8081,7413],{"className":8080},[1113],[1115,8082],{"className":8083,"ariaHidden":1121},[1118,1648,1120],[1110,8085,8086,8087,8106,8107,8120,8121,8134,8135,1497],{},"Hustota pravděpodobnosti ",[1115,8088,8090],{"className":8089},[1668],[1670,8091,8092],{"xmlns":1672},[1674,8093,8094,8104],{},[1677,8095,8096,8098,8100,8102],{},[1683,8097,6885],{},[1811,8099,1994],{"stretchy":1993},[1683,8101,6834],{},[1811,8103,2005],{"stretchy":1993},[1691,8105,6915],{"encoding":1693}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,8108,8110],{"className":8109},[1668],[1670,8111,8112],{"xmlns":1672},[1674,8113,8114,8118],{},[1677,8115,8116],{},[1683,8117,6846],{},[1691,8119,6846],{"encoding":1693}," nahuštěny v okolí bodu ",[1115,8122,8124],{"className":8123},[1668],[1670,8125,8126],{"xmlns":1672},[1674,8127,8128,8132],{},[1677,8129,8130],{},[1683,8131,6834],{},[1691,8133,6834],{"encoding":1693},". Je vždy nezáporná a platí pro ni ",[1115,8136,8138],{"className":8137},[1668],[1670,8139,8140],{"xmlns":1672},[1674,8141,8142,8174],{},[1677,8143,8144,8156,8158,8160,8162,8164,8166,8168,8170,8172],{},[3473,8145,8146,8148,8154],{},[1811,8147,7890],{},[1677,8149,8150,8152],{},[1811,8151,3184],{},[1683,8153,7551],{"mathvariant":2240},[1683,8155,7551],{"mathvariant":2240},[1683,8157,6885],{},[1811,8159,1994],{"stretchy":1993},[1683,8161,6834],{},[1811,8163,2005],{"stretchy":1993},[3028,8165,3030],{},[1683,8167,7911],{},[1683,8169,6834],{},[1811,8171,2101],{},[1687,8173,1914],{},[1691,8175,8176],{"encoding":1693},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,8178,8179],{},"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.",[1153,8181,8183],{"id":8182},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,8185,8186,8189],{},[1136,8187,8188],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,8191,8193],{"className":8192},[1668],[1670,8194,8195],{"xmlns":1672,"display":2083},[1674,8196,8197,8242],{},[1677,8198,8199,8201,8203,8205,8207,8209,8221,8223,8226,8228,8230,8232,8234,8236,8238,8240],{},[1683,8200,1395],{},[1811,8202,1994],{"stretchy":1993},[1683,8204,6846],{},[1811,8206,2005],{"stretchy":1993},[1811,8208,2101],{},[3473,8210,8211,8213,8219],{},[1811,8212,7890],{},[1677,8214,8215,8217],{},[1811,8216,3184],{},[1683,8218,7551],{"mathvariant":2240},[1683,8220,7551],{"mathvariant":2240},[1683,8222,6834],{},[1811,8224,8225],{},"⋅",[1683,8227,6885],{},[1811,8229,1994],{"stretchy":1993},[1683,8231,6834],{},[1811,8233,2005],{"stretchy":1993},[3028,8235,3030],{},[1683,8237,7911],{},[1683,8239,6834],{},[1683,8241,1497],{"mathvariant":2240},[1691,8243,8244],{"encoding":1693},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,8246,8247],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,8249,8250,5862,8253,2077],{},[1136,8251,8252],{},"Rozptyl",[1136,8254,8255],{},"směrodatná odchylka",[1115,8257,8259],{"className":8258},[1668],[1670,8260,8261],{"xmlns":1672,"display":2083},[1674,8262,8263,8403],{},[1677,8264,8265,8267,8269,8271,8273,8275,8287,8290,8292,8294,8296,8298,8300,8302,8309,8311,8313,8315,8317,8319,8321,8323,8325,8337,8343,8345,8347,8349,8351,8353,8355,8357,8359,8361,8363,8365,8367,8369,8375,8377,8379,8381,8383,8385,8387,8389,8401],{},[1683,8266,1387],{},[1811,8268,1994],{"stretchy":1993},[1683,8270,6846],{},[1811,8272,2005],{"stretchy":1993},[1811,8274,2101],{},[3473,8276,8277,8279,8285],{},[1811,8278,7890],{},[1677,8280,8281,8283],{},[1811,8282,3184],{},[1683,8284,7551],{"mathvariant":2240},[1683,8286,7551],{"mathvariant":2240},[1811,8288,8289],{"stretchy":1993},"[",[1683,8291,6834],{},[1811,8293,3184],{},[1683,8295,1395],{},[1811,8297,1994],{"stretchy":1993},[1683,8299,6846],{},[1811,8301,2005],{"stretchy":1993},[1706,8303,8304,8307],{},[1811,8305,8306],{"stretchy":1993},"]",[1687,8308,1713],{},[1683,8310,6885],{},[1811,8312,1994],{"stretchy":1993},[1683,8314,6834],{},[1811,8316,2005],{"stretchy":1993},[3028,8318,3030],{},[1683,8320,7911],{},[1683,8322,6834],{},[1811,8324,2101],{},[3473,8326,8327,8329,8335],{},[1811,8328,7890],{},[1677,8330,8331,8333],{},[1811,8332,3184],{},[1683,8334,7551],{"mathvariant":2240},[1683,8336,7551],{"mathvariant":2240},[1706,8338,8339,8341],{},[1683,8340,6834],{},[1687,8342,1713],{},[1683,8344,6885],{},[1811,8346,1994],{"stretchy":1993},[1683,8348,6834],{},[1811,8350,2005],{"stretchy":1993},[3028,8352,3030],{},[1683,8354,7911],{},[1683,8356,6834],{},[1811,8358,3184],{},[1811,8360,8289],{"stretchy":1993},[1683,8362,1395],{},[1811,8364,1994],{"stretchy":1993},[1683,8366,6846],{},[1811,8368,2005],{"stretchy":1993},[1706,8370,8371,8373],{},[1811,8372,8306],{"stretchy":1993},[1687,8374,1713],{},[1811,8376,1917],{"separator":1121},[2131,8378],{"width":2133},[1683,8380,7013],{},[1811,8382,1994],{"stretchy":1993},[1683,8384,6846],{},[1811,8386,2005],{"stretchy":1993},[1811,8388,2101],{},[4574,8390,8391],{},[1677,8392,8393,8395,8397,8399],{},[1683,8394,1387],{},[1811,8396,1994],{"stretchy":1993},[1683,8398,6846],{},[1811,8400,2005],{"stretchy":1993},[1683,8402,1497],{"mathvariant":2240},[1691,8404,8405],{"encoding":1693},"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)}.",[1110,8407,8408,8409,8412],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1127,8410,886],{"className":8411,"dataFsResolvedFilePath":1288,"href":1286},[1131],".)",[1110,8414,8415,8418,8419,8432,8433,8451,8452,8465],{},[1136,8416,8417],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,8420,8422],{"className":8421},[1668],[1670,8423,8424],{"xmlns":1672},[1674,8425,8426,8430],{},[1677,8427,8428],{},[1683,8429,6846],{},[1691,8431,6846],{"encoding":1693}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,8434,8436],{"className":8435},[1668],[1670,8437,8438],{"xmlns":1672},[1674,8439,8440,8448],{},[1677,8441,8442],{},[1680,8443,8444,8446],{},[1683,8445,6834],{},[1683,8447,1110],{},[1691,8449,8450],{"encoding":1693},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,8453,8455],{"className":8454},[1668],[1670,8456,8457],{"xmlns":1672},[1674,8458,8459,8463],{},[1677,8460,8461],{},[1683,8462,1110],{},[1691,8464,1110],{"encoding":1693}," platí",[1115,8467,8469],{"className":8468},[1668],[1670,8470,8471],{"xmlns":1672,"display":2083},[1674,8472,8473,8493],{},[1677,8474,8475,8477,8479,8485,8487,8489,8491],{},[1683,8476,1403],{},[1811,8478,1994],{"stretchy":1993},[1680,8480,8481,8483],{},[1683,8482,6834],{},[1683,8484,1110],{},[1811,8486,2005],{"stretchy":1993},[1811,8488,2101],{},[1683,8490,1110],{},[1683,8492,1497],{"mathvariant":2240},[1691,8494,8495],{"encoding":1693},"F(x_p) = p.",[1110,8497,8498,8499,8527,8528,8555,8556,8575,8576,8595,8596,1497],{},"V intervalu ",[1115,8500,8502],{"className":8501},[1668],[1670,8503,8504],{"xmlns":1672},[1674,8505,8506,8524],{},[1677,8507,8508,8510,8512,8514,8516,8522],{},[1811,8509,1994],{"stretchy":1993},[1811,8511,3184],{},[1683,8513,7551],{"mathvariant":2240},[1811,8515,7008],{"separator":1121},[1680,8517,8518,8520],{},[1683,8519,6834],{},[1683,8521,1110],{},[1811,8523,2005],{"stretchy":1993},[1691,8525,8526],{"encoding":1693},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,8529,8531],{"className":8530},[1668],[1670,8532,8533],{"xmlns":1672},[1674,8534,8535,8552],{},[1677,8536,8537,8540,8546,8548,8550],{},[1811,8538,8539],{"stretchy":1993},"⟨",[1680,8541,8542,8544],{},[1683,8543,6834],{},[1683,8545,1110],{},[1811,8547,7008],{"separator":1121},[1683,8549,7551],{"mathvariant":2240},[1811,8551,2005],{"stretchy":1993},[1691,8553,8554],{"encoding":1693},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,8557,8559],{"className":8558},[1668],[1670,8560,8561],{"xmlns":1672},[1674,8562,8563,8572],{},[1677,8564,8565],{},[1680,8566,8567,8569],{},[1683,8568,6834],{},[1687,8570,8571],{},"0,5",[1691,8573,8574],{"encoding":1693},"x_{0{,}5}",", dolní kvartil ",[1115,8577,8579],{"className":8578},[1668],[1670,8580,8581],{"xmlns":1672},[1674,8582,8583,8592],{},[1677,8584,8585],{},[1680,8586,8587,8589],{},[1683,8588,6834],{},[1687,8590,8591],{},"0,25",[1691,8593,8594],{"encoding":1693},"x_{0{,}25}"," a horní kvartil ",[1115,8597,8599],{"className":8598},[1668],[1670,8600,8601],{"xmlns":1672},[1674,8602,8603,8612],{},[1677,8604,8605],{},[1680,8606,8607,8609],{},[1683,8608,6834],{},[1687,8610,8611],{},"0,75",[1691,8613,8614],{"encoding":1693},"x_{0{,}75}",[1153,8616,6988],{"id":8617},"normální-rozdělení",[1110,8619,8620,8621,8634,8635,1418,8638,8665],{},"Spojitá náhodná veličina ",[1115,8622,8624],{"className":8623},[1668],[1670,8625,8626],{"xmlns":1672},[1674,8627,8628,8632],{},[1677,8629,8630],{},[1683,8631,6846],{},[1691,8633,6846],{"encoding":1693}," má ",[1136,8636,8637],{},"normální rozdělení",[1115,8639,8641],{"className":8640},[1668],[1670,8642,8643],{"xmlns":1672},[1674,8644,8645,8663],{},[1677,8646,8647,8649,8651,8653,8655,8661],{},[1683,8648,7000],{},[1811,8650,1994],{"stretchy":1993},[1683,8652,7005],{},[1811,8654,7008],{"separator":1121},[1706,8656,8657,8659],{},[1683,8658,7013],{},[1687,8660,1713],{},[1811,8662,2005],{"stretchy":1993},[1691,8664,7020],{"encoding":1693},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,8667,8669],{"className":8668},[1668],[1670,8670,8671],{"xmlns":1672,"display":2083},[1674,8672,8673,8825],{},[1677,8674,8675,8677,8679,8681,8683,8685,8702,8739,8741,8743,8745,8747,8749,8751,8753,8769,8781,8817,8819,8821,8823],{},[1683,8676,6885],{},[1811,8678,1994],{"stretchy":1993},[1683,8680,6834],{},[1811,8682,2005],{"stretchy":1993},[1811,8684,2101],{},[2859,8686,8687,8689],{},[1687,8688,1914],{},[1677,8690,8691,8693],{},[1683,8692,7013],{},[4574,8694,8695],{},[1677,8696,8697,8699],{},[1687,8698,1713],{},[1683,8700,8701],{},"π",[1706,8703,8704,8707],{},[1683,8705,8706],{},"e",[1677,8708,8709,8711],{},[1811,8710,3184],{},[2859,8712,8713,8729],{},[1677,8714,8715,8717,8719,8721,8723],{},[1811,8716,1994],{"stretchy":1993},[1683,8718,6834],{},[1811,8720,3184],{},[1683,8722,7005],{},[1706,8724,8725,8727],{},[1811,8726,2005],{"stretchy":1993},[1687,8728,1713],{},[1677,8730,8731,8733],{},[1687,8732,1713],{},[1706,8734,8735,8737],{},[1683,8736,7013],{},[1687,8738,1713],{},[1811,8740,1917],{"separator":1121},[2131,8742],{"width":2133},[1683,8744,1403],{},[1811,8746,1994],{"stretchy":1993},[1683,8748,6834],{},[1811,8750,2005],{"stretchy":1993},[1811,8752,2101],{},[2859,8754,8755,8757],{},[1687,8756,1914],{},[1677,8758,8759,8761],{},[1683,8760,7013],{},[4574,8762,8763],{},[1677,8764,8765,8767],{},[1687,8766,1713],{},[1683,8768,8701],{},[3473,8770,8771,8773,8779],{},[1811,8772,7890],{},[1677,8774,8775,8777],{},[1811,8776,3184],{},[1683,8778,7551],{"mathvariant":2240},[1683,8780,6834],{},[1706,8782,8783,8785],{},[1683,8784,8706],{},[1677,8786,8787,8789],{},[1811,8788,3184],{},[2859,8790,8791,8807],{},[1677,8792,8793,8795,8797,8799,8801],{},[1811,8794,1994],{"stretchy":1993},[1683,8796,7258],{},[1811,8798,3184],{},[1683,8800,7005],{},[1706,8802,8803,8805],{},[1811,8804,2005],{"stretchy":1993},[1687,8806,1713],{},[1677,8808,8809,8811],{},[1687,8810,1713],{},[1706,8812,8813,8815],{},[1683,8814,7013],{},[1687,8816,1713],{},[3028,8818,3030],{},[1683,8820,7911],{},[1683,8822,7258],{},[1811,8824,1917],{"separator":1121},[1691,8826,8827],{"encoding":1693},"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,",[1110,8829,8830,8831,3071,8855,1497],{},"přičemž ",[1115,8832,8834],{"className":8833},[1668],[1670,8835,8836],{"xmlns":1672},[1674,8837,8838,8852],{},[1677,8839,8840,8842,8844,8846,8848,8850],{},[1683,8841,1395],{},[1811,8843,1994],{"stretchy":1993},[1683,8845,6846],{},[1811,8847,2005],{"stretchy":1993},[1811,8849,2101],{},[1683,8851,7005],{},[1691,8853,8854],{"encoding":1693},"E(X) = \\mu",[1115,8856,8858],{"className":8857},[1668],[1670,8859,8860],{"xmlns":1672},[1674,8861,8862,8880],{},[1677,8863,8864,8866,8868,8870,8872,8874],{},[1683,8865,1387],{},[1811,8867,1994],{"stretchy":1993},[1683,8869,6846],{},[1811,8871,2005],{"stretchy":1993},[1811,8873,2101],{},[1706,8875,8876,8878],{},[1683,8877,7013],{},[1687,8879,1713],{},[1691,8881,8882],{"encoding":1693},"D(X) = \\sigma^2",[1110,8884,8885],{},[4504,8886],{"alt":8887,"className":8888,"src":8889},"mask-nv-normalni",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,8891,8892,8893,8896,8897,8911,8912,8931,8932,8948,8949,8962,8963,1497],{},"Křivka hustoty se nazývá ",[1136,8894,8895],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,8898,8900],{"className":8899},[1668],[1670,8901,8902],{"xmlns":1672},[1674,8903,8904,8908],{},[1677,8905,8906],{},[1683,8907,7005],{},[1691,8909,8910],{"encoding":1693},"\\mu",", kde má ",[1115,8913,8915],{"className":8914},[1668],[1670,8916,8917],{"xmlns":1672},[1674,8918,8919,8929],{},[1677,8920,8921,8923,8925,8927],{},[1683,8922,6885],{},[1811,8924,1994],{"stretchy":1993},[1683,8926,6834],{},[1811,8928,2005],{"stretchy":1993},[1691,8930,6915],{"encoding":1693}," globální maximum, a ve vzdálenosti ",[1115,8933,8935],{"className":8934},[1668],[1670,8936,8937],{"xmlns":1672},[1674,8938,8939,8945],{},[1677,8940,8941,8943],{},[1687,8942,3712],{},[1683,8944,7013],{},[1691,8946,8947],{"encoding":1693},"3\\sigma"," od ",[1115,8950,8952],{"className":8951},[1668],[1670,8953,8954],{"xmlns":1672},[1674,8955,8956,8960],{},[1677,8957,8958],{},[1683,8959,7005],{},[1691,8961,8910],{"encoding":1693}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,8964,8966],{"className":8965},[1668],[1670,8967,8968],{"xmlns":1672},[1674,8969,8970,8994],{},[1677,8971,8972,8974,8976,8978,8980,8982,8984,8986,8988,8990,8992],{},[1811,8973,1994],{"stretchy":1993},[1683,8975,7005],{},[1811,8977,3184],{},[1687,8979,3712],{},[1683,8981,7013],{},[1811,8983,7008],{"separator":1121},[1683,8985,7005],{},[1811,8987,5598],{},[1687,8989,3712],{},[1683,8991,7013],{},[1811,8993,2005],{"stretchy":1993},[1691,8995,8996],{"encoding":1693},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,8998,8999,9000,1418,9003,9027,9028,1497],{},"Zvláštní postavení má ",[1136,9001,9002],{},"normované normální rozdělení",[1115,9004,9006],{"className":9005},[1668],[1670,9007,9008],{"xmlns":1672},[1674,9009,9010,9024],{},[1677,9011,9012,9014,9016,9018,9020,9022],{},[1683,9013,7000],{},[1811,9015,1994],{"stretchy":1993},[1687,9017,1689],{},[1811,9019,7008],{"separator":1121},[1687,9021,1914],{},[1811,9023,2005],{"stretchy":1993},[1691,9025,9026],{"encoding":1693},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,9029,9031],{"className":9030},[1668],[1670,9032,9033],{"xmlns":1672},[1674,9034,9035,9056],{},[1677,9036,9037,9040,9042,9044,9046,9048,9050,9052,9054],{},[1683,9038,9039],{},"Z",[1811,9041,2101],{},[1811,9043,1994],{"stretchy":1993},[1683,9045,6846],{},[1811,9047,3184],{},[1683,9049,7005],{},[1811,9051,2005],{"stretchy":1993},[1683,9053,4725],{"mathvariant":2240},[1683,9055,7013],{},[1691,9057,9058],{"encoding":1693},"Z = (X-\\mu)\u002F\\sigma",[9060,9061],"graph-mount",{"spec":9062},"{\"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\"}]}",[1103,9064,9066,9073],{"className":9065,"dataCallout":6534},[1106,6533],[1110,9067,9069,9072],{"className":9068},[1113],[1115,9070],{"className":9071,"ariaHidden":1121},[1118,6541,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,9074,9075,9076,9103,9104,9107,9108,3071,9110,5862,9112,9114,9115,1418,9118,9131,9132,9158,9159,9162,9163,1497],{},"Zápis ",[1115,9077,9079],{"className":9078},[1668],[1670,9080,9081],{"xmlns":1672},[1674,9082,9083,9101],{},[1677,9084,9085,9087,9089,9091,9093,9099],{},[1683,9086,7000],{},[1811,9088,1994],{"stretchy":1993},[1683,9090,7005],{},[1811,9092,7008],{"separator":1121},[1706,9094,9095,9097],{},[1683,9096,7013],{},[1687,9098,1713],{},[1811,9100,2005],{"stretchy":1993},[1691,9102,7020],{"encoding":1693}," v definici používá ",[1136,9105,9106],{},"rozptyl",". Funkce ",[3590,9109,7024],{},[3590,9111,7027],{},[3590,9113,7030],{}," v R ale jako třetí argument berou ",[1136,9116,9117],{},"směrodatnou odchylku",[1115,9119,9121],{"className":9120},[1668],[1670,9122,9123],{"xmlns":1672},[1674,9124,9125,9129],{},[1677,9126,9127],{},[1683,9128,7013],{},[1691,9130,7045],{"encoding":1693},". Má-li náhodná veličina rozdělení ",[1115,9133,9135],{"className":9134},[1668],[1670,9136,9137],{"xmlns":1672},[1674,9138,9139,9155],{},[1677,9140,9141,9143,9145,9148,9150,9153],{},[1683,9142,7000],{},[1811,9144,1994],{"stretchy":1993},[1687,9146,9147],{},"10",[1811,9149,7008],{"separator":1121},[1687,9151,9152],{},"0,12",[1811,9154,2005],{"stretchy":1993},[1691,9156,9157],{"encoding":1693},"N(10; 0{,}12)",", je ",[3590,9160,9161],{},"sd = sqrt(0.12)",", ne ",[3590,9164,9165],{},"sd = 0.12",[1110,9167,9168],{},"V R:",[3814,9170,9172],{"className":3816,"code":9171,"language":71,"meta":1603,"style":1603},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3590,9173,9174,9184,9195],{"__ignoreMap":1603},[1115,9175,9176,9178,9180,9182],{"class":3822,"line":10},[1115,9177,7024],{"class":3833},[1115,9179,1994],{"class":3837},[1115,9181,1689],{"class":3845},[1115,9183,4022],{"class":3837},[1115,9185,9186,9188,9190,9193],{"class":3822,"line":27},[1115,9187,7027],{"class":3833},[1115,9189,1994],{"class":3837},[1115,9191,9192],{"class":3845},"1.96",[1115,9194,4022],{"class":3837},[1115,9196,9197,9199,9201,9204],{"class":3822,"line":148},[1115,9198,7030],{"class":3833},[1115,9200,1994],{"class":3837},[1115,9202,9203],{"class":3845},"0.975",[1115,9205,4022],{"class":3837},[3814,9207,9210],{"className":9208,"code":9209,"language":4044,"meta":1603},[4042],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3590,9211,9209],{"__ignoreMap":1603},[1110,9213,9214,9217,9218,9242,9243,2009,9246,5862,9267,9270],{},[3590,9215,9216],{},"dnorm(0)"," je hodnota hustoty ",[1115,9219,9221],{"className":9220},[1668],[1670,9222,9223],{"xmlns":1672},[1674,9224,9225,9239],{},[1677,9226,9227,9229,9231,9233,9235,9237],{},[1683,9228,7000],{},[1811,9230,1994],{"stretchy":1993},[1687,9232,1689],{},[1811,9234,7008],{"separator":1121},[1687,9236,1914],{},[1811,9238,2005],{"stretchy":1993},[1691,9240,9241],{"encoding":1693},"N(0;1)"," v bodě 0, ",[3590,9244,9245],{},"pnorm(1.96)",[1115,9247,9249],{"className":9248},[1668],[1670,9250,9251],{"xmlns":1672},[1674,9252,9253,9264],{},[1677,9254,9255,9257,9259,9262],{},[1683,9256,1403],{},[1811,9258,1994],{"stretchy":1993},[1687,9260,9261],{},"1,96",[1811,9263,2005],{"stretchy":1993},[1691,9265,9266],{"encoding":1693},"F(1{,}96)",[3590,9268,9269],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,9272,9274,9281],{"className":9273,"dataCallout":3597},[1106,3596],[1110,9275,9277,9280],{"className":9276},[1113],[1115,9278],{"className":9279,"ariaHidden":1121},[1118,3604,1120],"Příklad: Návštěvnost zábavního parku",[1110,9282,9283,9284,9319],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,9285,9287],{"className":9286},[1668],[1670,9288,9289],{"xmlns":1672},[1674,9290,9291,9316],{},[1677,9292,9293,9295,9298,9300,9302,9305,9307,9314],{},[1683,9294,6846],{},[1811,9296,9297],{},"∼",[1683,9299,7000],{},[1811,9301,1994],{"stretchy":1993},[1687,9303,9304],{},"230",[1811,9306,7008],{"separator":1121},[1706,9308,9309,9312],{},[1687,9310,9311],{},"27,5",[1687,9313,1713],{},[1811,9315,2005],{"stretchy":1993},[1691,9317,9318],{"encoding":1693},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,9321,9322],{},[4504,9323],{"alt":9324,"className":9325,"src":9326},"mask-nv-priklad-park",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3814,9328,9330],{"className":3816,"code":9329,"language":71,"meta":1603,"style":1603},"pnorm(180, mean = 230, sd = 27.5)\n",[3590,9331,9332],{"__ignoreMap":1603},[1115,9333,9334,9336,9338,9341,9343,9346,9348,9351,9353,9356,9358,9361],{"class":3822,"line":10},[1115,9335,7027],{"class":3833},[1115,9337,1994],{"class":3837},[1115,9339,9340],{"class":3845},"180",[1115,9342,1917],{"class":3829},[1115,9344,9345],{"class":3825}," mean",[1115,9347,3918],{"class":3829},[1115,9349,9350],{"class":3845}," 230",[1115,9352,1917],{"class":3829},[1115,9354,9355],{"class":3825}," sd",[1115,9357,3918],{"class":3829},[1115,9359,9360],{"class":3845}," 27.5",[1115,9362,4022],{"class":3837},[3814,9364,9367],{"className":9365,"code":9366,"language":4044,"meta":1603},[4042],"[1] 0.03451817\n",[3590,9368,9366],{"__ignoreMap":1603},[1110,9370,9371],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,9373,9375,9382],{"className":9374,"dataCallout":3597},[1106,3596],[1110,9376,9378,9381],{"className":9377},[1113],[1115,9379],{"className":9380,"ariaHidden":1121},[1118,3604,1120],"Příklad: Délka výrobku",[1110,9383,9384,9385,9419],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,9386,9388],{"className":9387},[1668],[1670,9389,9390],{"xmlns":1672},[1674,9391,9392,9416],{},[1677,9393,9394,9396,9398,9400,9402,9405,9407,9414],{},[1683,9395,6846],{},[1811,9397,9297],{},[1683,9399,7000],{},[1811,9401,1994],{"stretchy":1993},[1687,9403,9404],{},"42",[1811,9406,7008],{"separator":1121},[1706,9408,9409,9412],{},[1687,9410,9411],{},"1,2",[1687,9413,1713],{},[1811,9415,2005],{"stretchy":1993},[1691,9417,9418],{"encoding":1693},"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?",[1110,9421,9422],{},[4504,9423],{"alt":9424,"className":9425,"src":9426},"mask-nv-priklad-delka",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3814,9428,9430],{"className":3816,"code":9429,"language":71,"meta":1603,"style":1603},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3590,9431,9432],{"__ignoreMap":1603},[1115,9433,9434,9436,9438,9441,9443,9445,9447,9450,9452,9454,9456,9459,9461,9463,9466,9468,9471,9473,9475,9477,9479,9481,9483,9485,9487],{"class":3822,"line":10},[1115,9435,7027],{"class":3833},[1115,9437,1994],{"class":3837},[1115,9439,9440],{"class":3845},"43",[1115,9442,1917],{"class":3829},[1115,9444,9345],{"class":3825},[1115,9446,3918],{"class":3829},[1115,9448,9449],{"class":3845}," 42",[1115,9451,1917],{"class":3829},[1115,9453,9355],{"class":3825},[1115,9455,3918],{"class":3829},[1115,9457,9458],{"class":3845}," 1.2",[1115,9460,4722],{"class":3837},[1115,9462,4759],{"class":3829},[1115,9464,9465],{"class":3833}," pnorm",[1115,9467,1994],{"class":3837},[1115,9469,9470],{"class":3845},"41",[1115,9472,1917],{"class":3829},[1115,9474,9345],{"class":3825},[1115,9476,3918],{"class":3829},[1115,9478,9449],{"class":3845},[1115,9480,1917],{"class":3829},[1115,9482,9355],{"class":3825},[1115,9484,3918],{"class":3829},[1115,9486,9458],{"class":3845},[1115,9488,4022],{"class":3837},[3814,9490,9493],{"className":9491,"code":9492,"language":4044,"meta":1603},[4042],"[1] 0.5953432\n",[3590,9494,9492],{"__ignoreMap":1603},[1110,9496,9497],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,9499,9501,9508],{"className":9500,"dataCallout":3597},[1106,3596],[1110,9502,9504,9507],{"className":9503},[1113],[1115,9505],{"className":9506,"ariaHidden":1121},[1118,3604,1120],"Příklad: Obsah ampulky",[1110,9509,9510,9511,9534,9535,9561],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,9512,9514],{"className":9513},[1668],[1670,9515,9516],{"xmlns":1672},[1674,9517,9518,9532],{},[1677,9519,9520,9522,9524,9526,9528,9530],{},[1683,9521,7000],{},[1811,9523,1994],{"stretchy":1993},[1687,9525,9147],{},[1811,9527,7008],{"separator":1121},[1687,9529,9152],{},[1811,9531,2005],{"stretchy":1993},[1691,9533,9157],{"encoding":1693},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,9536,9538],{"className":9537},[1668],[1670,9539,9540],{"xmlns":1672},[1674,9541,9542,9558],{},[1677,9543,9544,9546,9548,9552,9555],{},[1683,9545,7013],{},[1811,9547,2101],{},[4574,9549,9550],{},[1687,9551,9152],{},[1811,9553,9554],{},"≈",[1687,9556,9557],{},"0,346",[1691,9559,9560],{"encoding":1693},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,9563,9564],{},[4504,9565],{"alt":9566,"className":9567,"src":9568},"mask-nv-priklad-ampulka",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3814,9570,9572],{"className":3816,"code":9571,"language":71,"meta":1603,"style":1603},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3590,9573,9574],{"__ignoreMap":1603},[1115,9575,9576,9578,9580,9583,9585,9587,9589,9592,9594,9596,9598,9600,9602,9605],{"class":3822,"line":10},[1115,9577,7027],{"class":3833},[1115,9579,1994],{"class":3837},[1115,9581,9582],{"class":3845},"9.8",[1115,9584,1917],{"class":3829},[1115,9586,9345],{"class":3825},[1115,9588,3918],{"class":3829},[1115,9590,9591],{"class":3845}," 10",[1115,9593,1917],{"class":3829},[1115,9595,9355],{"class":3825},[1115,9597,3918],{"class":3829},[1115,9599,4699],{"class":3833},[1115,9601,1994],{"class":3837},[1115,9603,9604],{"class":3845},"0.12",[1115,9606,9607],{"class":3837},"))\n",[3814,9609,9612],{"className":9610,"code":9611,"language":4044,"meta":1603},[4042],"[1] 0.2818514\n",[3590,9613,9611],{"__ignoreMap":1603},[1110,9615,9616],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1153,9618,9620],{"id":9619},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,9622,9623,9624,9627,9628,9631,9632,9635,9636,4725,9639,9642,9643,9646],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3590,9625,9626],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3590,9629,9630],{},"p*"," distribuční funkce (s ",[3590,9633,9634],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3590,9637,9638],{},"TRUE",[3590,9640,9641],{},"FALSE",", pro horní chvost) a ",[3590,9644,9645],{},"q*"," kvantilová funkce.",[1158,9648,9649,9755],{},[1161,9650,9651],{},[1164,9652,9653,9656,9702,9728],{},[1167,9654,9655],{},"Rozdělení",[1167,9657,9658,9682,9683],{},[1115,9659,9661],{"className":9660},[1668],[1670,9662,9663],{"xmlns":1672},[1674,9664,9665,9679],{},[1677,9666,9667,9669,9671,9673,9675,9677],{},[1683,9668,6841],{},[1811,9670,1994],{"stretchy":1993},[1683,9672,6846],{},[1811,9674,2101],{},[1683,9676,7374],{},[1811,9678,2005],{"stretchy":1993},[1691,9680,9681],{"encoding":1693},"P(X=k)"," \u002F ",[1115,9684,9686],{"className":9685},[1668],[1670,9687,9688],{"xmlns":1672},[1674,9689,9690,9700],{},[1677,9691,9692,9694,9696,9698],{},[1683,9693,6885],{},[1811,9695,1994],{"stretchy":1993},[1683,9697,6834],{},[1811,9699,2005],{"stretchy":1993},[1691,9701,6915],{"encoding":1693},[1167,9703,9704],{},[1115,9705,9707],{"className":9706},[1668],[1670,9708,9709],{"xmlns":1672},[1674,9710,9711,9725],{},[1677,9712,9713,9715,9717,9719,9721,9723],{},[1683,9714,6841],{},[1811,9716,1994],{"stretchy":1993},[1683,9718,6846],{},[1811,9720,6849],{},[1683,9722,7374],{},[1811,9724,2005],{"stretchy":1993},[1691,9726,9727],{"encoding":1693},"P(X \\le k)",[1167,9729,9730,9731],{},"horní chvost ",[1115,9732,9734],{"className":9733},[1668],[1670,9735,9736],{"xmlns":1672},[1674,9737,9738,9752],{},[1677,9739,9740,9742,9744,9746,9748,9750],{},[1683,9741,6841],{},[1811,9743,1994],{"stretchy":1993},[1683,9745,6846],{},[1811,9747,1813],{},[1683,9749,7374],{},[1811,9751,2005],{"stretchy":1993},[1691,9753,9754],{"encoding":1693},"P(X>k)",[1174,9756,9757,9803,9847,9888,9937],{},[1164,9758,9759,9788,9793,9798],{},[1179,9760,9761,9762],{},"Binomické ",[1115,9763,9765],{"className":9764},[1668],[1670,9766,9767],{"xmlns":1672},[1674,9768,9769,9785],{},[1677,9770,9771,9773,9775,9777,9779,9781,9783],{},[1683,9772,1371],{},[1683,9774,1997],{},[1811,9776,1994],{"stretchy":1993},[1683,9778,1809],{},[1811,9780,1917],{"separator":1121},[1683,9782,1110],{},[1811,9784,2005],{"stretchy":1993},[1691,9786,9787],{"encoding":1693},"Bi(n,p)",[1179,9789,9790],{},[3590,9791,9792],{},"dbinom(k, n, p)",[1179,9794,9795],{},[3590,9796,9797],{},"pbinom(k, n, p)",[1179,9799,9800],{},[3590,9801,9802],{},"pbinom(k, n, p, FALSE)",[1164,9804,9805,9832,9837,9842],{},[1179,9806,9807,9808],{},"Poissonovo ",[1115,9809,9811],{"className":9810},[1668],[1670,9812,9813],{"xmlns":1672},[1674,9814,9815,9829],{},[1677,9816,9817,9819,9822,9824,9827],{},[1683,9818,6841],{},[1683,9820,9821],{},"o",[1811,9823,1994],{"stretchy":1993},[1683,9825,9826],{},"λ",[1811,9828,2005],{"stretchy":1993},[1691,9830,9831],{"encoding":1693},"Po(\\lambda)",[1179,9833,9834],{},[3590,9835,9836],{},"dpois(k, lambda)",[1179,9838,9839],{},[3590,9840,9841],{},"ppois(k, lambda)",[1179,9843,9844],{},[3590,9845,9846],{},"ppois(k, lambda, FALSE)",[1164,9848,9849,9873,9878,9883],{},[1179,9850,9851,9852],{},"Geometrické ",[1115,9853,9855],{"className":9854},[1668],[1670,9856,9857],{"xmlns":1672},[1674,9858,9859,9870],{},[1677,9860,9861,9864,9866,9868],{},[1683,9862,9863],{},"G",[1811,9865,1994],{"stretchy":1993},[1683,9867,1110],{},[1811,9869,2005],{"stretchy":1993},[1691,9871,9872],{"encoding":1693},"G(p)",[1179,9874,9875],{},[3590,9876,9877],{},"dgeom(k, p)",[1179,9879,9880],{},[3590,9881,9882],{},"pgeom(k, p)",[1179,9884,9885],{},[3590,9886,9887],{},"pgeom(k, p, FALSE)",[1164,9889,9890,9922,9927,9932],{},[1179,9891,9892,9893],{},"Hypergeometrické ",[1115,9894,9896],{"className":9895},[1668],[1670,9897,9898],{"xmlns":1672},[1674,9899,9900,9919],{},[1677,9901,9902,9904,9906,9908,9910,9913,9915,9917],{},[1683,9903,1685],{},[1811,9905,1994],{"stretchy":1993},[1683,9907,7000],{},[1811,9909,1917],{"separator":1121},[1683,9911,9912],{},"M",[1811,9914,1917],{"separator":1121},[1683,9916,1809],{},[1811,9918,2005],{"stretchy":1993},[1691,9920,9921],{"encoding":1693},"H(N,M,n)",[1179,9923,9924],{},[3590,9925,9926],{},"dhyper(k, M, N-M, n)",[1179,9928,9929],{},[3590,9930,9931],{},"phyper(k, M, N-M, n)",[1179,9933,9934],{},[3590,9935,9936],{},"phyper(k, M, N-M, n, FALSE)",[1164,9938,9939,9963,9968,9973],{},[1179,9940,9941,9942],{},"Exponenciální ",[1115,9943,9945],{"className":9944},[1668],[1670,9946,9947],{"xmlns":1672},[1674,9948,9949,9960],{},[1677,9950,9951,9953,9955,9958],{},[1683,9952,1395],{},[1811,9954,1994],{"stretchy":1993},[1683,9956,9957],{},"δ",[1811,9959,2005],{"stretchy":1993},[1691,9961,9962],{"encoding":1693},"E(\\delta)",[1179,9964,9965],{},[3590,9966,9967],{},"dexp(k, 1\u002Fdelta)",[1179,9969,9970],{},[3590,9971,9972],{},"pexp(k, 1\u002Fdelta)",[1179,9974,9975],{},[3590,9976,9977],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,9979,9981,9988],{"className":9980,"dataCallout":6534},[1106,6533],[1110,9982,9984,9987],{"className":9983},[1113],[1115,9985],{"className":9986,"ariaHidden":1121},[1118,6541,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,9989,9990,9991,9994,9995,10009,10010,9162,10013,1497],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3590,9992,9993],{},"rate","). Je-li ",[1115,9996,9998],{"className":9997},[1668],[1670,9999,10000],{"xmlns":1672},[1674,10001,10002,10006],{},[1677,10003,10004],{},[1683,10005,9957],{},[1691,10007,10008],{"encoding":1693},"\\delta"," střední doba do události, do R se dosazuje ",[3590,10011,10012],{},"1\u002Fdelta",[3590,10014,10015],{},"delta",[1110,10017,10018,10019,10051,10052,10070],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,10020,10022],{"className":10021},[1668],[1670,10023,10024],{"xmlns":1672},[1674,10025,10026,10048],{},[1677,10027,10028,10030,10032,10034,10036,10038,10041,10043,10046],{},[1683,10029,6846],{},[1811,10031,9297],{},[1683,10033,1371],{},[1683,10035,1997],{},[1811,10037,1994],{"stretchy":1993},[1687,10039,10040],{},"5",[1811,10042,7008],{"separator":1121},[1687,10044,10045],{},"0,95",[1811,10047,2005],{"stretchy":1993},[1691,10049,10050],{"encoding":1693},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,10053,10055],{"className":10054},[1668],[1670,10056,10057],{"xmlns":1672},[1674,10058,10059,10067],{},[1677,10060,10061,10063,10065],{},[1683,10062,9957],{},[1811,10064,2101],{},[1687,10066,10040],{},[1691,10068,10069],{"encoding":1693},"\\delta = 5"," nastane událost do 3 jednotek času):",[3814,10072,10074],{"className":3816,"code":10073,"language":71,"meta":1603,"style":1603},"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",[3590,10075,10076,10090,10122,10151,10156,10165],{"__ignoreMap":1603},[1115,10077,10078,10080,10082,10085,10087],{"class":3822,"line":10},[1115,10079,6834],{"class":3825},[1115,10081,3830],{"class":3829},[1115,10083,10084],{"class":3845}," 0",[1115,10086,2077],{"class":3829},[1115,10088,10089],{"class":3845},"5\n",[1115,10091,10092,10095,10097,10100,10102,10104,10106,10109,10111,10114,10116,10118,10120],{"class":3822,"line":27},[1115,10093,10094],{"class":3833},"round",[1115,10096,1994],{"class":3837},[1115,10098,10099],{"class":3833},"dbinom",[1115,10101,1994],{"class":3837},[1115,10103,6834],{"class":3825},[1115,10105,1917],{"class":3829},[1115,10107,10108],{"class":3845}," 5",[1115,10110,1917],{"class":3829},[1115,10112,10113],{"class":3845}," 0.95",[1115,10115,2005],{"class":3837},[1115,10117,1917],{"class":3829},[1115,10119,3921],{"class":3845},[1115,10121,4022],{"class":3837},[1115,10123,10124,10126,10128,10131,10133,10135,10137,10139,10141,10143,10145,10147,10149],{"class":3822,"line":148},[1115,10125,10094],{"class":3833},[1115,10127,1994],{"class":3837},[1115,10129,10130],{"class":3833},"pbinom",[1115,10132,1994],{"class":3837},[1115,10134,6834],{"class":3825},[1115,10136,1917],{"class":3829},[1115,10138,10108],{"class":3845},[1115,10140,1917],{"class":3829},[1115,10142,10113],{"class":3845},[1115,10144,2005],{"class":3837},[1115,10146,1917],{"class":3829},[1115,10148,3921],{"class":3845},[1115,10150,4022],{"class":3837},[1115,10152,10153],{"class":3822,"line":111},[1115,10154,10155],{"emptyLinePlaceholder":1618},"\n",[1115,10157,10158,10160,10162],{"class":3822,"line":96},[1115,10159,10015],{"class":3825},[1115,10161,3830],{"class":3829},[1115,10163,10164],{"class":3845}," 5\n",[1115,10166,10167,10169,10171,10174,10176,10178,10180,10183,10185,10187,10190,10193,10195,10197,10199],{"class":3822,"line":89},[1115,10168,10094],{"class":3833},[1115,10170,1994],{"class":3837},[1115,10172,10173],{"class":3833},"pexp",[1115,10175,1994],{"class":3837},[1115,10177,3712],{"class":3845},[1115,10179,1917],{"class":3829},[1115,10181,10182],{"class":3825}," rate",[1115,10184,3918],{"class":3829},[1115,10186,4762],{"class":3845},[1115,10188,10189],{"class":3829}," \u002F",[1115,10191,10192],{"class":3825}," delta",[1115,10194,2005],{"class":3837},[1115,10196,1917],{"class":3829},[1115,10198,3921],{"class":3845},[1115,10200,4022],{"class":3837},[3814,10202,10205],{"className":10203,"code":10204,"language":4044,"meta":1603},[4042],"[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",[3590,10206,10204],{"__ignoreMap":1603},[1153,10208,10210],{"id":10209},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,10212,10213,10214,10217],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1127,10215,141],{"className":10216,"dataFsResolvedFilePath":1300,"href":1298},[1131],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,10219,10220,4073,10223,10236],{},[1136,10221,10222],{},"Studentovo rozdělení",[1115,10224,10226],{"className":10225},[1668],[1670,10227,10228],{"xmlns":1672},[1674,10229,10230,10234],{},[1677,10231,10232],{},[1683,10233,7374],{},[1691,10235,7374],{"encoding":1693}," stupni volnosti má hustotu pravděpodobnosti",[1115,10238,10240],{"className":10239},[1668],[1670,10241,10242],{"xmlns":1672,"display":2083},[1674,10243,10244,10340],{},[1677,10245,10246,10248,10250,10252,10254,10256,10288,10326,10328,10330,10332,10334,10338],{},[1683,10247,6885],{},[1811,10249,1994],{"stretchy":1993},[1683,10251,6834],{},[1811,10253,2005],{"stretchy":1993},[1811,10255,2101],{},[2859,10257,10258,10260],{},[1687,10259,1914],{},[1677,10261,10262,10264,10284],{},[1683,10263,1371],{},[1677,10265,10266,10268,10274,10276,10282],{},[1811,10267,1994],{"fence":1121},[2859,10269,10270,10272],{},[1687,10271,1914],{},[1687,10273,1713],{},[1811,10275,1917],{"separator":1121},[2859,10277,10278,10280],{},[1683,10279,7374],{},[1687,10281,1713],{},[1811,10283,2005],{"fence":1121},[4574,10285,10286],{},[1683,10287,7374],{},[1706,10289,10290,10310],{},[1677,10291,10292,10294,10296,10298,10308],{},[1811,10293,1994],{"fence":1121},[1687,10295,1914],{},[1811,10297,5598],{},[2859,10299,10300,10306],{},[1706,10301,10302,10304],{},[1683,10303,6834],{},[1687,10305,1713],{},[1683,10307,7374],{},[1811,10309,2005],{"fence":1121},[1677,10311,10312,10314],{},[1811,10313,3184],{},[2859,10315,10316,10324],{},[1677,10317,10318,10320,10322],{},[1683,10319,7374],{},[1811,10321,5598],{},[1687,10323,1914],{},[1687,10325,1713],{},[1811,10327,1917],{"separator":1121},[2131,10329],{"width":2133},[1683,10331,6834],{},[1811,10333,7133],{},[1683,10335,10337],{"mathvariant":10336},"double-struck","R",[1811,10339,1917],{"separator":1121},[1691,10341,10342],{"encoding":1693},"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},",[1110,10344,4628,10345,10358,10359,10372,10373,10386],{},[1115,10346,10348],{"className":10347},[1668],[1670,10349,10350],{"xmlns":1672},[1674,10351,10352,10356],{},[1677,10353,10354],{},[1683,10355,1371],{},[1691,10357,1371],{"encoding":1693}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,10360,10362],{"className":10361},[1668],[1670,10363,10364],{"xmlns":1672},[1674,10365,10366,10370],{},[1677,10367,10368],{},[1683,10369,7374],{},[1691,10371,7374],{"encoding":1693}," určuje tvar křivky — s rostoucím ",[1115,10374,10376],{"className":10375},[1668],[1670,10377,10378],{"xmlns":1672},[1674,10379,10380,10384],{},[1677,10381,10382],{},[1683,10383,7374],{},[1691,10385,7374],{"encoding":1693}," se rozdělení blíží normálnímu.",[1110,10388,10389,4073,10392,10405],{},[1136,10390,10391],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,10393,10395],{"className":10394},[1668],[1670,10396,10397],{"xmlns":1672},[1674,10398,10399,10403],{},[1677,10400,10401],{},[1683,10402,7374],{},[1691,10404,7374],{"encoding":1693}," stupni volnosti:",[1115,10407,10409],{"className":10408},[1668],[1670,10410,10411],{"xmlns":1672,"display":2083},[1674,10412,10413,10498],{},[1677,10414,10415,10417,10419,10421,10423,10425,10456,10472,10486,10488,10490,10492,10494,10496],{},[1683,10416,6885],{},[1811,10418,1994],{"stretchy":1993},[1683,10420,6834],{},[1811,10422,2005],{"stretchy":1993},[1811,10424,2101],{},[2859,10426,10427,10429],{},[1687,10428,1914],{},[1677,10430,10431,10443,10446,10448,10450,10452,10454],{},[1706,10432,10433,10435],{},[1687,10434,1713],{},[1677,10436,10437,10439,10441],{},[1683,10438,7374],{},[1683,10440,4725],{"mathvariant":2240},[1687,10442,1713],{},[1683,10444,10445],{"mathvariant":2240},"Γ",[1811,10447,1994],{"stretchy":1993},[1683,10449,7374],{},[1683,10451,4725],{"mathvariant":2240},[1687,10453,1713],{},[1811,10455,2005],{"stretchy":1993},[1706,10457,10458,10460],{},[1683,10459,6834],{},[1677,10461,10462,10464,10466,10468,10470],{},[1683,10463,7374],{},[1683,10465,4725],{"mathvariant":2240},[1687,10467,1713],{},[1811,10469,3184],{},[1687,10471,1914],{},[1706,10473,10474,10476],{},[1683,10475,8706],{},[1677,10477,10478,10480,10482,10484],{},[1811,10479,3184],{},[1683,10481,6834],{},[1683,10483,4725],{"mathvariant":2240},[1687,10485,1713],{},[1811,10487,1917],{"separator":1121},[2131,10489],{"width":2133},[1683,10491,6834],{},[1811,10493,1813],{},[1687,10495,1689],{},[1811,10497,1917],{"separator":1121},[1691,10499,10500],{"encoding":1693},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,10502,4628,10503,10517],{},[1115,10504,10506],{"className":10505},[1668],[1670,10507,10508],{"xmlns":1672},[1674,10509,10510,10514],{},[1677,10511,10512],{},[1683,10513,10445],{"mathvariant":2240},[1691,10515,10516],{"encoding":1693},"\\Gamma"," je funkce gama.",[1110,10519,10520,10523,10524,5862,10542,2077],{},[1136,10521,10522],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,10525,10527],{"className":10526},[1668],[1670,10528,10529],{"xmlns":1672},[1674,10530,10531,10539],{},[1677,10532,10533],{},[1680,10534,10535,10537],{},[1683,10536,7374],{},[1687,10538,1914],{},[1691,10540,10541],{"encoding":1693},"k_1",[1115,10543,10545],{"className":10544},[1668],[1670,10546,10547],{"xmlns":1672},[1674,10548,10549,10557],{},[1677,10550,10551],{},[1680,10552,10553,10555],{},[1683,10554,7374],{},[1687,10556,1713],{},[1691,10558,10559],{"encoding":1693},"k_2",[1115,10561,10563],{"className":10562},[1668],[1670,10564,10565],{"xmlns":1672,"display":2083},[1674,10566,10567,10732],{},[1677,10568,10569,10571,10573,10575,10577,10579,10615,10649,10669,10721,10723,10725,10727,10729],{},[1683,10570,6885],{},[1811,10572,1994],{"stretchy":1993},[1683,10574,6834],{},[1811,10576,2005],{"stretchy":1993},[1811,10578,2101],{},[2859,10580,10581,10583],{},[1687,10582,1914],{},[1677,10584,10585,10587],{},[1683,10586,1371],{},[1677,10588,10589,10591,10601,10603,10613],{},[1811,10590,1994],{"fence":1121},[2859,10592,10593,10599],{},[1680,10594,10595,10597],{},[1683,10596,7374],{},[1687,10598,1914],{},[1687,10600,1713],{},[1811,10602,1917],{"separator":1121},[2859,10604,10605,10611],{},[1680,10606,10607,10609],{},[1683,10608,7374],{},[1687,10610,1713],{},[1687,10612,1713],{},[1811,10614,2005],{"fence":1121},[1706,10616,10617,10637],{},[1677,10618,10619,10621,10635],{},[1811,10620,1994],{"fence":1121},[2859,10622,10623,10629],{},[1680,10624,10625,10627],{},[1683,10626,7374],{},[1687,10628,1914],{},[1680,10630,10631,10633],{},[1683,10632,7374],{},[1687,10634,1713],{},[1811,10636,2005],{"fence":1121},[1677,10638,10639,10645,10647],{},[1680,10640,10641,10643],{},[1683,10642,7374],{},[1687,10644,1914],{},[1683,10646,4725],{"mathvariant":2240},[1687,10648,1713],{},[1706,10650,10651,10653],{},[1683,10652,6834],{},[1677,10654,10655,10661,10663,10665,10667],{},[1680,10656,10657,10659],{},[1683,10658,7374],{},[1687,10660,1914],{},[1683,10662,4725],{"mathvariant":2240},[1687,10664,1713],{},[1811,10666,3184],{},[1687,10668,1914],{},[1706,10670,10671,10697],{},[1677,10672,10673,10675,10677,10679,10693,10695],{},[1811,10674,1994],{"fence":1121},[1687,10676,1914],{},[1811,10678,5598],{},[2859,10680,10681,10687],{},[1680,10682,10683,10685],{},[1683,10684,7374],{},[1687,10686,1914],{},[1680,10688,10689,10691],{},[1683,10690,7374],{},[1687,10692,1713],{},[1683,10694,6834],{},[1811,10696,2005],{"fence":1121},[1677,10698,10699,10701],{},[1811,10700,3184],{},[2859,10702,10703,10719],{},[1677,10704,10705,10711,10713],{},[1680,10706,10707,10709],{},[1683,10708,7374],{},[1687,10710,1914],{},[1811,10712,5598],{},[1680,10714,10715,10717],{},[1683,10716,7374],{},[1687,10718,1713],{},[1687,10720,1713],{},[1811,10722,1917],{"separator":1121},[2131,10724],{"width":2133},[1683,10726,6834],{},[1811,10728,1813],{},[1687,10730,10731],{},"0.",[1691,10733,10734],{"encoding":1693},"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.",[1110,10736,10737],{},[4504,10738],{"alt":10739,"className":10740,"src":10741},"mask-nv-specialni-rozdeleni",[1131,4508],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[9060,10743],{"spec":10744},"{\"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\":[]}",[1110,10746,10747],{},"R funkce pro tato tři rozdělení:",[1158,10749,10750,10764],{},[1161,10751,10752],{},[1164,10753,10754,10756,10759,10761],{},[1167,10755,9655],{},[1167,10757,10758],{},"hustota",[1167,10760,6818],{},[1167,10762,10763],{},"kvantil",[1174,10765,10766,10806,10850],{},[1164,10767,10768,10791,10796,10801],{},[1179,10769,10770,10771],{},"Studentovo ",[1115,10772,10774],{"className":10773},[1668],[1670,10775,10776],{"xmlns":1672},[1674,10777,10778,10788],{},[1677,10779,10780,10782,10784,10786],{},[1683,10781,7258],{},[1811,10783,1994],{"stretchy":1993},[1683,10785,7374],{},[1811,10787,2005],{"stretchy":1993},[1691,10789,10790],{"encoding":1693},"t(k)",[1179,10792,10793],{},[3590,10794,10795],{},"dt(x, df = k)",[1179,10797,10798],{},[3590,10799,10800],{},"pt(x, df = k)",[1179,10802,10803],{},[3590,10804,10805],{},"qt(p, df = k)",[1164,10807,10808,10835,10840,10845],{},[1179,10809,10810,10811],{},"Pearsonovo ",[1115,10812,10814],{"className":10813},[1668],[1670,10815,10816],{"xmlns":1672},[1674,10817,10818,10832],{},[1677,10819,10820,10826,10828,10830],{},[1706,10821,10822,10824],{},[1683,10823,1710],{},[1687,10825,1713],{},[1811,10827,1994],{"stretchy":1993},[1683,10829,7374],{},[1811,10831,2005],{"stretchy":1993},[1691,10833,10834],{"encoding":1693},"\\chi^2(k)",[1179,10836,10837],{},[3590,10838,10839],{},"dchisq(x, df = k)",[1179,10841,10842],{},[3590,10843,10844],{},"pchisq(x, df = k)",[1179,10846,10847],{},[3590,10848,10849],{},"qchisq(p, df = k)",[1164,10851,10852,10887,10892,10897],{},[1179,10853,10854,10855],{},"Fisherovo-Snedecorovo ",[1115,10856,10858],{"className":10857},[1668],[1670,10859,10860],{"xmlns":1672},[1674,10861,10862,10884],{},[1677,10863,10864,10866,10868,10874,10876,10882],{},[1683,10865,1403],{},[1811,10867,1994],{"stretchy":1993},[1680,10869,10870,10872],{},[1683,10871,7374],{},[1687,10873,1914],{},[1811,10875,1917],{"separator":1121},[1680,10877,10878,10880],{},[1683,10879,7374],{},[1687,10881,1713],{},[1811,10883,2005],{"stretchy":1993},[1691,10885,10886],{"encoding":1693},"F(k_1, k_2)",[1179,10888,10889],{},[3590,10890,10891],{},"df(x, df1 = k1, df2 = k2)",[1179,10893,10894],{},[3590,10895,10896],{},"pf(x, df1 = k1, df2 = k2)",[1179,10898,10899],{},[3590,10900,10901],{},"qf(p, df1 = k1, df2 = k2)",[1110,10903,10904],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3814,10906,10908],{"className":3816,"code":10907,"language":71,"meta":1603,"style":1603},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3590,10909,10910,10931,10951],{"__ignoreMap":1603},[1115,10911,10912,10915,10917,10919,10921,10924,10926,10929],{"class":3822,"line":10},[1115,10913,10914],{"class":3833},"qt",[1115,10916,1994],{"class":3837},[1115,10918,9203],{"class":3845},[1115,10920,1917],{"class":3829},[1115,10922,10923],{"class":3825}," df",[1115,10925,3918],{"class":3829},[1115,10927,10928],{"class":3845}," 9",[1115,10930,4022],{"class":3837},[1115,10932,10933,10936,10938,10941,10943,10945,10947,10949],{"class":3822,"line":27},[1115,10934,10935],{"class":3833},"qchisq",[1115,10937,1994],{"class":3837},[1115,10939,10940],{"class":3845},"0.95",[1115,10942,1917],{"class":3829},[1115,10944,10923],{"class":3825},[1115,10946,3918],{"class":3829},[1115,10948,10928],{"class":3845},[1115,10950,4022],{"class":3837},[1115,10952,10953,10956,10958,10960,10962,10965,10967,10970,10972,10975,10977,10979],{"class":3822,"line":148},[1115,10954,10955],{"class":3833},"qf",[1115,10957,1994],{"class":3837},[1115,10959,10940],{"class":3845},[1115,10961,1917],{"class":3829},[1115,10963,10964],{"class":3825}," df1",[1115,10966,3918],{"class":3829},[1115,10968,10969],{"class":3845}," 3",[1115,10971,1917],{"class":3829},[1115,10973,10974],{"class":3825}," df2",[1115,10976,3918],{"class":3829},[1115,10978,9591],{"class":3845},[1115,10980,4022],{"class":3837},[3814,10982,10985],{"className":10983,"code":10984,"language":4044,"meta":1603},[4042],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3590,10986,10984],{"__ignoreMap":1603},[1153,10988,6529],{"id":6528},[1503,10990,10991,11077,11127],{},[1265,10992,10993,10996,10997,11024,11025,4725,11027,4725,11029,11031,11032,11052,11053,11076],{},[1136,10994,10995],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,10998,11000],{"className":10999},[1668],[1670,11001,11002],{"xmlns":1672},[1674,11003,11004,11022],{},[1677,11005,11006,11008,11010,11012,11014,11020],{},[1683,11007,7000],{},[1811,11009,1994],{"stretchy":1993},[1683,11011,7005],{},[1811,11013,7008],{"separator":1121},[1706,11015,11016,11018],{},[1683,11017,7013],{},[1687,11019,1713],{},[1811,11021,2005],{"stretchy":1993},[1691,11023,7020],{"encoding":1693}," používá rozptyl, ale ",[3590,11026,7024],{},[3590,11028,7027],{},[3590,11030,7030],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,11033,11035],{"className":11034},[1668],[1670,11036,11037],{"xmlns":1672},[1674,11038,11039,11049],{},[1677,11040,11041],{},[4574,11042,11043],{},[1706,11044,11045,11047],{},[1683,11046,7013],{},[1687,11048,1713],{},[1691,11050,11051],{"encoding":1693},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,11054,11056],{"className":11055},[1668],[1670,11057,11058],{"xmlns":1672},[1674,11059,11060,11073],{},[1677,11061,11062,11068,11071],{},[1706,11063,11064,11066],{},[1683,11065,7013],{},[1687,11067,1713],{},[1811,11069,11070],{"mathvariant":2240},"≠",[1687,11072,1914],{},[1691,11074,11075],{"encoding":1693},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1265,11078,11079,11106,11107,11126],{},[1136,11080,11081,11105],{},[1115,11082,11084],{"className":11083},[1668],[1670,11085,11086],{"xmlns":1672},[1674,11087,11088,11102],{},[1677,11089,11090,11092,11094,11096,11098,11100],{},[1683,11091,6841],{},[1811,11093,1994],{"stretchy":1993},[1683,11095,6846],{},[1811,11097,2101],{},[1683,11099,6834],{},[1811,11101,2005],{"stretchy":1993},[1691,11103,11104],{"encoding":1693},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,11108,11110],{"className":11109},[1668],[1670,11111,11112],{"xmlns":1672},[1674,11113,11114,11124],{},[1677,11115,11116,11118,11120,11122],{},[1683,11117,6885],{},[1811,11119,1994],{"stretchy":1993},[1683,11121,6834],{},[1811,11123,2005],{"stretchy":1993},[1691,11125,6915],{"encoding":1693}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1265,11128,11129,1418,11132,11149,11150,11167,11168,11171,11172,1497],{},[1136,11130,11131],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,11133,11135],{"className":11134},[1668],[1670,11136,11137],{"xmlns":1672},[1674,11138,11139,11147],{},[1677,11140,11141],{},[1680,11142,11143,11145],{},[1683,11144,7374],{},[1687,11146,1914],{},[1691,11148,10541],{"encoding":1693}," (čitatel) a ",[1115,11151,11153],{"className":11152},[1668],[1670,11154,11155],{"xmlns":1672},[1674,11156,11157,11165],{},[1677,11158,11159],{},[1680,11160,11161,11163],{},[1683,11162,7374],{},[1687,11164,1713],{},[1691,11166,10559],{"encoding":1693}," (jmenovatel) nejsou zaměnitelné — ",[3590,11169,11170],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3590,11173,11174],{},"qf(p, df2, df1)",[1153,11176,1501],{"id":1500},[1503,11178,11179,11184,11189,11194,11200,11205,11211],{},[1265,11180,11181],{},[1127,11182,1133],{"className":11183,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,11185,11186],{},[1127,11187,886],{"className":11188,"dataFsResolvedFilePath":1288,"href":1286},[1131],[1265,11190,11191],{},[1127,11192,141],{"className":11193,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1265,11195,11196],{},[1127,11197,11199],{"className":11198,"dataFsResolvedFilePath":1312,"href":1310},[1131],"regresni-a-korelacni-analyza",[1265,11201,11202],{},[1127,11203,716],{"className":11204,"dataFsResolvedFilePath":1324,"href":1322},[1131],[1265,11206,11207],{},[1127,11208,11210],{"className":11209,"dataFsResolvedFilePath":1336,"href":1334},[1131],"regulacni-diagramy-a-indexy-zpusobilosti",[1265,11212,11213],{},[1127,11214,6753],{"className":11215,"dataFsResolvedFilePath":1550,"href":1548},[1131],[1153,11217,1554],{"id":934},[1110,11219,1557,11220,1561],{},[1420,11221,1560],{},[6761,11223,11224],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: 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.sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1603,"searchDepth":27,"depth":27,"links":11226},[11227,11228,11229,11230,11231,11232,11233,11234,11235,11236],{"id":7079,"depth":27,"text":7080},{"id":7387,"depth":27,"text":7388},{"id":8073,"depth":27,"text":8074},{"id":8182,"depth":27,"text":8183},{"id":8617,"depth":27,"text":6988},{"id":9619,"depth":27,"text":9620},{"id":10209,"depth":27,"text":10210},{"id":6528,"depth":27,"text":6529},{"id":1500,"depth":27,"text":1501},{"id":934,"depth":27,"text":1554},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":1515,"description":1603},[11241,11242,11243],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002F01 náhodné veličiny - návod R.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":11248,"title":1521,"body":11249,"course":23,"courses":1614,"created":1615,"description":1603,"extension":1616,"meta":16000,"navigation":1618,"path":16001,"seo":16002,"sources":16003,"stem":16010,"tags":16011,"type":6782,"updated":1615,"__hash__":16012},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":11250,"toc":15991},[11251,11254,11348,11352,11362,11488,11495,11506,11510,11553,11558,11660,11670,11675,11814,11890,11894,11995,12076,12083,12154,12173,12175,12391,12397,12407,12414,12417,12471,12477,12487,12500,12646,12649,12662,12981,12987,12990,12994,13073,13107,13136,13138,13216,13222,13283,13290,13303,13380,13496,13546,13559,13714,13720,13747,13751,13776,13779,13992,14060,14161,14168,14181,14684,14690,14722,14982,15135,15246,15275,15281,15288,15294,15307,15737,15743,15746,15748,15943,15945,15982,15984,15988],[1099,11252,1521],{"id":11253},"popisná-statistika-a-datové-soubory",[1103,11255,11257,11263],{"className":11256,"dataCallout":1641},[1106,1640],[1110,11258,11260,1649],{"className":11259},[1113],[1115,11261],{"className":11262,"ariaHidden":1121},[1118,1648,1120],[1503,11264,11265,11268,11271,11298,11345],{},[1265,11266,11267],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1265,11269,11270],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1265,11272,11273,11274,1497],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,11275,11277],{"className":11276},[1668],[1670,11278,11279],{"xmlns":1672},[1674,11280,11281,11295],{},[1677,11282,11283,11289,11291,11293],{},[1680,11284,11285,11287],{},[1683,11286,1403],{},[1683,11288,1809],{},[1811,11290,1994],{"stretchy":1993},[1683,11292,6834],{},[1811,11294,2005],{"stretchy":1993},[1691,11296,11297],{"encoding":1693},"F_n(x)",[1265,11299,11300,11301,11344],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,11302,11304],{"className":11303},[1668],[1670,11305,11306],{"xmlns":1672},[1674,11307,11308,11341],{},[1677,11309,11310,11317,11319,11325,11327,11333,11335],{},[1680,11311,11312,11315],{},[1683,11313,11314],{},"I",[1683,11316,2002],{},[1811,11318,1917],{"separator":1121},[1680,11320,11321,11323],{},[1683,11322,9039],{},[1683,11324,2002],{},[1811,11326,1917],{"separator":1121},[1680,11328,11329,11331],{},[1683,11330,6885],{},[1683,11332,2002],{},[1811,11334,1917],{"separator":1121},[1680,11336,11337,11339],{},[1683,11338,1110],{},[1683,11340,2002],{},[1691,11342,11343],{"encoding":1693},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1265,11346,11347],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1153,11349,11351],{"id":11350},"základní-pojmy","Základní pojmy",[1110,11353,11354,11357,11358,11361],{},[1127,11355,1133],{"className":11356,"dataFsResolvedFilePath":1132,"href":1129},[1131]," pracuje s ",[1136,11359,11360],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1503,11363,11364,11370,11394,11400,11475],{},[1265,11365,11366,11369],{},[1136,11367,11368],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1265,11371,11372,11375,11376],{},[1136,11373,11374],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1503,11377,11378,11389],{},[1265,11379,11380,11382,11383,11385,11386,11388],{},[1136,11381,1855],{}," (vyjádřitelné číslem) — dále ",[1136,11384,6807],{}," (spočetně mnoho hodnot) nebo ",[1136,11387,6811],{}," (libovolná hodnota v intervalu);",[1265,11390,11391,11393],{},[1136,11392,1848],{}," (vyjádřitelné slovně).",[1265,11395,11396,11399],{},[1136,11397,11398],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1265,11401,11402,11405,11406,1497],{},[1136,11403,11404],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,11407,11409],{"className":11408},[1668],[1670,11410,11411],{"xmlns":1672},[1674,11412,11413,11472],{},[1677,11414,11415,11417,11419,11421,11424,11426,11429,11432,11434,11437,11439,11441,11444,11446,11449,11451,11453,11455,11457,11459,11461,11463,11465,11467,11470],{},[1811,11416,1994],{"stretchy":1993},[1687,11418,3670],{},[3028,11420,3030],{},[1687,11422,11423],{},"500",[1811,11425,1917],{"separator":1121},[3028,11427,11428],{}," ",[1687,11430,11431],{},"38",[3028,11433,3030],{},[1687,11435,11436],{},"000",[1811,11438,1917],{"separator":1121},[3028,11440,11428],{},[1687,11442,11443],{},"37",[3028,11445,3030],{},[1687,11447,11448],{},"800",[1811,11450,1917],{"separator":1121},[3028,11452,11428],{},[1687,11454,9470],{},[3028,11456,3030],{},[1687,11458,11436],{},[1811,11460,1917],{"separator":1121},[3028,11462,11428],{},[1687,11464,3678],{},[3028,11466,3030],{},[1687,11468,11469],{},"200",[1811,11471,2005],{"stretchy":1993},[1691,11473,11474],{"encoding":1693},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1265,11476,11477,11478,3071,11481,5862,11484,11487],{},"Podle počtu sledovaných znaků rozlišujeme ",[1136,11479,11480],{},"jednorozměrné",[1136,11482,11483],{},"dvourozměrné",[1136,11485,11486],{},"vícerozměrné"," datové soubory.",[1110,11489,11490],{},[4504,11491],{"alt":11492,"className":11493,"src":11494},"mask-ilu-zakladni-soubor-vyber",[1131,4508],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,11496,11497,11498,11501,11502,11505],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1136,11499,11500],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1136,11503,11504],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1153,11507,11509],{"id":11508},"empirické-charakteristiky","Empirické charakteristiky",[1110,11511,11512,11513,11516,11517,11520,11521,11534,11535,11538,11539,11552],{},"Zpracováním datového souboru získáme ",[1136,11514,11515],{},"empirické charakteristiky"," a odhad ",[1136,11518,11519],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,11522,11524],{"className":11523},[1668],[1670,11525,11526],{"xmlns":1672},[1674,11527,11528,11532],{},[1677,11529,11530],{},[1683,11531,6846],{},[1691,11533,6846],{"encoding":1693},". Jde o ",[1136,11536,11537],{},"bodové odhady"," charakteristik ",[1115,11540,11542],{"className":11541},[1668],[1670,11543,11544],{"xmlns":1672},[1674,11545,11546,11550],{},[1677,11547,11548],{},[1683,11549,6846],{},[1691,11551,6846],{"encoding":1693},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,11554,11555],{},[1136,11556,11557],{},"Míry polohy",[1115,11559,11561],{"className":11560},[1668],[1670,11562,11563],{"xmlns":1672,"display":2083},[1674,11564,11565,11657],{},[1677,11566,11567,11574,11576,11582,11596,11602,11604],{},[2843,11568,11569,11571],{"accent":1121},[1683,11570,6834],{},[1811,11572,11573],{},"ˉ",[1811,11575,2101],{},[2859,11577,11578,11580],{},[1687,11579,1914],{},[1683,11581,1809],{},[2103,11583,11584,11586,11594],{},[1811,11585,2107],{},[1677,11587,11588,11590,11592],{},[1683,11589,1997],{},[1811,11591,2101],{},[1687,11593,1914],{},[1683,11595,1809],{},[1680,11597,11598,11600],{},[1683,11599,6834],{},[1683,11601,1997],{},[2131,11603],{"width":2133},[1677,11605,11606,11609,11616,11619,11626,11629,11635,11638,11646,11648,11654],{},[3028,11607,11608],{},"(v",[2843,11610,11611,11613],{"accent":1121},[3028,11612,7244],{},[1811,11614,11615],{},"ˊ",[3028,11617,11618],{},"b",[2843,11620,11621,11623],{"accent":1121},[3028,11622,8706],{},[1811,11624,11625],{},"ˇ",[3028,11627,11628],{},"rov",[2843,11630,11631,11633],{"accent":1121},[3028,11632,7244],{},[1811,11634,11615],{},[3028,11636,11637],{}," pr",[2843,11639,11640,11643],{"accent":1121},[3028,11641,11642],{},"u",[1811,11644,11645],{},"˚",[3028,11647,4592],{},[2843,11649,11650,11652],{"accent":1121},[3028,11651,8706],{},[1811,11653,11625],{},[3028,11655,11656],{},"r)",[1691,11658,11659],{"encoding":1693},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,11661,11662,11663,5862,11666,11669],{},"Dalšími mírami polohy jsou ",[1136,11664,11665],{},"medián",[1136,11667,11668],{},"modus"," (nejčetnější hodnota výběru).",[1110,11671,11672],{},[1136,11673,11674],{},"Míry variability",[1115,11676,11678],{"className":11677},[1668],[1670,11679,11680],{"xmlns":1672,"display":2083},[1674,11681,11682,11811],{},[1677,11683,11684,11690,11692,11704,11746,11748,11750,11752,11754,11762,11764],{},[1706,11685,11686,11688],{},[1683,11687,1974],{},[1687,11689,1713],{},[1811,11691,2101],{},[2859,11693,11694,11696],{},[1687,11695,1914],{},[1677,11697,11698,11700,11702],{},[1683,11699,1809],{},[1811,11701,3184],{},[1687,11703,1914],{},[1677,11705,11706,11708,11722,11730,11732,11734,11744],{},[1811,11707,1994],{"fence":1121},[2103,11709,11710,11712,11720],{},[1811,11711,2107],{},[1677,11713,11714,11716,11718],{},[1683,11715,1997],{},[1811,11717,2101],{},[1687,11719,1914],{},[1683,11721,1809],{},[3473,11723,11724,11726,11728],{},[1683,11725,6834],{},[1683,11727,1997],{},[1687,11729,1713],{},[1811,11731,3184],{},[1683,11733,1809],{},[1706,11735,11736,11742],{},[2843,11737,11738,11740],{"accent":1121},[1683,11739,6834],{},[1811,11741,11573],{},[1687,11743,1713],{},[1811,11745,2005],{"fence":1121},[1811,11747,1917],{"separator":1121},[2131,11749],{"width":2133},[1683,11751,1974],{},[1811,11753,2101],{},[4574,11755,11756],{},[1706,11757,11758,11760],{},[1683,11759,1974],{},[1687,11761,1713],{},[2131,11763],{"width":2133},[1677,11765,11766,11768,11774,11776,11782,11784,11790,11793,11799,11802,11808],{},[3028,11767,11608],{},[2843,11769,11770,11772],{"accent":1121},[3028,11771,7244],{},[1811,11773,11615],{},[3028,11775,11618],{},[2843,11777,11778,11780],{"accent":1121},[3028,11779,8706],{},[1811,11781,11625],{},[3028,11783,11628],{},[2843,11785,11786,11788],{"accent":1121},[3028,11787,7244],{},[1811,11789,11615],{},[3028,11791,11792],{}," rozptyl, sm",[2843,11794,11795,11797],{"accent":1121},[3028,11796,8706],{},[1811,11798,11625],{},[3028,11800,11801],{},"rodatn",[2843,11803,11804,11806],{"accent":1121},[3028,11805,1127],{},[1811,11807,11615],{},[3028,11809,11810],{}," odchylka)",[1691,11812,11813],{"encoding":1693},"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)}",[1115,11815,11817],{"className":11816},[1668],[1670,11818,11819],{"xmlns":1672,"display":2083},[1674,11820,11821,11887],{},[1677,11822,11823,11825,11827,11836,11838,11846,11848],{},[1683,11824,10337],{},[1811,11826,2101],{},[1680,11828,11829,11831,11834],{},[1683,11830,6834],{},[1683,11832,11833],{},"max",[1811,11835,4612],{},[1811,11837,3184],{},[1680,11839,11840,11842,11844],{},[1683,11841,6834],{},[1683,11843,4609],{},[1811,11845,4612],{},[2131,11847],{"width":2133},[1677,11849,11850,11853,11859,11861,11868,11871,11877,11879,11885],{},[3028,11851,11852],{},"(varia",[2843,11854,11855,11857],{"accent":1121},[3028,11856,3840],{},[1811,11858,11625],{},[3028,11860,1809],{},[2843,11862,11863,11866],{"accent":1121},[3028,11864,11865],{},"ı",[1811,11867,11615],{},[3028,11869,11870],{}," rozp",[2843,11872,11873,11875],{"accent":1121},[3028,11874,8706],{},[1811,11876,11625],{},[3028,11878,7258],{},[2843,11880,11881,11883],{"accent":1121},[3028,11882,11865],{},[1811,11884,11615],{},[3028,11886,2005],{},[1691,11888,11889],{"encoding":1693},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,11891,11892],{},[1136,11893,8417],{},[1110,11895,11896,11897,11920,11921,11943,11944,11965,11966,11994],{},"Kvantil ",[1115,11898,11900],{"className":11899},[1668],[1670,11901,11902],{"xmlns":1672},[1674,11903,11904,11917],{},[1677,11905,11906],{},[1680,11907,11908,11915],{},[2843,11909,11910,11912],{"accent":1121},[1683,11911,6834],{},[1811,11913,11914],{},"~",[1683,11916,1110],{},[1691,11918,11919],{"encoding":1693},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,11922,11924],{"className":11923},[1668],[1670,11925,11926],{"xmlns":1672},[1674,11927,11928,11940],{},[1677,11929,11930,11933,11935,11937],{},[1687,11931,11932],{},"100",[1683,11934,1110],{},[3028,11936,3030],{},[1683,11938,11939],{"mathvariant":2240},"%",[1691,11941,11942],{"encoding":1693},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,11945,11947],{"className":11946},[1668],[1670,11948,11949],{"xmlns":1672},[1674,11950,11951,11963],{},[1677,11952,11953],{},[1680,11954,11955,11961],{},[2843,11956,11957,11959],{"accent":1121},[1683,11958,6834],{},[1811,11960,11914],{},[1683,11962,1110],{},[1691,11964,11919],{"encoding":1693},", zbylých ",[1115,11967,11969],{"className":11968},[1668],[1670,11970,11971],{"xmlns":1672},[1674,11972,11973,11991],{},[1677,11974,11975,11977,11979,11981,11983,11985,11987,11989],{},[1687,11976,11932],{},[1811,11978,1994],{"stretchy":1993},[1687,11980,1914],{},[1811,11982,3184],{},[1683,11984,1110],{},[1811,11986,2005],{"stretchy":1993},[3028,11988,3030],{},[1683,11990,11939],{"mathvariant":2240},[1691,11992,11993],{"encoding":1693},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1503,11996,11997,12024],{},[1265,11998,11999,1418,12001,12023],{},[1136,12000,11665],{},[1115,12002,12004],{"className":12003},[1668],[1670,12005,12006],{"xmlns":1672},[1674,12007,12008,12020],{},[1677,12009,12010],{},[1680,12011,12012,12018],{},[2843,12013,12014,12016],{"accent":1121},[1683,12015,6834],{},[1811,12017,11914],{},[1687,12019,8571],{},[1691,12021,12022],{"encoding":1693},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1265,12025,12026,1418,12029,5862,12051,1418,12054,1497],{},[1136,12027,12028],{},"dolní kvartil",[1115,12030,12032],{"className":12031},[1668],[1670,12033,12034],{"xmlns":1672},[1674,12035,12036,12048],{},[1677,12037,12038],{},[1680,12039,12040,12046],{},[2843,12041,12042,12044],{"accent":1121},[1683,12043,6834],{},[1811,12045,11914],{},[1687,12047,8591],{},[1691,12049,12050],{"encoding":1693},"\\tilde{x}_{0{,}25}",[1136,12052,12053],{},"horní kvartil",[1115,12055,12057],{"className":12056},[1668],[1670,12058,12059],{"xmlns":1672},[1674,12060,12061,12073],{},[1677,12062,12063],{},[1680,12064,12065,12071],{},[2843,12066,12067,12069],{"accent":1121},[1683,12068,6834],{},[1811,12070,11914],{},[1687,12072,8611],{},[1691,12074,12075],{"encoding":1693},"\\tilde{x}_{0{,}75}",[1110,12077,12078,12079,12082],{},"Datový soubor se do R zadává buď přímo (",[3590,12080,12081],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3814,12084,12086],{"className":3816,"code":12085,"language":71,"meta":1603,"style":1603},"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",[3590,12087,12088,12149],{"__ignoreMap":1603},[1115,12089,12090,12092,12094,12096,12098,12101,12103,12106,12108,12111,12113,12116,12118,12120,12122,12124,12126,12129,12131,12134,12136,12138,12140,12142,12145],{"class":3822,"line":10},[1115,12091,6834],{"class":3825},[1115,12093,3830],{"class":3829},[1115,12095,3956],{"class":3833},[1115,12097,1994],{"class":3837},[1115,12099,12100],{"class":3845},"4.1",[1115,12102,1917],{"class":3829},[1115,12104,12105],{"class":3845}," 4.0",[1115,12107,1917],{"class":3829},[1115,12109,12110],{"class":3845}," 3.8",[1115,12112,1917],{"class":3829},[1115,12114,12115],{"class":3845}," 3.9",[1115,12117,1917],{"class":3829},[1115,12119,12110],{"class":3845},[1115,12121,1917],{"class":3829},[1115,12123,12110],{"class":3845},[1115,12125,1917],{"class":3829},[1115,12127,12128],{"class":3845}," 3.5",[1115,12130,1917],{"class":3829},[1115,12132,12133],{"class":3845}," 3.7",[1115,12135,1917],{"class":3829},[1115,12137,12105],{"class":3845},[1115,12139,1917],{"class":3829},[1115,12141,12105],{"class":3845},[1115,12143,12144],{"class":3837},")   ",[1115,12146,12148],{"class":12147},"sCsY4","# přímé zadání hodnot\n",[1115,12150,12151],{"class":3822,"line":27},[1115,12152,12153],{"class":12147},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,12155,12156,12157,12160,12161,12164,12165,12168,12169,12172],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3590,12158,12159],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3590,12162,12163],{},"read.table()"," vrací datovou tabulku (",[3590,12166,12167],{},"data.frame","), proto ",[3590,12170,12171],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,12174,9168],{},[3814,12176,12178],{"className":3816,"code":12177,"language":71,"meta":1603,"style":1603},"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",[3590,12179,12180,12237,12248,12259,12270,12281,12319,12345,12368],{"__ignoreMap":1603},[1115,12181,12182,12184,12186,12188,12190,12193,12195,12198,12200,12203,12205,12208,12210,12212,12214,12217,12219,12221,12223,12226,12228,12231,12233,12235],{"class":3822,"line":10},[1115,12183,6834],{"class":3825},[1115,12185,3830],{"class":3829},[1115,12187,3956],{"class":3833},[1115,12189,1994],{"class":3837},[1115,12191,12192],{"class":3845},"11.1",[1115,12194,1917],{"class":3829},[1115,12196,12197],{"class":3845}," 12.7",[1115,12199,1917],{"class":3829},[1115,12201,12202],{"class":3845}," 10.8",[1115,12204,1917],{"class":3829},[1115,12206,12207],{"class":3845}," 13.2",[1115,12209,1917],{"class":3829},[1115,12211,12197],{"class":3845},[1115,12213,1917],{"class":3829},[1115,12215,12216],{"class":3845}," 13.4",[1115,12218,1917],{"class":3829},[1115,12220,12197],{"class":3845},[1115,12222,1917],{"class":3829},[1115,12224,12225],{"class":3845}," 14.4",[1115,12227,1917],{"class":3829},[1115,12229,12230],{"class":3845}," 14.7",[1115,12232,1917],{"class":3829},[1115,12234,12225],{"class":3845},[1115,12236,4022],{"class":3837},[1115,12238,12239,12242,12244,12246],{"class":3822,"line":27},[1115,12240,12241],{"class":3833},"length",[1115,12243,1994],{"class":3837},[1115,12245,6834],{"class":3825},[1115,12247,4022],{"class":3837},[1115,12249,12250,12253,12255,12257],{"class":3822,"line":148},[1115,12251,12252],{"class":3833},"mean",[1115,12254,1994],{"class":3837},[1115,12256,6834],{"class":3825},[1115,12258,4022],{"class":3837},[1115,12260,12261,12264,12266,12268],{"class":3822,"line":111},[1115,12262,12263],{"class":3833},"var",[1115,12265,1994],{"class":3837},[1115,12267,6834],{"class":3825},[1115,12269,4022],{"class":3837},[1115,12271,12272,12275,12277,12279],{"class":3822,"line":96},[1115,12273,12274],{"class":3833},"sd",[1115,12276,1994],{"class":3837},[1115,12278,6834],{"class":3825},[1115,12280,4022],{"class":3837},[1115,12282,12283,12285,12287,12289,12292,12294,12296,12298,12300,12302,12304,12306,12308,12310,12313,12315,12317],{"class":3822,"line":89},[1115,12284,4609],{"class":3833},[1115,12286,1994],{"class":3837},[1115,12288,6834],{"class":3825},[1115,12290,12291],{"class":3837},"); ",[1115,12293,11833],{"class":3833},[1115,12295,1994],{"class":3837},[1115,12297,6834],{"class":3825},[1115,12299,12291],{"class":3837},[1115,12301,11833],{"class":3833},[1115,12303,1994],{"class":3837},[1115,12305,6834],{"class":3825},[1115,12307,4722],{"class":3837},[1115,12309,4759],{"class":3829},[1115,12311,12312],{"class":3833}," min",[1115,12314,1994],{"class":3837},[1115,12316,6834],{"class":3825},[1115,12318,4022],{"class":3837},[1115,12320,12321,12324,12326,12328,12330,12333,12335,12338,12340,12343],{"class":3822,"line":82},[1115,12322,12323],{"class":3833},"quantile",[1115,12325,1994],{"class":3837},[1115,12327,6834],{"class":3825},[1115,12329,1917],{"class":3829},[1115,12331,12332],{"class":3845}," 0.5",[1115,12334,1917],{"class":3829},[1115,12336,12337],{"class":3825}," type",[1115,12339,3918],{"class":3829},[1115,12341,12342],{"class":3845}," 6",[1115,12344,4022],{"class":3837},[1115,12346,12347,12349,12351,12353,12355,12358,12360,12362,12364,12366],{"class":3822,"line":75},[1115,12348,12323],{"class":3833},[1115,12350,1994],{"class":3837},[1115,12352,6834],{"class":3825},[1115,12354,1917],{"class":3829},[1115,12356,12357],{"class":3845}," 0.25",[1115,12359,1917],{"class":3829},[1115,12361,12337],{"class":3825},[1115,12363,3918],{"class":3829},[1115,12365,12342],{"class":3845},[1115,12367,4022],{"class":3837},[1115,12369,12370,12372,12374,12376,12378,12381,12383,12385,12387,12389],{"class":3822,"line":4012},[1115,12371,12323],{"class":3833},[1115,12373,1994],{"class":3837},[1115,12375,6834],{"class":3825},[1115,12377,1917],{"class":3829},[1115,12379,12380],{"class":3845}," 0.75",[1115,12382,1917],{"class":3829},[1115,12384,12337],{"class":3825},[1115,12386,3918],{"class":3829},[1115,12388,12342],{"class":3845},[1115,12390,4022],{"class":3837},[3814,12392,12395],{"className":12393,"code":12394,"language":4044,"meta":1603},[4042],"[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",[3590,12396,12394],{"__ignoreMap":1603},[1110,12398,12399,12402,12403,12406],{},[3590,12400,12401],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3590,12404,12405],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,12408,12409],{},[4504,12410],{"alt":12411,"className":12412,"src":12413},"mask-ps-kvantily",[1131,4508],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,12415,12416],{},"Seřazení souboru a krabicový graf:",[3814,12418,12420],{"className":3816,"code":12419,"language":71,"meta":1603,"style":1603},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3590,12421,12422,12437,12460],{"__ignoreMap":1603},[1115,12423,12424,12427,12429,12431,12434],{"class":3822,"line":10},[1115,12425,12426],{"class":3833},"sort",[1115,12428,1994],{"class":3837},[1115,12430,6834],{"class":3825},[1115,12432,12433],{"class":3837},")                     ",[1115,12435,12436],{"class":12147},"# vzestupně\n",[1115,12438,12439,12441,12443,12445,12447,12450,12452,12454,12457],{"class":3822,"line":27},[1115,12440,12426],{"class":3833},[1115,12442,1994],{"class":3837},[1115,12444,6834],{"class":3825},[1115,12446,1917],{"class":3829},[1115,12448,12449],{"class":3825}," decreasing",[1115,12451,3918],{"class":3829},[1115,12453,3931],{"class":3845},[1115,12455,12456],{"class":3837},")  ",[1115,12458,12459],{"class":12147},"# sestupně\n",[1115,12461,12462,12465,12467,12469],{"class":3822,"line":148},[1115,12463,12464],{"class":3833},"boxplot",[1115,12466,1994],{"class":3837},[1115,12468,6834],{"class":3825},[1115,12470,4022],{"class":3837},[3814,12472,12475],{"className":12473,"code":12474,"language":4044,"meta":1603},[4042]," [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",[3590,12476,12474],{"__ignoreMap":1603},[1110,12478,12479,12482,12483,12486],{},[3590,12480,12481],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3590,12484,12485],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,12488,12490,12497],{"className":12489,"dataCallout":3597},[1106,3596],[1110,12491,12493,12496],{"className":12492},[1113],[1115,12494],{"className":12495,"ariaHidden":1121},[1118,3604,1120],"Příklad: Empirické charakteristiky",[1110,12498,12499],{},"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.",[1110,12501,12502,12503,3071,12526,3071,12549,3071,12568,12587,12588,8575,12615,12630,12631,1497],{},"Výstup R kódu výše dává ",[1115,12504,12506],{"className":12505},[1668],[1670,12507,12508],{"xmlns":1672},[1674,12509,12510,12523],{},[1677,12511,12512,12518,12520],{},[2843,12513,12514,12516],{"accent":1121},[1683,12515,6834],{},[1811,12517,11573],{},[1811,12519,2101],{},[1687,12521,12522],{},"13,01",[1691,12524,12525],{"encoding":1693},"\\bar{x}=13{,}01",[1115,12527,12529],{"className":12528},[1668],[1670,12530,12531],{"xmlns":1672},[1674,12532,12533,12546],{},[1677,12534,12535,12541,12543],{},[1706,12536,12537,12539],{},[1683,12538,1974],{},[1687,12540,1713],{},[1811,12542,2101],{},[1687,12544,12545],{},"1,75",[1691,12547,12548],{"encoding":1693},"s^2=1{,}75",[1115,12550,12552],{"className":12551},[1668],[1670,12553,12554],{"xmlns":1672},[1674,12555,12556,12565],{},[1677,12557,12558,12560,12562],{},[1683,12559,1974],{},[1811,12561,2101],{},[1687,12563,12564],{},"1,32",[1691,12566,12567],{"encoding":1693},"s=1{,}32",[1115,12569,12571],{"className":12570},[1668],[1670,12572,12573],{"xmlns":1672},[1674,12574,12575,12584],{},[1677,12576,12577,12579,12581],{},[1683,12578,10337],{},[1811,12580,2101],{},[1687,12582,12583],{},"3,9",[1691,12585,12586],{"encoding":1693},"R=3{,}9",", medián ",[1115,12589,12591],{"className":12590},[1668],[1670,12592,12593],{"xmlns":1672},[1674,12594,12595,12612],{},[1677,12596,12597,12607,12609],{},[1680,12598,12599,12605],{},[2843,12600,12601,12603],{"accent":1121},[1683,12602,6834],{},[1811,12604,11914],{},[1687,12606,8571],{},[1811,12608,2101],{},[1687,12610,12611],{},"12,95",[1691,12613,12614],{"encoding":1693},"\\tilde{x}_{0{,}5}=12{,}95",[1115,12616,12618],{"className":12617},[1668],[1670,12619,12620],{"xmlns":1672},[1674,12621,12622,12627],{},[1677,12623,12624],{},[1687,12625,12626],{},"12,3",[1691,12628,12629],{"encoding":1693},"12{,}3",", horní kvartil ",[1115,12632,12634],{"className":12633},[1668],[1670,12635,12636],{"xmlns":1672},[1674,12637,12638,12643],{},[1677,12639,12640],{},[1687,12641,12642],{},"14,4",[1691,12644,12645],{"encoding":1693},"14{,}4",[1110,12647,12648],{},"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.",[1103,12650,12652,12659],{"className":12651,"dataCallout":3597},[1106,3596],[1110,12653,12655,12658],{"className":12654},[1113],[1115,12656],{"className":12657,"ariaHidden":1121},[1118,3604,1120],"Příklad: Doba oprav televizorů",[1110,12660,12661],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3814,12663,12665],{"className":3816,"code":12664,"language":71,"meta":1603,"style":1603},"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",[3590,12666,12667,12727,12778,12825,12872,12920,12930,12940,12950,12970],{"__ignoreMap":1603},[1115,12668,12669,12672,12674,12676,12678,12680,12682,12685,12687,12690,12692,12695,12697,12700,12702,12705,12707,12710,12712,12715,12717,12720,12722,12725],{"class":3822,"line":10},[1115,12670,12671],{"class":3825},"x6",[1115,12673,3830],{"class":3829},[1115,12675,3956],{"class":3833},[1115,12677,1994],{"class":3837},[1115,12679,3695],{"class":3845},[1115,12681,1917],{"class":3829},[1115,12683,12684],{"class":3845}," 40.2",[1115,12686,1917],{"class":3829},[1115,12688,12689],{"class":3845}," 41.9",[1115,12691,1917],{"class":3829},[1115,12693,12694],{"class":3845}," 43.4",[1115,12696,1917],{"class":3829},[1115,12698,12699],{"class":3845}," 42.8",[1115,12701,1917],{"class":3829},[1115,12703,12704],{"class":3845}," 42.3",[1115,12706,1917],{"class":3829},[1115,12708,12709],{"class":3845}," 43.2",[1115,12711,1917],{"class":3829},[1115,12713,12714],{"class":3845}," 45",[1115,12716,1917],{"class":3829},[1115,12718,12719],{"class":3845}," 41.5",[1115,12721,1917],{"class":3829},[1115,12723,12724],{"class":3845}," 42.7",[1115,12726,3858],{"class":3829},[1115,12728,12729,12732,12734,12737,12739,12742,12744,12747,12749,12752,12754,12757,12759,12762,12764,12767,12769,12771,12773,12776],{"class":3822,"line":27},[1115,12730,12731],{"class":3845},"        43.9",[1115,12733,1917],{"class":3829},[1115,12735,12736],{"class":3845}," 40.1",[1115,12738,1917],{"class":3829},[1115,12740,12741],{"class":3845}," 43.3",[1115,12743,1917],{"class":3829},[1115,12745,12746],{"class":3845}," 41.1",[1115,12748,1917],{"class":3829},[1115,12750,12751],{"class":3845}," 42.5",[1115,12753,1917],{"class":3829},[1115,12755,12756],{"class":3845}," 42.4",[1115,12758,1917],{"class":3829},[1115,12760,12761],{"class":3845}," 41.4",[1115,12763,1917],{"class":3829},[1115,12765,12766],{"class":3845}," 40.8",[1115,12768,1917],{"class":3829},[1115,12770,9449],{"class":3845},[1115,12772,1917],{"class":3829},[1115,12774,12775],{"class":3845}," 44.7",[1115,12777,3858],{"class":3829},[1115,12779,12780,12783,12785,12787,12789,12791,12793,12796,12798,12801,12803,12806,12808,12810,12812,12815,12817,12819,12821,12823],{"class":3822,"line":148},[1115,12781,12782],{"class":3845},"        41.2",[1115,12784,1917],{"class":3829},[1115,12786,12689],{"class":3845},[1115,12788,1917],{"class":3829},[1115,12790,12756],{"class":3845},[1115,12792,1917],{"class":3829},[1115,12794,12795],{"class":3845}," 44.4",[1115,12797,1917],{"class":3829},[1115,12799,12800],{"class":3845}," 40.5",[1115,12802,1917],{"class":3829},[1115,12804,12805],{"class":3845}," 39.7",[1115,12807,1917],{"class":3829},[1115,12809,12746],{"class":3845},[1115,12811,1917],{"class":3829},[1115,12813,12814],{"class":3845}," 41",[1115,12816,1917],{"class":3829},[1115,12818,12689],{"class":3845},[1115,12820,1917],{"class":3829},[1115,12822,12766],{"class":3845},[1115,12824,3858],{"class":3829},[1115,12826,12827,12830,12832,12834,12836,12839,12841,12843,12845,12847,12849,12852,12854,12857,12859,12861,12863,12866,12868,12870],{"class":3822,"line":111},[1115,12828,12829],{"class":3845},"        43",[1115,12831,1917],{"class":3829},[1115,12833,12699],{"class":3845},[1115,12835,1917],{"class":3829},[1115,12837,12838],{"class":3845}," 42.9",[1115,12840,1917],{"class":3829},[1115,12842,12724],{"class":3845},[1115,12844,1917],{"class":3829},[1115,12846,12741],{"class":3845},[1115,12848,1917],{"class":3829},[1115,12850,12851],{"class":3845}," 42.2",[1115,12853,1917],{"class":3829},[1115,12855,12856],{"class":3845}," 39.2",[1115,12858,1917],{"class":3829},[1115,12860,12719],{"class":3845},[1115,12862,1917],{"class":3829},[1115,12864,12865],{"class":3845}," 41.6",[1115,12867,1917],{"class":3829},[1115,12869,12724],{"class":3845},[1115,12871,3858],{"class":3829},[1115,12873,12874,12877,12879,12881,12883,12886,12888,12890,12892,12895,12897,12900,12902,12905,12907,12909,12911,12914,12916,12918],{"class":3822,"line":96},[1115,12875,12876],{"class":3845},"        45",[1115,12878,1917],{"class":3829},[1115,12880,12704],{"class":3845},[1115,12882,1917],{"class":3829},[1115,12884,12885],{"class":3845}," 43.6",[1115,12887,1917],{"class":3829},[1115,12889,12709],{"class":3845},[1115,12891,1917],{"class":3829},[1115,12893,12894],{"class":3845}," 38.8",[1115,12896,1917],{"class":3829},[1115,12898,12899],{"class":3845}," 43",[1115,12901,1917],{"class":3829},[1115,12903,12904],{"class":3845}," 44.2",[1115,12906,1917],{"class":3829},[1115,12908,12899],{"class":3845},[1115,12910,1917],{"class":3829},[1115,12912,12913],{"class":3845}," 40",[1115,12915,1917],{"class":3829},[1115,12917,12795],{"class":3845},[1115,12919,4022],{"class":3837},[1115,12921,12922,12924,12926,12928],{"class":3822,"line":89},[1115,12923,12241],{"class":3833},[1115,12925,1994],{"class":3837},[1115,12927,12671],{"class":3825},[1115,12929,4022],{"class":3837},[1115,12931,12932,12934,12936,12938],{"class":3822,"line":82},[1115,12933,12252],{"class":3833},[1115,12935,1994],{"class":3837},[1115,12937,12671],{"class":3825},[1115,12939,4022],{"class":3837},[1115,12941,12942,12944,12946,12948],{"class":3822,"line":75},[1115,12943,12274],{"class":3833},[1115,12945,1994],{"class":3837},[1115,12947,12671],{"class":3825},[1115,12949,4022],{"class":3837},[1115,12951,12952,12954,12956,12958,12960,12962,12964,12966,12968],{"class":3822,"line":4012},[1115,12953,11833],{"class":3833},[1115,12955,1994],{"class":3837},[1115,12957,12671],{"class":3825},[1115,12959,4722],{"class":3837},[1115,12961,4759],{"class":3829},[1115,12963,12312],{"class":3833},[1115,12965,1994],{"class":3837},[1115,12967,12671],{"class":3825},[1115,12969,4022],{"class":3837},[1115,12971,12972,12975,12977,12979],{"class":3822,"line":72},[1115,12973,12974],{"class":3833},"median",[1115,12976,1994],{"class":3837},[1115,12978,12671],{"class":3825},[1115,12980,4022],{"class":3837},[3814,12982,12985],{"className":12983,"code":12984,"language":4044,"meta":1603},[4042],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3590,12986,12984],{"__ignoreMap":1603},[1110,12988,12989],{},"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.",[1153,12991,12993],{"id":12992},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,12995,12996,12997,13010,13011,1418,13014,13037,13038,13072],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,12998,13000],{"className":12999},[1668],[1670,13001,13002],{"xmlns":1672},[1674,13003,13004,13008],{},[1677,13005,13006],{},[1683,13007,6846],{},[1691,13009,6846],{"encoding":1693},", lze sestrojit ",[1136,13012,13013],{},"empirickou distribuční funkci",[1115,13015,13017],{"className":13016},[1668],[1670,13018,13019],{"xmlns":1672},[1674,13020,13021,13035],{},[1677,13022,13023,13029,13031,13033],{},[1680,13024,13025,13027],{},[1683,13026,1403],{},[1683,13028,1809],{},[1811,13030,1994],{"stretchy":1993},[1683,13032,6834],{},[1811,13034,2005],{"stretchy":1993},[1691,13036,11297],{"encoding":1693},". Pro datový soubor ",[1115,13039,13041],{"className":13040},[1668],[1670,13042,13043],{"xmlns":1672},[1674,13044,13045,13069],{},[1677,13046,13047,13049,13055,13057,13059,13061,13067],{},[1811,13048,1994],{"stretchy":1993},[1680,13050,13051,13053],{},[1683,13052,6834],{},[1687,13054,1914],{},[1811,13056,1917],{"separator":1121},[1811,13058,1920],{},[1811,13060,1917],{"separator":1121},[1680,13062,13063,13065],{},[1683,13064,6834],{},[1683,13066,1809],{},[1811,13068,2005],{"stretchy":1993},[1691,13070,13071],{"encoding":1693},"(x_1,\\dots,x_n)"," je",[1115,13074,13076],{"className":13075},[1668],[1670,13077,13078],{"xmlns":1672,"display":2083},[1674,13079,13080,13104],{},[1677,13081,13082,13088,13090,13092,13094,13096,13102],{},[1680,13083,13084,13086],{},[1683,13085,1403],{},[1683,13087,1809],{},[1811,13089,1994],{"stretchy":1993},[1683,13091,6834],{},[1811,13093,2005],{"stretchy":1993},[1811,13095,2101],{},[2859,13097,13098,13100],{},[1683,13099,7374],{},[1683,13101,1809],{},[1811,13103,1917],{"separator":1121},[1691,13105,13106],{"encoding":1693},"F_n(x) = \\frac{k}{n},",[1110,13108,4628,13109,13122,13123,1497],{},[1115,13110,13112],{"className":13111},[1668],[1670,13113,13114],{"xmlns":1672},[1674,13115,13116,13120],{},[1677,13117,13118],{},[1683,13119,7374],{},[1691,13121,7374],{"encoding":1693}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,13124,13126],{"className":13125},[1668],[1670,13127,13128],{"xmlns":1672},[1674,13129,13130,13134],{},[1677,13131,13132],{},[1683,13133,6834],{},[1691,13135,6834],{"encoding":1693},[1110,13137,9168],{},[3814,13139,13141],{"className":3816,"code":13140,"language":71,"meta":1603,"style":1603},"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",[3590,13142,13143,13158,13173,13191,13205],{"__ignoreMap":1603},[1115,13144,13145,13147,13149,13152,13154,13156],{"class":3822,"line":10},[1115,13146,6885],{"class":3825},[1115,13148,3830],{"class":3829},[1115,13150,13151],{"class":3833}," ecdf",[1115,13153,1994],{"class":3837},[1115,13155,6834],{"class":3825},[1115,13157,4022],{"class":3837},[1115,13159,13160,13163,13165,13167,13170],{"class":3822,"line":27},[1115,13161,13162],{"class":3833},"knots",[1115,13164,1994],{"class":3837},[1115,13166,6885],{"class":3825},[1115,13168,13169],{"class":3837},")        ",[1115,13171,13172],{"class":12147},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,13174,13175,13177,13179,13181,13183,13185,13188],{"class":3822,"line":148},[1115,13176,6885],{"class":3833},[1115,13178,1994],{"class":3837},[1115,13180,13162],{"class":3833},[1115,13182,1994],{"class":3837},[1115,13184,6885],{"class":3825},[1115,13186,13187],{"class":3837},"))      ",[1115,13189,13190],{"class":12147},"# hodnoty Fn(x) v těchto bodech\n",[1115,13192,13193,13195,13197,13199,13202],{"class":3822,"line":111},[1115,13194,6885],{"class":3833},[1115,13196,1994],{"class":3837},[1115,13198,3665],{"class":3845},[1115,13200,13201],{"class":3837},")            ",[1115,13203,13204],{"class":12147},"# Fn v libovolném bodě\n",[1115,13206,13207,13210,13212,13214],{"class":3822,"line":96},[1115,13208,13209],{"class":3833},"plot",[1115,13211,1994],{"class":3837},[1115,13213,6885],{"class":3825},[1115,13215,4022],{"class":3837},[3814,13217,13220],{"className":13218,"code":13219,"language":4044,"meta":1603},[4042],"[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",[3590,13221,13219],{"__ignoreMap":1603},[1110,13223,13224,13227,13228,13246,13247,13250,13251,13264,13265,1497],{},[3590,13225,13226],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,13229,13231],{"className":13230},[1668],[1670,13232,13233],{"xmlns":1672},[1674,13234,13235,13243],{},[1677,13236,13237],{},[1680,13238,13239,13241],{},[1683,13240,1403],{},[1683,13242,1809],{},[1691,13244,13245],{"encoding":1693},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3590,13248,13249],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,13252,13254],{"className":13253},[1668],[1670,13255,13256],{"xmlns":1672},[1674,13257,13258,13262],{},[1677,13259,13260],{},[1683,13261,7374],{},[1691,13263,7374],{"encoding":1693},"-násobek ",[1115,13266,13268],{"className":13267},[1668],[1670,13269,13270],{"xmlns":1672},[1674,13271,13272,13280],{},[1677,13273,13274,13276,13278],{},[1687,13275,1914],{},[1683,13277,4725],{"mathvariant":2240},[1683,13279,1809],{},[1691,13281,13282],{"encoding":1693},"1\u002Fn",[1110,13284,13285],{},[4504,13286],{"alt":13287,"className":13288,"src":13289},"mask-ps-ecdf",[1131,4508],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,13291,13293,13300],{"className":13292,"dataCallout":3597},[1106,3596],[1110,13294,13296,13299],{"className":13295},[1113],[1115,13297],{"className":13298,"ariaHidden":1121},[1118,3604,1120],"Příklad: Empirická distribuční funkce",[1110,13301,13302],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,13304,13305,13306,1497],{},"Uspořádaný soubor je ",[1115,13307,13309],{"className":13308},[1668],[1670,13310,13311],{"xmlns":1672},[1674,13312,13313,13377],{},[1677,13314,13315,13318,13320,13322,13325,13327,13329,13332,13334,13336,13338,13340,13342,13344,13346,13348,13351,13353,13355,13358,13360,13362,13364,13366,13368,13370,13372,13374],{},[1687,13316,13317],{},"10,8",[1811,13319,7008],{"separator":1121},[3028,13321,11428],{},[1687,13323,13324],{},"11,1",[1811,13326,7008],{"separator":1121},[3028,13328,11428],{},[1687,13330,13331],{},"12,7",[1811,13333,7008],{"separator":1121},[3028,13335,11428],{},[1687,13337,13331],{},[1811,13339,7008],{"separator":1121},[3028,13341,11428],{},[1687,13343,13331],{},[1811,13345,7008],{"separator":1121},[3028,13347,11428],{},[1687,13349,13350],{},"13,2",[1811,13352,7008],{"separator":1121},[3028,13354,11428],{},[1687,13356,13357],{},"13,4",[1811,13359,7008],{"separator":1121},[3028,13361,11428],{},[1687,13363,12642],{},[1811,13365,7008],{"separator":1121},[3028,13367,11428],{},[1687,13369,12642],{},[1811,13371,7008],{"separator":1121},[3028,13373,11428],{},[1687,13375,13376],{},"14,7",[1691,13378,13379],{"encoding":1693},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1158,13381,13382,13415],{},[1161,13383,13384],{},[1164,13385,13386,13401,13403,13405,13407,13409,13411,13413],{},[1167,13387,13388],{},[1115,13389,13391],{"className":13390},[1668],[1670,13392,13393],{"xmlns":1672},[1674,13394,13395,13399],{},[1677,13396,13397],{},[1683,13398,6834],{},[1691,13400,6834],{"encoding":1693},[1167,13402,13317],{},[1167,13404,13324],{},[1167,13406,13331],{},[1167,13408,13350],{},[1167,13410,13357],{},[1167,13412,12642],{},[1167,13414,13376],{},[1174,13416,13417,13449],{},[1164,13418,13419,13434,13436,13438,13440,13442,13445,13447],{},[1179,13420,13421],{},[1115,13422,13424],{"className":13423},[1668],[1670,13425,13426],{"xmlns":1672},[1674,13427,13428,13432],{},[1677,13429,13430],{},[1683,13431,7374],{},[1691,13433,7374],{"encoding":1693},[1179,13435,1914],{},[1179,13437,1713],{},[1179,13439,10040],{},[1179,13441,4085],{},[1179,13443,13444],{},"7",[1179,13446,3715],{},[1179,13448,9147],{},[1164,13450,13451,13476,13479,13482,13484,13487,13490,13493],{},[1179,13452,13453],{},[1115,13454,13456],{"className":13455},[1668],[1670,13457,13458],{"xmlns":1672},[1674,13459,13460,13474],{},[1677,13461,13462,13468,13470,13472],{},[1680,13463,13464,13466],{},[1683,13465,1403],{},[1683,13467,1809],{},[1811,13469,1994],{"stretchy":1993},[1683,13471,6834],{},[1811,13473,2005],{"stretchy":1993},[1691,13475,11297],{"encoding":1693},[1179,13477,13478],{},"0,1",[1179,13480,13481],{},"0,2",[1179,13483,8571],{},[1179,13485,13486],{},"0,6",[1179,13488,13489],{},"0,7",[1179,13491,13492],{},"0,9",[1179,13494,13495],{},"1,0",[1110,13497,13498,13499,13521,13522,13545],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,13500,13502],{"className":13501},[1668],[1670,13503,13504],{"xmlns":1672},[1674,13505,13506,13518],{},[1677,13507,13508,13510,13512,13514,13516],{},[1687,13509,1914],{},[1683,13511,4725],{"mathvariant":2240},[1683,13513,1809],{},[1811,13515,2101],{},[1687,13517,13478],{},[1691,13519,13520],{"encoding":1693},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,13523,13525],{"className":13524},[1668],[1670,13526,13527],{"xmlns":1672},[1674,13528,13529,13542],{},[1677,13530,13531,13533,13535,13537,13539],{},[1687,13532,3712],{},[1683,13534,4725],{"mathvariant":2240},[1683,13536,1809],{},[1811,13538,2101],{},[1687,13540,13541],{},"0,3",[1691,13543,13544],{"encoding":1693},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,13547,13549,13556],{"className":13548,"dataCallout":3597},[1106,3596],[1110,13550,13552,13555],{"className":13551},[1113],[1115,13553],{"className":13554,"ariaHidden":1121},[1118,3604,1120],"Příklad: Odpad materiálu",[1110,13557,13558],{},"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.",[3814,13560,13562],{"className":3816,"code":13561,"language":71,"meta":1603,"style":1603},"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",[3590,13563,13564,13615,13625,13635,13645,13665,13675,13690,13700],{"__ignoreMap":1603},[1115,13565,13566,13569,13571,13573,13575,13577,13579,13581,13583,13585,13587,13589,13591,13593,13595,13597,13599,13601,13603,13605,13607,13609,13611,13613],{"class":3822,"line":10},[1115,13567,13568],{"class":3825},"x4",[1115,13570,3830],{"class":3829},[1115,13572,3956],{"class":3833},[1115,13574,1994],{"class":3837},[1115,13576,12100],{"class":3845},[1115,13578,1917],{"class":3829},[1115,13580,12105],{"class":3845},[1115,13582,1917],{"class":3829},[1115,13584,12110],{"class":3845},[1115,13586,1917],{"class":3829},[1115,13588,12115],{"class":3845},[1115,13590,1917],{"class":3829},[1115,13592,12110],{"class":3845},[1115,13594,1917],{"class":3829},[1115,13596,12110],{"class":3845},[1115,13598,1917],{"class":3829},[1115,13600,12128],{"class":3845},[1115,13602,1917],{"class":3829},[1115,13604,12133],{"class":3845},[1115,13606,1917],{"class":3829},[1115,13608,12105],{"class":3845},[1115,13610,1917],{"class":3829},[1115,13612,12105],{"class":3845},[1115,13614,4022],{"class":3837},[1115,13616,13617,13619,13621,13623],{"class":3822,"line":27},[1115,13618,12241],{"class":3833},[1115,13620,1994],{"class":3837},[1115,13622,13568],{"class":3825},[1115,13624,4022],{"class":3837},[1115,13626,13627,13629,13631,13633],{"class":3822,"line":148},[1115,13628,12252],{"class":3833},[1115,13630,1994],{"class":3837},[1115,13632,13568],{"class":3825},[1115,13634,4022],{"class":3837},[1115,13636,13637,13639,13641,13643],{"class":3822,"line":111},[1115,13638,12274],{"class":3833},[1115,13640,1994],{"class":3837},[1115,13642,13568],{"class":3825},[1115,13644,4022],{"class":3837},[1115,13646,13647,13649,13651,13653,13655,13657,13659,13661,13663],{"class":3822,"line":96},[1115,13648,11833],{"class":3833},[1115,13650,1994],{"class":3837},[1115,13652,13568],{"class":3825},[1115,13654,4722],{"class":3837},[1115,13656,4759],{"class":3829},[1115,13658,12312],{"class":3833},[1115,13660,1994],{"class":3837},[1115,13662,13568],{"class":3825},[1115,13664,4022],{"class":3837},[1115,13666,13667,13669,13671,13673],{"class":3822,"line":89},[1115,13668,12974],{"class":3833},[1115,13670,1994],{"class":3837},[1115,13672,13568],{"class":3825},[1115,13674,4022],{"class":3837},[1115,13676,13677,13680,13682,13684,13686,13688],{"class":3822,"line":82},[1115,13678,13679],{"class":3825},"f4",[1115,13681,3830],{"class":3829},[1115,13683,13151],{"class":3833},[1115,13685,1994],{"class":3837},[1115,13687,13568],{"class":3825},[1115,13689,4022],{"class":3837},[1115,13691,13692,13694,13696,13698],{"class":3822,"line":75},[1115,13693,13162],{"class":3833},[1115,13695,1994],{"class":3837},[1115,13697,13679],{"class":3825},[1115,13699,4022],{"class":3837},[1115,13701,13702,13704,13706,13708,13710,13712],{"class":3822,"line":4012},[1115,13703,13679],{"class":3833},[1115,13705,1994],{"class":3837},[1115,13707,13162],{"class":3833},[1115,13709,1994],{"class":3837},[1115,13711,13679],{"class":3825},[1115,13713,9607],{"class":3837},[3814,13715,13718],{"className":13716,"code":13717,"language":4044,"meta":1603},[4042],"[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",[3590,13719,13717],{"__ignoreMap":1603},[1110,13721,13722,13723,13746],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,13724,13726],{"className":13725},[1668],[1670,13727,13728],{"xmlns":1672},[1674,13729,13730,13744],{},[1677,13731,13732,13738,13740,13742],{},[1680,13733,13734,13736],{},[1683,13735,1403],{},[1683,13737,1809],{},[1811,13739,1994],{"stretchy":1993},[1683,13741,6834],{},[1811,13743,2005],{"stretchy":1993},[1691,13745,11297],{"encoding":1693},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1153,13748,13750],{"id":13749},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,13752,13753,13754,13757,13758,13771,13772,13775],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1136,13755,13756],{},"roztřídí",": variační rozpětí ",[1115,13759,13761],{"className":13760},[1668],[1670,13762,13763],{"xmlns":1672},[1674,13764,13765,13769],{},[1677,13766,13767],{},[1683,13768,10337],{},[1691,13770,10337],{"encoding":1693}," se rozdělí na určitý počet ",[1136,13773,13774],{},"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.",[1110,13777,13778],{},"Výsledkem je tabulka četností se sloupci:",[1503,13780,13781,13861,13882,13903],{},[1265,13782,13783,13801,13802,13815,13816,13860],{},[1115,13784,13786],{"className":13785},[1668],[1670,13787,13788],{"xmlns":1672},[1674,13789,13790,13798],{},[1677,13791,13792],{},[1680,13793,13794,13796],{},[1683,13795,11314],{},[1683,13797,2002],{},[1691,13799,13800],{"encoding":1693},"I_j"," — ",[1115,13803,13805],{"className":13804},[1668],[1670,13806,13807],{"xmlns":1672},[1674,13808,13809,13813],{},[1677,13810,13811],{},[1683,13812,2002],{},[1691,13814,2002],{"encoding":1693},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,13817,13819],{"className":13818},[1668],[1670,13820,13821],{"xmlns":1672},[1674,13822,13823,13857],{},[1677,13824,13825,13831,13833,13835,13841,13843,13855],{},[1680,13826,13827,13829],{},[1683,13828,11314],{},[1683,13830,2002],{},[1811,13832,2101],{},[1811,13834,8539],{"stretchy":1993},[1680,13836,13837,13839],{},[1683,13838,3840],{},[1683,13840,2002],{},[1811,13842,7008],{"separator":1121},[1680,13844,13845,13847],{},[1683,13846,3840],{},[1677,13848,13849,13851,13853],{},[1683,13850,2002],{},[1811,13852,5598],{},[1687,13854,1914],{},[1811,13856,2005],{"stretchy":1993},[1691,13858,13859],{"encoding":1693},"I_j = \\langle c_j; c_{j+1})","),",[1265,13862,13863,13881],{},[1115,13864,13866],{"className":13865},[1668],[1670,13867,13868],{"xmlns":1672},[1674,13869,13870,13878],{},[1677,13871,13872],{},[1680,13873,13874,13876],{},[1683,13875,9039],{},[1683,13877,2002],{},[1691,13879,13880],{"encoding":1693},"Z_j"," — střed (reprezentant) intervalu,",[1265,13883,13884,13902],{},[1115,13885,13887],{"className":13886},[1668],[1670,13888,13889],{"xmlns":1672},[1674,13890,13891,13899],{},[1677,13892,13893],{},[1680,13894,13895,13897],{},[1683,13896,6885],{},[1683,13898,2002],{},[1691,13900,13901],{"encoding":1693},"f_j"," — četnost, počet hodnot v intervalu,",[1265,13904,13905,13935,13936,5862,13964,1497],{},[1115,13906,13908],{"className":13907},[1668],[1670,13909,13910],{"xmlns":1672},[1674,13911,13912,13932],{},[1677,13913,13914,13920,13922,13928,13930],{},[1680,13915,13916,13918],{},[1683,13917,1110],{},[1683,13919,2002],{},[1811,13921,2101],{},[1680,13923,13924,13926],{},[1683,13925,6885],{},[1683,13927,2002],{},[1683,13929,4725],{"mathvariant":2240},[1683,13931,1809],{},[1691,13933,13934],{"encoding":1693},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,13937,13939],{"className":13938},[1668],[1670,13940,13941],{"xmlns":1672},[1674,13942,13943,13961],{},[1677,13944,13945,13951,13957,13959],{},[1680,13946,13947,13949],{},[1811,13948,2107],{},[1683,13950,2002],{},[1680,13952,13953,13955],{},[1683,13954,6885],{},[1683,13956,2002],{},[1811,13958,2101],{},[1683,13960,1809],{},[1691,13962,13963],{"encoding":1693},"\\sum_j f_j = n",[1115,13965,13967],{"className":13966},[1668],[1670,13968,13969],{"xmlns":1672},[1674,13970,13971,13989],{},[1677,13972,13973,13979,13985,13987],{},[1680,13974,13975,13977],{},[1811,13976,2107],{},[1683,13978,2002],{},[1680,13980,13981,13983],{},[1683,13982,1110],{},[1683,13984,2002],{},[1811,13986,2101],{},[1687,13988,1914],{},[1691,13990,13991],{"encoding":1693},"\\sum_j p_j = 1",[1110,13993,13994,13995,13998,13999,14002,14003,14006,14007,14010,14011,4728,14014,14031,14032,14035,14036,4728,14039,1932,14056,14059],{},"V R se třídění provádí příkazem ",[3590,13996,13997],{},"hist()"," — buď necháme R zvolit třídy samo (",[3590,14000,14001],{},"hist(x)","), nebo zadáme hranice přímo (",[3590,14004,14005],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3590,14008,14009],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3590,14012,14013],{},"y$counts",[1115,14015,14017],{"className":14016},[1668],[1670,14018,14019],{"xmlns":1672},[1674,14020,14021,14029],{},[1677,14022,14023],{},[1680,14024,14025,14027],{},[1683,14026,6885],{},[1683,14028,2002],{},[1691,14030,13901],{"encoding":1693},"), ",[3590,14033,14034],{},"y$breaks"," (hranice tříd), ",[3590,14037,14038],{},"y$mids",[1115,14040,14042],{"className":14041},[1668],[1670,14043,14044],{"xmlns":1672},[1674,14045,14046,14054],{},[1677,14047,14048],{},[1680,14049,14050,14052],{},[1683,14051,9039],{},[1683,14053,2002],{},[1691,14055,13880],{"encoding":1693},[3590,14057,14058],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,14061,14062,14063,14080,14081,14083,14084,14120,14121,14124,14125,1497],{},"Interval ",[1115,14064,14066],{"className":14065},[1668],[1670,14067,14068],{"xmlns":1672},[1674,14069,14070,14078],{},[1677,14071,14072],{},[1680,14073,14074,14076],{},[1683,14075,11314],{},[1683,14077,2002],{},[1691,14079,13800],{"encoding":1693}," je ve výchozím nastavení ",[3590,14082,13997],{}," zleva otevřený a zprava uzavřený, ",[1115,14085,14087],{"className":14086},[1668],[1670,14088,14089],{"xmlns":1672},[1674,14090,14091,14117],{},[1677,14092,14093,14095,14101,14103,14115],{},[1811,14094,1994],{"stretchy":1993},[1680,14096,14097,14099],{},[1683,14098,3840],{},[1683,14100,2002],{},[1811,14102,7008],{"separator":1121},[1680,14104,14105,14107],{},[1683,14106,3840],{},[1677,14108,14109,14111,14113],{},[1683,14110,2002],{},[1811,14112,5598],{},[1687,14114,1914],{},[1811,14116,7558],{"stretchy":1993},[1691,14118,14119],{"encoding":1693},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3590,14122,14123],{},"right = FALSE"," třídy obrátí na ",[1115,14126,14128],{"className":14127},[1668],[1670,14129,14130],{"xmlns":1672},[1674,14131,14132,14158],{},[1677,14133,14134,14136,14142,14144,14156],{},[1811,14135,8539],{"stretchy":1993},[1680,14137,14138,14140],{},[1683,14139,3840],{},[1683,14141,2002],{},[1811,14143,7008],{"separator":1121},[1680,14145,14146,14148],{},[1683,14147,3840],{},[1677,14149,14150,14152,14154],{},[1683,14151,2002],{},[1811,14153,5598],{},[1687,14155,1914],{},[1811,14157,2005],{"stretchy":1993},[1691,14159,14160],{"encoding":1693},"\\langle c_j; c_{j+1})",[1110,14162,14163],{},[4504,14164],{"alt":14165,"className":14166,"src":14167},"mask-ps-histogram-trideni",[1131,4508],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,14169,14171,14178],{"className":14170,"dataCallout":3597},[1106,3596],[1110,14172,14174,14177],{"className":14173},[1113],[1115,14175],{"className":14176,"ariaHidden":1121},[1118,3604,1120],"Příklad: Třídění datového souboru",[1110,14179,14180],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3814,14182,14184],{"className":3816,"code":14183,"language":71,"meta":1603,"style":1603},"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",[3590,14185,14186,14243,14294,14344,14395,14445,14493,14533,14543,14563,14627,14636,14666],{"__ignoreMap":1603},[1115,14187,14188,14191,14193,14195,14197,14200,14202,14205,14207,14210,14212,14215,14217,14219,14221,14223,14225,14227,14229,14232,14234,14236,14238,14241],{"class":3822,"line":10},[1115,14189,14190],{"class":3825},"x9",[1115,14192,3830],{"class":3829},[1115,14194,3956],{"class":3833},[1115,14196,1994],{"class":3837},[1115,14198,14199],{"class":3845},"101",[1115,14201,1917],{"class":3829},[1115,14203,14204],{"class":3845}," 338",[1115,14206,1917],{"class":3829},[1115,14208,14209],{"class":3845}," 150",[1115,14211,1917],{"class":3829},[1115,14213,14214],{"class":3845}," 47",[1115,14216,1917],{"class":3829},[1115,14218,9591],{"class":3845},[1115,14220,1917],{"class":3829},[1115,14222,4301],{"class":3845},[1115,14224,1917],{"class":3829},[1115,14226,3855],{"class":3845},[1115,14228,1917],{"class":3829},[1115,14230,14231],{"class":3845}," 392",[1115,14233,1917],{"class":3829},[1115,14235,10108],{"class":3845},[1115,14237,1917],{"class":3829},[1115,14239,14240],{"class":3845}," 73",[1115,14242,3858],{"class":3829},[1115,14244,14245,14248,14250,14253,14255,14258,14260,14263,14265,14267,14269,14272,14274,14277,14279,14282,14284,14287,14289,14292],{"class":3822,"line":27},[1115,14246,14247],{"class":3845},"        367",[1115,14249,1917],{"class":3829},[1115,14251,14252],{"class":3845}," 54",[1115,14254,1917],{"class":3829},[1115,14256,14257],{"class":3845}," 114",[1115,14259,1917],{"class":3829},[1115,14261,14262],{"class":3845}," 213",[1115,14264,1917],{"class":3829},[1115,14266,3873],{"class":3845},[1115,14268,1917],{"class":3829},[1115,14270,14271],{"class":3845}," 341",[1115,14273,1917],{"class":3829},[1115,14275,14276],{"class":3845}," 313",[1115,14278,1917],{"class":3829},[1115,14280,14281],{"class":3845}," 112",[1115,14283,1917],{"class":3829},[1115,14285,14286],{"class":3845}," 343",[1115,14288,1917],{"class":3829},[1115,14290,14291],{"class":3845}," 151",[1115,14293,3858],{"class":3829},[1115,14295,14296,14299,14301,14304,14306,14309,14311,14314,14316,14319,14321,14323,14325,14328,14330,14332,14334,14337,14339,14342],{"class":3822,"line":148},[1115,14297,14298],{"class":3845},"        9",[1115,14300,1917],{"class":3829},[1115,14302,14303],{"class":3845}," 160",[1115,14305,1917],{"class":3829},[1115,14307,14308],{"class":3845}," 18",[1115,14310,1917],{"class":3829},[1115,14312,14313],{"class":3845}," 113",[1115,14315,1917],{"class":3829},[1115,14317,14318],{"class":3845}," 77",[1115,14320,1917],{"class":3829},[1115,14322,3873],{"class":3845},[1115,14324,1917],{"class":3829},[1115,14326,14327],{"class":3845}," 159",[1115,14329,1917],{"class":3829},[1115,14331,3855],{"class":3845},[1115,14333,1917],{"class":3829},[1115,14335,14336],{"class":3845}," 119",[1115,14338,1917],{"class":3829},[1115,14340,14341],{"class":3845}," 130",[1115,14343,3858],{"class":3829},[1115,14345,14346,14349,14351,14354,14356,14359,14361,14363,14365,14368,14370,14373,14375,14378,14380,14383,14385,14388,14390,14393],{"class":3822,"line":111},[1115,14347,14348],{"class":3845},"        140",[1115,14350,1917],{"class":3829},[1115,14352,14353],{"class":3845}," 161",[1115,14355,1917],{"class":3829},[1115,14357,14358],{"class":3845}," 379",[1115,14360,1917],{"class":3829},[1115,14362,14252],{"class":3845},[1115,14364,1917],{"class":3829},[1115,14366,14367],{"class":3845}," 373",[1115,14369,1917],{"class":3829},[1115,14371,14372],{"class":3845}," 168",[1115,14374,1917],{"class":3829},[1115,14376,14377],{"class":3845}," 365",[1115,14379,1917],{"class":3829},[1115,14381,14382],{"class":3845}," 110",[1115,14384,1917],{"class":3829},[1115,14386,14387],{"class":3845}," 145",[1115,14389,1917],{"class":3829},[1115,14391,14392],{"class":3845}," 88",[1115,14394,3858],{"class":3829},[1115,14396,14397,14400,14402,14405,14407,14410,14412,14415,14417,14420,14422,14424,14426,14429,14431,14433,14435,14438,14440,14443],{"class":3822,"line":96},[1115,14398,14399],{"class":3845},"        74",[1115,14401,1917],{"class":3829},[1115,14403,14404],{"class":3845}," 46",[1115,14406,1917],{"class":3829},[1115,14408,14409],{"class":3845}," 246",[1115,14411,1917],{"class":3829},[1115,14413,14414],{"class":3845}," 259",[1115,14416,1917],{"class":3829},[1115,14418,14419],{"class":3845}," 19",[1115,14421,1917],{"class":3829},[1115,14423,14336],{"class":3845},[1115,14425,1917],{"class":3829},[1115,14427,14428],{"class":3845}," 48",[1115,14430,1917],{"class":3829},[1115,14432,10969],{"class":3845},[1115,14434,1917],{"class":3829},[1115,14436,14437],{"class":3845}," 163",[1115,14439,1917],{"class":3829},[1115,14441,14442],{"class":3845}," 179",[1115,14444,3858],{"class":3829},[1115,14446,14447,14450,14452,14454,14456,14459,14461,14464,14466,14469,14471,14473,14475,14477,14479,14481,14483,14486,14488,14491],{"class":3822,"line":89},[1115,14448,14449],{"class":3845},"        194",[1115,14451,1917],{"class":3829},[1115,14453,4266],{"class":3845},[1115,14455,1917],{"class":3829},[1115,14457,14458],{"class":3845}," 49",[1115,14460,1917],{"class":3829},[1115,14462,14463],{"class":3845}," 501",[1115,14465,1917],{"class":3829},[1115,14467,14468],{"class":3845}," 193",[1115,14470,1917],{"class":3829},[1115,14472,14419],{"class":3845},[1115,14474,1917],{"class":3829},[1115,14476,10108],{"class":3845},[1115,14478,1917],{"class":3829},[1115,14480,4301],{"class":3845},[1115,14482,1917],{"class":3829},[1115,14484,14485],{"class":3845}," 221",[1115,14487,1917],{"class":3829},[1115,14489,14490],{"class":3845}," 300",[1115,14492,3858],{"class":3829},[1115,14494,14495,14498,14500,14502,14504,14507,14509,14512,14514,14517,14519,14522,14524,14526,14528,14531],{"class":3822,"line":82},[1115,14496,14497],{"class":3845},"        88",[1115,14499,1917],{"class":3829},[1115,14501,3850],{"class":3845},[1115,14503,1917],{"class":3829},[1115,14505,14506],{"class":3845}," 428",[1115,14508,1917],{"class":3829},[1115,14510,14511],{"class":3845}," 249",[1115,14513,1917],{"class":3829},[1115,14515,14516],{"class":3845}," 25",[1115,14518,1917],{"class":3829},[1115,14520,14521],{"class":3845}," 209",[1115,14523,1917],{"class":3829},[1115,14525,14252],{"class":3845},[1115,14527,1917],{"class":3829},[1115,14529,14530],{"class":3845}," 91",[1115,14532,4022],{"class":3837},[1115,14534,14535,14537,14539,14541],{"class":3822,"line":75},[1115,14536,12241],{"class":3833},[1115,14538,1994],{"class":3837},[1115,14540,14190],{"class":3825},[1115,14542,4022],{"class":3837},[1115,14544,14545,14547,14549,14551,14553,14555,14557,14559,14561],{"class":3822,"line":4012},[1115,14546,11833],{"class":3833},[1115,14548,1994],{"class":3837},[1115,14550,14190],{"class":3825},[1115,14552,4722],{"class":3837},[1115,14554,4759],{"class":3829},[1115,14556,12312],{"class":3833},[1115,14558,1994],{"class":3837},[1115,14560,14190],{"class":3825},[1115,14562,4022],{"class":3837},[1115,14564,14565,14568,14570,14573,14575,14577,14579,14582,14584,14587,14589,14591,14593,14596,14598,14601,14603,14605,14607,14609,14612,14614,14616,14618,14621,14623,14625],{"class":3822,"line":72},[1115,14566,14567],{"class":3825},"y9",[1115,14569,3830],{"class":3829},[1115,14571,14572],{"class":3833}," hist",[1115,14574,1994],{"class":3837},[1115,14576,14190],{"class":3825},[1115,14578,1917],{"class":3829},[1115,14580,14581],{"class":3825}," br",[1115,14583,3918],{"class":3829},[1115,14585,14586],{"class":3833}," seq",[1115,14588,1994],{"class":3837},[1115,14590,1689],{"class":3845},[1115,14592,1917],{"class":3829},[1115,14594,14595],{"class":3845}," 550",[1115,14597,1917],{"class":3829},[1115,14599,14600],{"class":3825}," by",[1115,14602,3918],{"class":3829},[1115,14604,6366],{"class":3845},[1115,14606,2005],{"class":3837},[1115,14608,1917],{"class":3829},[1115,14610,14611],{"class":3825}," right",[1115,14613,3918],{"class":3829},[1115,14615,6459],{"class":3845},[1115,14617,1917],{"class":3829},[1115,14619,14620],{"class":3825}," plot",[1115,14622,3918],{"class":3829},[1115,14624,6459],{"class":3845},[1115,14626,4022],{"class":3837},[1115,14628,14629,14631,14633],{"class":3822,"line":25},[1115,14630,14567],{"class":3825},[1115,14632,4035],{"class":3829},[1115,14634,14635],{"class":3825},"counts\n",[1115,14637,14638,14640,14642,14644,14646,14649,14651,14654,14656,14658,14660,14662,14664],{"class":3822,"line":65},[1115,14639,10094],{"class":3833},[1115,14641,1994],{"class":3837},[1115,14643,14567],{"class":3825},[1115,14645,4035],{"class":3829},[1115,14647,14648],{"class":3825},"counts",[1115,14650,10189],{"class":3829},[1115,14652,14653],{"class":3833}," length",[1115,14655,1994],{"class":3837},[1115,14657,14190],{"class":3825},[1115,14659,2005],{"class":3837},[1115,14661,1917],{"class":3829},[1115,14663,10969],{"class":3845},[1115,14665,4022],{"class":3837},[1115,14667,14668,14670,14672,14674,14676,14678,14680,14682],{"class":3822,"line":63},[1115,14669,12252],{"class":3833},[1115,14671,1994],{"class":3837},[1115,14673,14190],{"class":3825},[1115,14675,12291],{"class":3837},[1115,14677,12274],{"class":3833},[1115,14679,1994],{"class":3837},[1115,14681,14190],{"class":3825},[1115,14683,4022],{"class":3837},[3814,14685,14688],{"className":14686,"code":14687,"language":4044,"meta":1603},[4042],"[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",[3590,14689,14687],{"__ignoreMap":1603},[1110,14691,14692,14693,14721],{},"Variační rozpětí je ",[1115,14694,14696],{"className":14695},[1668],[1670,14697,14698],{"xmlns":1672},[1674,14699,14700,14718],{},[1677,14701,14702,14704,14706,14709,14711,14713,14715],{},[1683,14703,10337],{},[1811,14705,2101],{},[1687,14707,14708],{},"501",[1811,14710,3184],{},[1687,14712,1713],{},[1811,14714,2101],{},[1687,14716,14717],{},"499",[1691,14719,14720],{"encoding":1693},"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:",[1158,14723,14724,14820],{},[1161,14725,14726],{},[1164,14727,14728,14743,14762,14781,14800],{},[1167,14729,14730],{},[1115,14731,14733],{"className":14732},[1668],[1670,14734,14735],{"xmlns":1672},[1674,14736,14737,14741],{},[1677,14738,14739],{},[1683,14740,2002],{},[1691,14742,2002],{"encoding":1693},[1167,14744,14745],{},[1115,14746,14748],{"className":14747},[1668],[1670,14749,14750],{"xmlns":1672},[1674,14751,14752,14760],{},[1677,14753,14754],{},[1680,14755,14756,14758],{},[1683,14757,11314],{},[1683,14759,2002],{},[1691,14761,13800],{"encoding":1693},[1167,14763,14764],{},[1115,14765,14767],{"className":14766},[1668],[1670,14768,14769],{"xmlns":1672},[1674,14770,14771,14779],{},[1677,14772,14773],{},[1680,14774,14775,14777],{},[1683,14776,9039],{},[1683,14778,2002],{},[1691,14780,13880],{"encoding":1693},[1167,14782,14783],{},[1115,14784,14786],{"className":14785},[1668],[1670,14787,14788],{"xmlns":1672},[1674,14789,14790,14798],{},[1677,14791,14792],{},[1680,14793,14794,14796],{},[1683,14795,6885],{},[1683,14797,2002],{},[1691,14799,13901],{"encoding":1693},[1167,14801,14802],{},[1115,14803,14805],{"className":14804},[1668],[1670,14806,14807],{"xmlns":1672},[1674,14808,14809,14817],{},[1677,14810,14811],{},[1680,14812,14813,14815],{},[1683,14814,1110],{},[1683,14816,2002],{},[1691,14818,14819],{"encoding":1693},"p_j",[1174,14821,14822,14837,14852,14867,14880,14895,14910,14924,14939,14953,14968],{},[1164,14823,14824,14826,14829,14831,14834],{},[1179,14825,1914],{},[1179,14827,14828],{},"⟨0; 50)",[1179,14830,4179],{},[1179,14832,14833],{},"19",[1179,14835,14836],{},"0,279",[1164,14838,14839,14841,14844,14847,14849],{},[1179,14840,1713],{},[1179,14842,14843],{},"⟨50; 100)",[1179,14845,14846],{},"75",[1179,14848,2374],{},[1179,14850,14851],{},"0,162",[1164,14853,14854,14856,14859,14862,14864],{},[1179,14855,3712],{},[1179,14857,14858],{},"⟨100; 150)",[1179,14860,14861],{},"125",[1179,14863,9147],{},[1179,14865,14866],{},"0,147",[1164,14868,14869,14871,14874,14876,14878],{},[1179,14870,3662],{},[1179,14872,14873],{},"⟨150; 200)",[1179,14875,7594],{},[1179,14877,9147],{},[1179,14879,14866],{},[1164,14881,14882,14884,14887,14890,14892],{},[1179,14883,10040],{},[1179,14885,14886],{},"⟨200; 250)",[1179,14888,14889],{},"225",[1179,14891,10040],{},[1179,14893,14894],{},"0,074",[1164,14896,14897,14899,14902,14905,14907],{},[1179,14898,4085],{},[1179,14900,14901],{},"⟨250; 300)",[1179,14903,14904],{},"275",[1179,14906,1914],{},[1179,14908,14909],{},"0,015",[1164,14911,14912,14914,14917,14920,14922],{},[1179,14913,13444],{},[1179,14915,14916],{},"⟨300; 350)",[1179,14918,14919],{},"325",[1179,14921,10040],{},[1179,14923,14894],{},[1164,14925,14926,14929,14932,14935,14937],{},[1179,14927,14928],{},"8",[1179,14930,14931],{},"⟨350; 400)",[1179,14933,14934],{},"375",[1179,14936,10040],{},[1179,14938,14894],{},[1164,14940,14941,14943,14946,14949,14951],{},[1179,14942,3715],{},[1179,14944,14945],{},"⟨400; 450)",[1179,14947,14948],{},"425",[1179,14950,1914],{},[1179,14952,14909],{},[1164,14954,14955,14957,14960,14963,14965],{},[1179,14956,9147],{},[1179,14958,14959],{},"⟨450; 500)",[1179,14961,14962],{},"475",[1179,14964,1689],{},[1179,14966,14967],{},"0,000",[1164,14969,14970,14972,14975,14978,14980],{},[1179,14971,2374],{},[1179,14973,14974],{},"⟨500; ∞)",[1179,14976,14977],{},"525",[1179,14979,1914],{},[1179,14981,14909],{},[1110,14983,14984,14985,15002,15003,15020,15021,3071,15044,3071,15072,15091,15092,3071,15115,15134],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,14986,14988],{"className":14987},[1668],[1670,14989,14990],{"xmlns":1672},[1674,14991,14992,15000],{},[1677,14993,14994],{},[1680,14995,14996,14998],{},[1683,14997,9039],{},[1683,14999,2002],{},[1691,15001,13880],{"encoding":1693}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,15004,15006],{"className":15005},[1668],[1670,15007,15008],{"xmlns":1672},[1674,15009,15010,15018],{},[1677,15011,15012],{},[1680,15013,15014,15016],{},[1683,15015,9039],{},[1683,15017,2002],{},[1691,15019,13880],{"encoding":1693},") vycházejí ",[1115,15022,15024],{"className":15023},[1668],[1670,15025,15026],{"xmlns":1672},[1674,15027,15028,15041],{},[1677,15029,15030,15036,15038],{},[2843,15031,15032,15034],{"accent":1121},[1683,15033,6834],{},[1811,15035,11573],{},[1811,15037,9554],{},[1687,15039,15040],{},"149,26",[1691,15042,15043],{"encoding":1693},"\\bar{x} \\approx 149{,}26",[1115,15045,15047],{"className":15046},[1668],[1670,15048,15049],{"xmlns":1672},[1674,15050,15051,15069],{},[1677,15052,15053,15059,15061,15064,15066],{},[1706,15054,15055,15057],{},[1683,15056,1974],{},[1687,15058,1713],{},[1811,15060,9554],{},[1687,15062,15063],{},"15",[3028,15065,3030],{},[1687,15067,15068],{},"484,5",[1691,15070,15071],{"encoding":1693},"s^2 \\approx 15\\,484{,}5",[1115,15073,15075],{"className":15074},[1668],[1670,15076,15077],{"xmlns":1672},[1674,15078,15079,15088],{},[1677,15080,15081,15083,15085],{},[1683,15082,1974],{},[1811,15084,9554],{},[1687,15086,15087],{},"124,44",[1691,15089,15090],{"encoding":1693},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,15093,15095],{"className":15094},[1668],[1670,15096,15097],{"xmlns":1672},[1674,15098,15099,15112],{},[1677,15100,15101,15107,15109],{},[2843,15102,15103,15105],{"accent":1121},[1683,15104,6834],{},[1811,15106,11573],{},[1811,15108,2101],{},[1687,15110,15111],{},"145,44",[1691,15113,15114],{"encoding":1693},"\\bar{x}=145{,}44",[1115,15116,15118],{"className":15117},[1668],[1670,15119,15120],{"xmlns":1672},[1674,15121,15122,15131],{},[1677,15123,15124,15126,15128],{},[1683,15125,1974],{},[1811,15127,2101],{},[1687,15129,15130],{},"126,13",[1691,15132,15133],{"encoding":1693},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,15136,15137,15138,15141,15142,15178,15179,15197,15198,15212,15213,15239,15240,15242,15243,4987],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1136,15139,15140],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,15143,15145],{"className":15144},[1668],[1670,15146,15147],{"xmlns":1672},[1674,15148,15149,15175],{},[1677,15150,15151,15153,15155,15157,15159,15161,15163],{},[1683,15152,6885],{},[1811,15154,1994],{"stretchy":1993},[1683,15156,6834],{},[1811,15158,2005],{"stretchy":1993},[1811,15160,2101],{},[1683,15162,9826],{},[1706,15164,15165,15167],{},[1683,15166,8706],{},[1677,15168,15169,15171,15173],{},[1811,15170,3184],{},[1683,15172,9826],{},[1683,15174,6834],{},[1691,15176,15177],{"encoding":1693},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,15180,15182],{"className":15181},[1668],[1670,15183,15184],{"xmlns":1672},[1674,15185,15186,15194],{},[1677,15187,15188,15190,15192],{},[1683,15189,6834],{},[1811,15191,3471],{},[1687,15193,1689],{},[1691,15195,15196],{"encoding":1693},"x \\ge 0",", s parametrem ",[1115,15199,15201],{"className":15200},[1668],[1670,15202,15203],{"xmlns":1672},[1674,15204,15205,15209],{},[1677,15206,15207],{},[1683,15208,9826],{},[1691,15210,15211],{"encoding":1693},"\\lambda"," odhadnutým jako ",[1115,15214,15216],{"className":15215},[1668],[1670,15217,15218],{"xmlns":1672},[1674,15219,15220,15236],{},[1677,15221,15222,15224,15226,15228,15230],{},[1683,15223,9826],{},[1811,15225,2101],{},[1687,15227,1914],{},[1683,15229,4725],{"mathvariant":2240},[2843,15231,15232,15234],{"accent":1121},[1683,15233,6834],{},[1811,15235,11573],{},[1691,15237,15238],{"encoding":1693},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3590,15241,9993],{}," parametrem ",[3590,15244,15245],{},"dexp()",[3814,15247,15249],{"className":3816,"code":15248,"language":71,"meta":1603,"style":1603},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3590,15250,15251,15270],{"__ignoreMap":1603},[1115,15252,15253,15256,15258,15260,15262,15264,15266,15268],{"class":3822,"line":10},[1115,15254,15255],{"class":3825},"rate9",[1115,15257,3830],{"class":3829},[1115,15259,4762],{"class":3845},[1115,15261,10189],{"class":3829},[1115,15263,9345],{"class":3833},[1115,15265,1994],{"class":3837},[1115,15267,14190],{"class":3825},[1115,15269,4022],{"class":3837},[1115,15271,15272],{"class":3822,"line":27},[1115,15273,15274],{"class":3825},"rate9\n",[3814,15276,15279],{"className":15277,"code":15278,"language":4044,"meta":1603},[4042],"[1] 0.006875632\n",[3590,15280,15278],{"__ignoreMap":1603},[1110,15282,15283],{},[4504,15284],{"alt":15285,"className":15286,"src":15287},"mask-ps-hustota-fit",[1131,4508],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,15289,15290,15291,1497],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1127,15292,1527],{"className":15293,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1103,15295,15297,15304],{"className":15296,"dataCallout":3597},[1106,3596],[1110,15298,15300,15303],{"className":15299},[1113],[1115,15301],{"className":15302,"ariaHidden":1121},[1118,3604,1120],"Příklad: Doba života výrobku",[1110,15305,15306],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3814,15308,15310],{"className":3816,"code":15309,"language":71,"meta":1603,"style":1603},"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",[3590,15311,15312,15373,15424,15475,15526,15578,15588,15614,15634,15692,15701,15709],{"__ignoreMap":1603},[1115,15313,15314,15317,15319,15321,15323,15326,15328,15331,15333,15336,15338,15341,15343,15346,15348,15351,15353,15356,15358,15361,15363,15366,15368,15371],{"class":3822,"line":10},[1115,15315,15316],{"class":3825},"x5",[1115,15318,3830],{"class":3829},[1115,15320,3956],{"class":3833},[1115,15322,1994],{"class":3837},[1115,15324,15325],{"class":3845},"63",[1115,15327,1917],{"class":3829},[1115,15329,15330],{"class":3845}," 156",[1115,15332,1917],{"class":3829},[1115,15334,15335],{"class":3845}," 184",[1115,15337,1917],{"class":3829},[1115,15339,15340],{"class":3845}," 786",[1115,15342,1917],{"class":3829},[1115,15344,15345],{"class":3845}," 822",[1115,15347,1917],{"class":3829},[1115,15349,15350],{"class":3845}," 278",[1115,15352,1917],{"class":3829},[1115,15354,15355],{"class":3845}," 15",[1115,15357,1917],{"class":3829},[1115,15359,15360],{"class":3845}," 561",[1115,15362,1917],{"class":3829},[1115,15364,15365],{"class":3845}," 229",[1115,15367,1917],{"class":3829},[1115,15369,15370],{"class":3845}," 8",[1115,15372,3858],{"class":3829},[1115,15374,15375,15378,15380,15383,15385,15387,15389,15392,15394,15397,15399,15402,15404,15407,15409,15412,15414,15417,15419,15422],{"class":3822,"line":27},[1115,15376,15377],{"class":3845},"        4",[1115,15379,1917],{"class":3829},[1115,15381,15382],{"class":3845}," 35",[1115,15384,1917],{"class":3829},[1115,15386,14240],{"class":3845},[1115,15388,1917],{"class":3829},[1115,15390,15391],{"class":3845}," 203",[1115,15393,1917],{"class":3829},[1115,15395,15396],{"class":3845}," 178",[1115,15398,1917],{"class":3829},[1115,15400,15401],{"class":3845}," 323",[1115,15403,1917],{"class":3829},[1115,15405,15406],{"class":3845}," 275",[1115,15408,1917],{"class":3829},[1115,15410,15411],{"class":3845}," 176",[1115,15413,1917],{"class":3829},[1115,15415,15416],{"class":3845}," 427",[1115,15418,1917],{"class":3829},[1115,15420,15421],{"class":3845}," 196",[1115,15423,3858],{"class":3829},[1115,15425,15426,15429,15431,15434,15436,15439,15441,15444,15446,15449,15451,15454,15456,15459,15461,15463,15465,15468,15470,15473],{"class":3822,"line":148},[1115,15427,15428],{"class":3845},"        415",[1115,15430,1917],{"class":3829},[1115,15432,15433],{"class":3845}," 140",[1115,15435,1917],{"class":3829},[1115,15437,15438],{"class":3845}," 17",[1115,15440,1917],{"class":3829},[1115,15442,15443],{"class":3845}," 293",[1115,15445,1917],{"class":3829},[1115,15447,15448],{"class":3845}," 991",[1115,15450,1917],{"class":3829},[1115,15452,15453],{"class":3845}," 100",[1115,15455,1917],{"class":3829},[1115,15457,15458],{"class":3845}," 189",[1115,15460,1917],{"class":3829},[1115,15462,15411],{"class":3845},[1115,15464,1917],{"class":3829},[1115,15466,15467],{"class":3845}," 672",[1115,15469,1917],{"class":3829},[1115,15471,15472],{"class":3845}," 134",[1115,15474,3858],{"class":3829},[1115,15476,15477,15480,15482,15485,15487,15490,15492,15495,15497,15499,15501,15504,15506,15509,15511,15514,15516,15519,15521,15524],{"class":3822,"line":111},[1115,15478,15479],{"class":3845},"        529",[1115,15481,1917],{"class":3829},[1115,15483,15484],{"class":3845}," 310",[1115,15486,1917],{"class":3829},[1115,15488,15489],{"class":3845}," 22",[1115,15491,1917],{"class":3829},[1115,15493,15494],{"class":3845}," 69",[1115,15496,1917],{"class":3829},[1115,15498,14341],{"class":3845},[1115,15500,1917],{"class":3829},[1115,15502,15503],{"class":3845}," 272",[1115,15505,1917],{"class":3829},[1115,15507,15508],{"class":3845}," 117",[1115,15510,1917],{"class":3829},[1115,15512,15513],{"class":3845}," 169",[1115,15515,1917],{"class":3829},[1115,15517,15518],{"class":3845}," 466",[1115,15520,1917],{"class":3829},[1115,15522,15523],{"class":3845}," 286",[1115,15525,3858],{"class":3829},[1115,15527,15528,15531,15533,15536,15538,15541,15543,15546,15548,15551,15553,15556,15558,15561,15563,15566,15568,15571,15573,15576],{"class":3822,"line":96},[1115,15529,15530],{"class":3845},"        46",[1115,15532,1917],{"class":3829},[1115,15534,15535],{"class":3845}," 236",[1115,15537,1917],{"class":3829},[1115,15539,15540],{"class":3845}," 387",[1115,15542,1917],{"class":3829},[1115,15544,15545],{"class":3845}," 92",[1115,15547,1917],{"class":3829},[1115,15549,15550],{"class":3845}," 177",[1115,15552,1917],{"class":3829},[1115,15554,15555],{"class":3845}," 188",[1115,15557,1917],{"class":3829},[1115,15559,15560],{"class":3845}," 124",[1115,15562,1917],{"class":3829},[1115,15564,15565],{"class":3845}," 385",[1115,15567,1917],{"class":3829},[1115,15569,15570],{"class":3845}," 174",[1115,15572,1917],{"class":3829},[1115,15574,15575],{"class":3845}," 23",[1115,15577,4022],{"class":3837},[1115,15579,15580,15582,15584,15586],{"class":3822,"line":89},[1115,15581,12241],{"class":3833},[1115,15583,1994],{"class":3837},[1115,15585,15316],{"class":3825},[1115,15587,4022],{"class":3837},[1115,15589,15590,15592,15594,15596,15598,15600,15602,15604,15606,15608,15610,15612],{"class":3822,"line":82},[1115,15591,12252],{"class":3833},[1115,15593,1994],{"class":3837},[1115,15595,15316],{"class":3825},[1115,15597,12291],{"class":3837},[1115,15599,12274],{"class":3833},[1115,15601,1994],{"class":3837},[1115,15603,15316],{"class":3825},[1115,15605,12291],{"class":3837},[1115,15607,12974],{"class":3833},[1115,15609,1994],{"class":3837},[1115,15611,15316],{"class":3825},[1115,15613,4022],{"class":3837},[1115,15615,15616,15618,15620,15622,15624,15626,15628,15630,15632],{"class":3822,"line":75},[1115,15617,11833],{"class":3833},[1115,15619,1994],{"class":3837},[1115,15621,15316],{"class":3825},[1115,15623,4722],{"class":3837},[1115,15625,4759],{"class":3829},[1115,15627,12312],{"class":3833},[1115,15629,1994],{"class":3837},[1115,15631,15316],{"class":3825},[1115,15633,4022],{"class":3837},[1115,15635,15636,15639,15641,15643,15645,15647,15649,15651,15653,15655,15657,15659,15661,15664,15666,15668,15670,15672,15674,15676,15678,15680,15682,15684,15686,15688,15690],{"class":3822,"line":4012},[1115,15637,15638],{"class":3825},"y5",[1115,15640,3830],{"class":3829},[1115,15642,14572],{"class":3833},[1115,15644,1994],{"class":3837},[1115,15646,15316],{"class":3825},[1115,15648,1917],{"class":3829},[1115,15650,14581],{"class":3825},[1115,15652,3918],{"class":3829},[1115,15654,14586],{"class":3833},[1115,15656,1994],{"class":3837},[1115,15658,1689],{"class":3845},[1115,15660,1917],{"class":3829},[1115,15662,15663],{"class":3845}," 1050",[1115,15665,1917],{"class":3829},[1115,15667,14600],{"class":3825},[1115,15669,3918],{"class":3829},[1115,15671,14209],{"class":3845},[1115,15673,2005],{"class":3837},[1115,15675,1917],{"class":3829},[1115,15677,14611],{"class":3825},[1115,15679,3918],{"class":3829},[1115,15681,6459],{"class":3845},[1115,15683,1917],{"class":3829},[1115,15685,14620],{"class":3825},[1115,15687,3918],{"class":3829},[1115,15689,6459],{"class":3845},[1115,15691,4022],{"class":3837},[1115,15693,15694,15696,15698],{"class":3822,"line":72},[1115,15695,15638],{"class":3825},[1115,15697,4035],{"class":3829},[1115,15699,15700],{"class":3825},"mids\n",[1115,15702,15703,15705,15707],{"class":3822,"line":25},[1115,15704,15638],{"class":3825},[1115,15706,4035],{"class":3829},[1115,15708,14635],{"class":3825},[1115,15710,15711,15713,15715,15717,15719,15721,15723,15725,15727,15729,15731,15733,15735],{"class":3822,"line":65},[1115,15712,10094],{"class":3833},[1115,15714,1994],{"class":3837},[1115,15716,15638],{"class":3825},[1115,15718,4035],{"class":3829},[1115,15720,14648],{"class":3825},[1115,15722,10189],{"class":3829},[1115,15724,14653],{"class":3833},[1115,15726,1994],{"class":3837},[1115,15728,15316],{"class":3825},[1115,15730,2005],{"class":3837},[1115,15732,1917],{"class":3829},[1115,15734,10969],{"class":3845},[1115,15736,4022],{"class":3837},[3814,15738,15741],{"className":15739,"code":15740,"language":4044,"meta":1603},[4042],"[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",[3590,15742,15740],{"__ignoreMap":1603},[1110,15744,15745],{},"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.",[1153,15747,6529],{"id":6528},[1503,15749,15750,15768,15869,15937],{},[1265,15751,15752,1418,15755,15758,15759,15762,15763,15765,15766,1497],{},[1136,15753,15754],{},"Výchozí typ kvantilu v R.",[3590,15756,15757],{},"quantile()"," bez argumentu ",[3590,15760,15761],{},"type"," používá jiný výpočetní vzorec (",[3590,15764,12405],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3590,15767,12401],{},[1265,15769,15770,15775,15776,15778,15779,15814,15815,15850,15851,15868],{},[1136,15771,15772,15773,1497],{},"Výchozí ohraničení tříd v ",[3590,15774,13997],{}," Bez ",[3590,15777,14123],{}," jsou třídy zprava uzavřené, ",[1115,15780,15782],{"className":15781},[1668],[1670,15783,15784],{"xmlns":1672},[1674,15785,15786,15812],{},[1677,15787,15788,15790,15796,15798,15810],{},[1811,15789,1994],{"stretchy":1993},[1680,15791,15792,15794],{},[1683,15793,3840],{},[1683,15795,2002],{},[1811,15797,7008],{"separator":1121},[1680,15799,15800,15802],{},[1683,15801,3840],{},[1677,15803,15804,15806,15808],{},[1683,15805,2002],{},[1811,15807,5598],{},[1687,15809,1914],{},[1811,15811,7558],{"stretchy":1993},[1691,15813,14119],{"encoding":1693}," — opačně než konvence ",[1115,15816,15818],{"className":15817},[1668],[1670,15819,15820],{"xmlns":1672},[1674,15821,15822,15848],{},[1677,15823,15824,15826,15832,15834,15846],{},[1811,15825,8539],{"stretchy":1993},[1680,15827,15828,15830],{},[1683,15829,3840],{},[1683,15831,2002],{},[1811,15833,7008],{"separator":1121},[1680,15835,15836,15838],{},[1683,15837,3840],{},[1677,15839,15840,15842,15844],{},[1683,15841,2002],{},[1811,15843,5598],{},[1687,15845,1914],{},[1811,15847,2005],{"stretchy":1993},[1691,15849,14160],{"encoding":1693}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,15852,15854],{"className":15853},[1668],[1670,15855,15856],{"xmlns":1672},[1674,15857,15858,15866],{},[1677,15859,15860],{},[1680,15861,15862,15864],{},[1683,15863,6885],{},[1683,15865,2002],{},[1691,15867,13901],{"encoding":1693}," vyjdou jinak.",[1265,15870,15871,1418,15874,15892,15893,15906,15907,9162,15920,1497],{},[1136,15872,15873],{},"Rozptyl vs. směrodatná odchylka.",[1115,15875,15877],{"className":15876},[1668],[1670,15878,15879],{"xmlns":1672},[1674,15880,15881,15889],{},[1677,15882,15883],{},[1706,15884,15885,15887],{},[1683,15886,1974],{},[1687,15888,1713],{},[1691,15890,15891],{"encoding":1693},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,15894,15896],{"className":15895},[1668],[1670,15897,15898],{"xmlns":1672},[1674,15899,15900,15904],{},[1677,15901,15902],{},[1683,15903,1974],{},[1691,15905,1974],{"encoding":1693}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,15908,15910],{"className":15909},[1668],[1670,15911,15912],{"xmlns":1672},[1674,15913,15914,15918],{},[1677,15915,15916],{},[1683,15917,1974],{},[1691,15919,1974],{"encoding":1693},[1115,15921,15923],{"className":15922},[1668],[1670,15924,15925],{"xmlns":1672},[1674,15926,15927,15935],{},[1677,15928,15929],{},[1706,15930,15931,15933],{},[1683,15932,1974],{},[1687,15934,1713],{},[1691,15936,15891],{"encoding":1693},[1265,15938,15939,15942],{},[1136,15940,15941],{},"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.",[1153,15944,1501],{"id":1500},[1503,15946,15947,15952,15957,15962,15967,15972,15977],{},[1265,15948,15949],{},[1127,15950,1133],{"className":15951,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,15953,15954],{},[1127,15955,1515],{"className":15956,"dataFsResolvedFilePath":1275,"href":1273},[1131],[1265,15958,15959],{},[1127,15960,1527],{"className":15961,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1265,15963,15964],{},[1127,15965,1306],{"className":15966,"dataFsResolvedFilePath":1312,"href":1310},[1131],[1265,15968,15969],{},[1127,15970,1318],{"className":15971,"dataFsResolvedFilePath":1324,"href":1322},[1131],[1265,15973,15974],{},[1127,15975,1543],{"className":15976,"dataFsResolvedFilePath":1336,"href":1334},[1131],[1265,15978,15979],{},[1127,15980,6753],{"className":15981,"dataFsResolvedFilePath":1550,"href":1548},[1131],[1153,15983,1554],{"id":934},[1110,15985,1557,15986,1561],{},[1420,15987,1560],{},[6761,15989,15990],{},"html pre.shiki code .sP4rz, html 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příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":16014,"title":1306,"body":16015,"course":23,"courses":1614,"created":1615,"description":1603,"extension":1616,"meta":20705,"navigation":1618,"path":20706,"seo":20707,"sources":20708,"stem":20711,"tags":20712,"type":6782,"updated":1615,"__hash__":20713},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":16016,"toc":20678},[16017,16020,16247,16249,16317,16323,16326,16404,16415,16419,16638,16645,16705,16708,16715,16737,16741,16747,16809,16859,16864,16875,16987,16993,17123,17126,17164,17170,17289,17306,17433,17439,17483,17487,17500,17528,17534,17591,17618,17624,17680,17700,17706,17727,17734,17737,17976,17980,18092,18412,18469,18511,18518,18522,18528,18652,18658,18707,18711,18717,18778,18784,18823,18867,18873,18966,18970,18976,19018,19024,19084,19195,19301,19305,19310,19388,19423,19454,19514,19551,19558,19621,19624,19645,19651,19681,19724,19728,19745,19865,19869,19891,19895,19906,20007,20011,20083,20090,20093,20096,20107,20174,20177,20181,20205,20208,20211,20415,20424,20454,20456,20591,20604,20617,20630,20632,20669,20671,20675],[1099,16018,1306],{"id":16019},"regresní-a-korelační-analýza",[1103,16021,16023,16029],{"className":16022,"dataCallout":1641},[1106,1640],[1110,16024,16026,1649],{"className":16025},[1113],[1115,16027],{"className":16028,"ariaHidden":1121},[1118,1648,1120],[1503,16030,16031,16069,16116,16194,16208,16214],{},[1265,16032,16033,16036,16037,16050,16051,16064,16065,16068],{},[1136,16034,16035],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,16038,16040],{"className":16039},[1668],[1670,16041,16042],{"xmlns":1672},[1674,16043,16044,16048],{},[1677,16045,16046],{},[1683,16047,7244],{},[1691,16049,7244],{"encoding":1693}," na vysvětlujících proměnných ",[1115,16052,16054],{"className":16053},[1668],[1670,16055,16056],{"xmlns":1672},[1674,16057,16058,16062],{},[1677,16059,16060],{},[1683,16061,6834],{},[1691,16063,6834],{"encoding":1693}," (příčina → následek); ",[1136,16066,16067],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1265,16070,16071,16072,16075,16076,1497],{},"Parametry regresní funkce se odhadují ",[1136,16073,16074],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,16077,16079],{"className":16078},[1668],[1670,16080,16081],{"xmlns":1672},[1674,16082,16083,16113],{},[1677,16084,16085,16087,16089,16095,16097,16107],{},[1811,16086,2107],{},[1811,16088,1994],{"stretchy":1993},[1680,16090,16091,16093],{},[1683,16092,7244],{},[1683,16094,1997],{},[1811,16096,3184],{},[1680,16098,16099,16105],{},[2843,16100,16101,16103],{"accent":1121},[1683,16102,7244],{},[1811,16104,2849],{},[1683,16106,1997],{},[1706,16108,16109,16111],{},[1811,16110,2005],{"stretchy":1993},[1687,16112,1713],{},[1691,16114,16115],{"encoding":1693},"\\sum(y_i-\\hat y_i)^2",[1265,16117,16118,16119,1418,16122,16140,16141,1418,16144,16168,16169,1418,16172,1497],{},"Kvalitu fitu měří ",[1136,16120,16121],{},"index determinace",[1115,16123,16125],{"className":16124},[1668],[1670,16126,16127],{"xmlns":1672},[1674,16128,16129,16137],{},[1677,16130,16131],{},[1706,16132,16133,16135],{},[1683,16134,10337],{},[1687,16136,1713],{},[1691,16138,16139],{"encoding":1693},"R^2","; obecnou těsnost závislosti ",[1136,16142,16143],{},"index korelace",[1115,16145,16147],{"className":16146},[1668],[1670,16148,16149],{"xmlns":1672},[1674,16150,16151,16165],{},[1677,16152,16153,16155,16157],{},[1683,16154,11314],{},[1811,16156,2101],{},[4574,16158,16159],{},[1706,16160,16161,16163],{},[1683,16162,10337],{},[1687,16164,1713],{},[1691,16166,16167],{"encoding":1693},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1136,16170,16171],{},"koeficientu korelace",[1115,16173,16175],{"className":16174},[1668],[1670,16176,16177],{"xmlns":1672},[1674,16178,16179,16191],{},[1677,16180,16181],{},[1680,16182,16183,16185],{},[1683,16184,71],{},[1677,16186,16187,16189],{},[1683,16188,6834],{},[1683,16190,7244],{},[1691,16192,16193],{"encoding":1693},"r_{xy}",[1265,16195,16196,16197,16200,16201,16204,16205,1277],{},"Když přímka nestačí, volí se ",[1136,16198,16199],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1136,16202,16203],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3590,16206,16207],{},"nls2",[1265,16209,16210,16213],{},[1136,16211,16212],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1265,16215,16216,16217,3071,16220,3071,16223,3071,16226,3071,16229,3071,16232,3071,16235,3071,16238,3071,16241,3071,16244,1497],{},"V R: ",[3590,16218,16219],{},"lm()",[3590,16221,16222],{},"nls2()",[3590,16224,16225],{},"summary()",[3590,16227,16228],{},"confint()",[3590,16230,16231],{},"predict()",[3590,16233,16234],{},"step()",[3590,16236,16237],{},"car::vif()",[3590,16239,16240],{},"lmtest::dwtest()",[3590,16242,16243],{},"whitestrap::white_test()",[3590,16245,16246],{},"shapiro.test()",[1153,16248,11351],{"id":11350},[1110,16250,16251,16254,16255,5862,16268,16281,16282,16284,16285,16298,16299,16312,16313,16316],{},[1127,16252,1133],{"className":16253,"dataFsResolvedFilePath":1132,"href":1129},[1131]," pracuje se dvěma znaky ",[1115,16256,16258],{"className":16257},[1668],[1670,16259,16260],{"xmlns":1672},[1674,16261,16262,16266],{},[1677,16263,16264],{},[1683,16265,6834],{},[1691,16267,6834],{"encoding":1693},[1115,16269,16271],{"className":16270},[1668],[1670,16272,16273],{"xmlns":1672},[1674,16274,16275,16279],{},[1677,16276,16277],{},[1683,16278,7244],{},[1691,16280,7244],{"encoding":1693}," zjištěnými na stejných jednotkách. ",[1136,16283,16035],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,16286,16288],{"className":16287},[1668],[1670,16289,16290],{"xmlns":1672},[1674,16291,16292,16296],{},[1677,16293,16294],{},[1683,16295,6834],{},[1691,16297,6834],{"encoding":1693}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,16300,16302],{"className":16301},[1668],[1670,16303,16304],{"xmlns":1672},[1674,16305,16306,16310],{},[1677,16307,16308],{},[1683,16309,7244],{},[1691,16311,7244],{"encoding":1693}," v úloze následku. ",[1136,16314,16315],{},"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.",[1110,16318,16319,16320,1277],{},"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 (",[1136,16321,16322],{},"regresní funkce",[1110,16324,16325],{},"Druh regresní analýzy určuje struktura datového souboru:",[1503,16327,16328,16365],{},[1265,16329,16330,16333,16334,16347,16348,16361,16362,1917],{},[1136,16331,16332],{},"dvourozměrný datový soubor"," (jedna ",[1115,16335,16337],{"className":16336},[1668],[1670,16338,16339],{"xmlns":1672},[1674,16340,16341,16345],{},[1677,16342,16343],{},[1683,16344,6834],{},[1691,16346,6834],{"encoding":1693},", jedna ",[1115,16349,16351],{"className":16350},[1668],[1670,16352,16353],{"xmlns":1672},[1674,16354,16355,16359],{},[1677,16356,16357],{},[1683,16358,7244],{},[1691,16360,7244],{"encoding":1693},") → ",[1136,16363,16364],{},"regresní analýza dvou proměnných",[1265,16366,16367,16370,16371,16361,16401,1497],{},[1136,16368,16369],{},"vícerozměrný datový soubor"," (více ",[1115,16372,16374],{"className":16373},[1668],[1670,16375,16376],{"xmlns":1672},[1674,16377,16378,16398],{},[1677,16379,16380,16386,16388,16390,16392],{},[1680,16381,16382,16384],{},[1683,16383,6834],{},[1687,16385,1914],{},[1811,16387,1917],{"separator":1121},[1811,16389,1920],{},[1811,16391,1917],{"separator":1121},[1680,16393,16394,16396],{},[1683,16395,6834],{},[1683,16397,1110],{},[1691,16399,16400],{"encoding":1693},"x_1,\\dots,x_p",[1136,16402,16403],{},"vícenásobná regresní analýza",[1110,16405,16406,16407,16410,16411,16414],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1136,16408,16409],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1136,16412,16413],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1153,16416,16418],{"id":16417},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,16420,16421,16422,1418,16425,16479,16480,16498,16499,1418,16502,16558,16559,16577,16578,16595,16596,16634,16635,1497],{},"Rozlišují se ",[1136,16423,16424],{},"teoretická regresní funkce",[1115,16426,16428],{"className":16427},[1668],[1670,16429,16430],{"xmlns":1672},[1674,16431,16432,16476],{},[1677,16433,16434,16437,16439,16441,16443,16445,16447,16454,16456,16462,16464,16466,16468,16474],{},[1683,16435,16436],{},"η",[1811,16438,2101],{},[1683,16440,6885],{},[1811,16442,1994],{"stretchy":1993},[1683,16444,6834],{},[1811,16446,7008],{"separator":1121},[1680,16448,16449,16452],{},[1683,16450,16451],{},"β",[1687,16453,1689],{},[1811,16455,1917],{"separator":1121},[1680,16457,16458,16460],{},[1683,16459,16451],{},[1687,16461,1914],{},[1811,16463,1917],{"separator":1121},[1811,16465,1920],{},[1811,16467,1917],{"separator":1121},[1680,16469,16470,16472],{},[1683,16471,16451],{},[1683,16473,1110],{},[1811,16475,2005],{"stretchy":1993},[1691,16477,16478],{"encoding":1693},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,16481,16483],{"className":16482},[1668],[1670,16484,16485],{"xmlns":1672},[1674,16486,16487,16495],{},[1677,16488,16489],{},[1680,16490,16491,16493],{},[1683,16492,16451],{},[1683,16494,1997],{},[1691,16496,16497],{"encoding":1693},"\\beta_i"," — a ",[1136,16500,16501],{},"empirická regresní funkce",[1115,16503,16505],{"className":16504},[1668],[1670,16506,16507],{"xmlns":1672},[1674,16508,16509,16555],{},[1677,16510,16511,16517,16519,16521,16523,16525,16527,16533,16535,16541,16543,16545,16547,16553],{},[2843,16512,16513,16515],{"accent":1121},[1683,16514,7244],{},[1811,16516,2849],{},[1811,16518,2101],{},[1683,16520,6885],{},[1811,16522,1994],{"stretchy":1993},[1683,16524,6834],{},[1811,16526,7008],{"separator":1121},[1680,16528,16529,16531],{},[1683,16530,11618],{},[1687,16532,1689],{},[1811,16534,1917],{"separator":1121},[1680,16536,16537,16539],{},[1683,16538,11618],{},[1687,16540,1914],{},[1811,16542,1917],{"separator":1121},[1811,16544,1920],{},[1811,16546,1917],{"separator":1121},[1680,16548,16549,16551],{},[1683,16550,11618],{},[1683,16552,1110],{},[1811,16554,2005],{"stretchy":1993},[1691,16556,16557],{"encoding":1693},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,16560,16562],{"className":16561},[1668],[1670,16563,16564],{"xmlns":1672},[1674,16565,16566,16574],{},[1677,16567,16568],{},[1680,16569,16570,16572],{},[1683,16571,11618],{},[1683,16573,1997],{},[1691,16575,16576],{"encoding":1693},"b_i"," jsou odhadem ",[1115,16579,16581],{"className":16580},[1668],[1670,16582,16583],{"xmlns":1672},[1674,16584,16585,16593],{},[1677,16586,16587],{},[1680,16588,16589,16591],{},[1683,16590,16451],{},[1683,16592,1997],{},[1691,16594,16497],{"encoding":1693}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,16597,16599],{"className":16598},[1668],[1670,16600,16601],{"xmlns":1672},[1674,16602,16603,16631],{},[1677,16604,16605,16611,16613,16619,16621],{},[1680,16606,16607,16609],{},[1683,16608,8706],{},[1683,16610,1997],{},[1811,16612,2101],{},[1680,16614,16615,16617],{},[1683,16616,7244],{},[1683,16618,1997],{},[1811,16620,3184],{},[1680,16622,16623,16629],{},[2843,16624,16625,16627],{"accent":1121},[1683,16626,7244],{},[1811,16628,2849],{},[1683,16630,1997],{},[1691,16632,16633],{"encoding":1693},"e_i=y_i-\\hat y_i",", se nazývají ",[1136,16636,16637],{},"rezidua",[1110,16639,16640,16641,16644],{},"Nejpoužívanější metodou odhadu parametrů je ",[1136,16642,16643],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,16646,16648],{"className":16647},[1668],[1670,16649,16650],{"xmlns":1672,"display":2083},[1674,16651,16652,16702],{},[1677,16653,16654,16668,16670,16676,16678,16688,16694,16696,16698,16700],{},[2103,16655,16656,16658,16666],{},[1811,16657,2107],{},[1677,16659,16660,16662,16664],{},[1683,16661,1997],{},[1811,16663,2101],{},[1687,16665,1914],{},[1683,16667,1809],{},[1811,16669,1994],{"stretchy":1993},[1680,16671,16672,16674],{},[1683,16673,7244],{},[1683,16675,1997],{},[1811,16677,3184],{},[1680,16679,16680,16686],{},[2843,16681,16682,16684],{"accent":1121},[1683,16683,7244],{},[1811,16685,2849],{},[1683,16687,1997],{},[1706,16689,16690,16692],{},[1811,16691,2005],{"stretchy":1993},[1687,16693,1713],{},[1811,16695,7722],{},[1683,16697,4609],{},[1811,16699,4612],{},[1683,16701,1497],{"mathvariant":2240},[1691,16703,16704],{"encoding":1693},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,16706,16707],{},"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.",[1110,16709,16710],{},[4504,16711],{"alt":16712,"className":16713,"src":16714},"mask-ra-primka-rezidua",[1131,4508],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,16716,16717,16718,16736],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,16719,16721],{"className":16720},[1668],[1670,16722,16723],{"xmlns":1672},[1674,16724,16725,16733],{},[1677,16726,16727],{},[1680,16728,16729,16731],{},[1683,16730,8706],{},[1683,16732,1997],{},[1691,16734,16735],{"encoding":1693},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1153,16738,16740],{"id":16739},"regresní-přímka","Regresní přímka",[1110,16742,16743,16744,2077],{},"Nejjednodušší regresní funkcí je ",[1136,16745,16746],{},"regresní přímka",[1115,16748,16750],{"className":16749},[1668],[1670,16751,16752],{"xmlns":1672,"display":2083},[1674,16753,16754,16806],{},[1677,16755,16756,16758,16760,16766,16768,16774,16776,16778,16780,16786,16788,16794,16796,16802,16804],{},[1683,16757,16436],{},[1811,16759,2101],{},[1680,16761,16762,16764],{},[1683,16763,16451],{},[1687,16765,1689],{},[1811,16767,5598],{},[1680,16769,16770,16772],{},[1683,16771,16451],{},[1687,16773,1914],{},[1683,16775,6834],{},[1811,16777,1917],{"separator":1121},[2131,16779],{"width":2133},[2843,16781,16782,16784],{"accent":1121},[1683,16783,7244],{},[1811,16785,2849],{},[1811,16787,2101],{},[1680,16789,16790,16792],{},[1683,16791,11618],{},[1687,16793,1689],{},[1811,16795,5598],{},[1680,16797,16798,16800],{},[1683,16799,11618],{},[1687,16801,1914],{},[1683,16803,6834],{},[1683,16805,1497],{"mathvariant":2240},[1691,16807,16808],{"encoding":1693},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,16810,16811,16812,16830,16831,16844,16845,16858],{},"Koeficient ",[1115,16813,16815],{"className":16814},[1668],[1670,16816,16817],{"xmlns":1672},[1674,16818,16819,16827],{},[1677,16820,16821],{},[1680,16822,16823,16825],{},[1683,16824,11618],{},[1687,16826,1914],{},[1691,16828,16829],{"encoding":1693},"b_1"," udává změnu průměru ",[1115,16832,16834],{"className":16833},[1668],[1670,16835,16836],{"xmlns":1672},[1674,16837,16838,16842],{},[1677,16839,16840],{},[1683,16841,7244],{},[1691,16843,7244],{"encoding":1693}," při jednotkové změně ",[1115,16846,16848],{"className":16847},[1668],[1670,16849,16850],{"xmlns":1672},[1674,16851,16852,16856],{},[1677,16853,16854],{},[1683,16855,6834],{},[1691,16857,6834],{"encoding":1693},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[16860,16861,16863],"h3",{"id":16862},"v-r","V R",[1110,16865,16866,16867,16870,16871,16874],{},"Vstupní data se nahrají buď ze souboru (",[3590,16868,16869],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3590,16872,16873],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3814,16876,16878],{"className":3816,"code":16877,"language":71,"meta":1603,"style":1603},"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",[3590,16879,16880,16915,16956,16977],{"__ignoreMap":1603},[1115,16881,16882,16885,16887,16889,16891,16893,16895,16897,16899,16901,16903,16905,16907,16909,16911,16913],{"class":3822,"line":10},[1115,16883,16884],{"class":3825},"pocet_clenu",[1115,16886,3830],{"class":3829},[1115,16888,3956],{"class":3833},[1115,16890,1994],{"class":3837},[1115,16892,1914],{"class":3845},[1115,16894,1917],{"class":3829},[1115,16896,4301],{"class":3845},[1115,16898,1917],{"class":3829},[1115,16900,10969],{"class":3845},[1115,16902,1917],{"class":3829},[1115,16904,3921],{"class":3845},[1115,16906,1917],{"class":3829},[1115,16908,10108],{"class":3845},[1115,16910,1917],{"class":3829},[1115,16912,12342],{"class":3845},[1115,16914,4022],{"class":3837},[1115,16916,16917,16920,16922,16924,16926,16929,16931,16934,16936,16939,16941,16944,16946,16949,16951,16954],{"class":3822,"line":27},[1115,16918,16919],{"class":3825},"tydenni_vydaje",[1115,16921,3830],{"class":3829},[1115,16923,3956],{"class":3833},[1115,16925,1994],{"class":3837},[1115,16927,16928],{"class":3845},"490",[1115,16930,1917],{"class":3829},[1115,16932,16933],{"class":3845}," 820",[1115,16935,1917],{"class":3829},[1115,16937,16938],{"class":3845}," 1230",[1115,16940,1917],{"class":3829},[1115,16942,16943],{"class":3845}," 1570",[1115,16945,1917],{"class":3829},[1115,16947,16948],{"class":3845}," 1950",[1115,16950,1917],{"class":3829},[1115,16952,16953],{"class":3845}," 2320",[1115,16955,4022],{"class":3837},[1115,16957,16958,16960,16962,16965,16967,16969,16972,16975],{"class":3822,"line":148},[1115,16959,786],{"class":3825},[1115,16961,3830],{"class":3829},[1115,16963,16964],{"class":3833}," lm",[1115,16966,1994],{"class":3837},[1115,16968,16919],{"class":3825},[1115,16970,16971],{"class":3829}," ~",[1115,16973,16974],{"class":3825}," pocet_clenu",[1115,16976,4022],{"class":3837},[1115,16978,16979,16981,16983,16985],{"class":3822,"line":111},[1115,16980,1626],{"class":3833},[1115,16982,1994],{"class":3837},[1115,16984,786],{"class":3825},[1115,16986,4022],{"class":3837},[3814,16988,16991],{"className":16989,"code":16990,"language":4044,"meta":1603},[4042],"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",[3590,16992,16990],{"__ignoreMap":1603},[1110,16994,16995,16996,17028,17029,17032,17033,17063,17064,17094,17095,17098,17099,17122],{},"Odhadnutý model je ",[1115,16997,16999],{"className":16998},[1668],[1670,17000,17001],{"xmlns":1672},[1674,17002,17003,17025],{},[1677,17004,17005,17011,17013,17016,17018,17021,17023],{},[2843,17006,17007,17009],{"accent":1121},[1683,17008,7244],{},[1811,17010,2849],{},[1811,17012,2101],{},[1687,17014,17015],{},"108,7",[1811,17017,5598],{},[1687,17019,17020],{},"368,0",[3028,17022,3030],{},[1683,17024,6834],{},[1691,17026,17027],{"encoding":1693},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3590,17030,17031],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,17034,17036],{"className":17035},[1668],[1670,17037,17038],{"xmlns":1672},[1674,17039,17040,17060],{},[1677,17041,17042,17048,17050,17056,17058],{},[1680,17043,17044,17046],{},[1683,17045,1685],{},[1687,17047,1689],{},[1811,17049,2077],{},[1680,17051,17052,17054],{},[1683,17053,16451],{},[1683,17055,1997],{},[1811,17057,2101],{},[1687,17059,1689],{},[1691,17061,17062],{"encoding":1693},"H_0:\\beta_i=0"," proti ",[1115,17065,17067],{"className":17066},[1668],[1670,17068,17069],{"xmlns":1672},[1674,17070,17071,17091],{},[1677,17072,17073,17079,17081,17087,17089],{},[1680,17074,17075,17077],{},[1683,17076,1685],{},[1687,17078,1914],{},[1811,17080,2077],{},[1680,17082,17083,17085],{},[1683,17084,16451],{},[1683,17086,1997],{},[1811,17088,11070],{"mathvariant":2240},[1687,17090,1689],{},[1691,17092,17093],{"encoding":1693},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3590,17096,17097],{},"Multiple R-squared"," je index determinace ",[1115,17100,17102],{"className":17101},[1668],[1670,17103,17104],{"xmlns":1672},[1674,17105,17106,17119],{},[1677,17107,17108,17114,17116],{},[1706,17109,17110,17112],{},[1683,17111,10337],{},[1687,17113,1713],{},[1811,17115,2101],{},[1687,17117,17118],{},"0,9995",[1691,17120,17121],{"encoding":1693},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,17124,17125],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3814,17127,17129],{"className":3816,"code":17128,"language":71,"meta":1603,"style":1603},"coef(model)\nfitted(model)\nresiduals(model)\n",[3590,17130,17131,17142,17153],{"__ignoreMap":1603},[1115,17132,17133,17136,17138,17140],{"class":3822,"line":10},[1115,17134,17135],{"class":3833},"coef",[1115,17137,1994],{"class":3837},[1115,17139,786],{"class":3825},[1115,17141,4022],{"class":3837},[1115,17143,17144,17147,17149,17151],{"class":3822,"line":27},[1115,17145,17146],{"class":3833},"fitted",[1115,17148,1994],{"class":3837},[1115,17150,786],{"class":3825},[1115,17152,4022],{"class":3837},[1115,17154,17155,17158,17160,17162],{"class":3822,"line":148},[1115,17156,17157],{"class":3833},"residuals",[1115,17159,1994],{"class":3837},[1115,17161,786],{"class":3825},[1115,17163,4022],{"class":3837},[3814,17165,17168],{"className":17166,"code":17167,"language":4044,"meta":1603},[4042],"(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",[3590,17169,17167],{"__ignoreMap":1603},[1110,17171,17172,17175,17176,3071,17202,17205,17206,17228,17229,3071,17247,17250,17251,17288],{},[3590,17173,17174],{},"coef()"," vrací odhadnuté parametry ",[1115,17177,17179],{"className":17178},[1668],[1670,17180,17181],{"xmlns":1672},[1674,17182,17183,17199],{},[1677,17184,17185,17191,17193],{},[1680,17186,17187,17189],{},[1683,17188,11618],{},[1687,17190,1689],{},[1811,17192,1917],{"separator":1121},[1680,17194,17195,17197],{},[1683,17196,11618],{},[1687,17198,1914],{},[1691,17200,17201],{"encoding":1693},"b_0,b_1",[3590,17203,17204],{},"fitted()"," predikce ",[1115,17207,17209],{"className":17208},[1668],[1670,17210,17211],{"xmlns":1672},[1674,17212,17213,17225],{},[1677,17214,17215],{},[1680,17216,17217,17223],{},[2843,17218,17219,17221],{"accent":1121},[1683,17220,7244],{},[1811,17222,2849],{},[1683,17224,1997],{},[1691,17226,17227],{"encoding":1693},"\\hat y_i"," pro pozorované ",[1115,17230,17232],{"className":17231},[1668],[1670,17233,17234],{"xmlns":1672},[1674,17235,17236,17244],{},[1677,17237,17238],{},[1680,17239,17240,17242],{},[1683,17241,6834],{},[1683,17243,1997],{},[1691,17245,17246],{"encoding":1693},"x_i",[3590,17248,17249],{},"residuals()"," rezidua ",[1115,17252,17254],{"className":17253},[1668],[1670,17255,17256],{"xmlns":1672},[1674,17257,17258,17286],{},[1677,17259,17260,17266,17268,17274,17276],{},[1680,17261,17262,17264],{},[1683,17263,8706],{},[1683,17265,1997],{},[1811,17267,2101],{},[1680,17269,17270,17272],{},[1683,17271,7244],{},[1683,17273,1997],{},[1811,17275,3184],{},[1680,17277,17278,17284],{},[2843,17279,17280,17282],{"accent":1121},[1683,17281,7244],{},[1811,17283,2849],{},[1683,17285,1997],{},[1691,17287,16633],{"encoding":1693}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,17290,17291,17292,17305],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,17293,17295],{"className":17294},[1668],[1670,17296,17297],{"xmlns":1672},[1674,17298,17299,17303],{},[1677,17300,17301],{},[1683,17302,6834],{},[1691,17304,6834],{"encoding":1693}," (zde 7 a 8 členů domácnosti):",[3814,17307,17309],{"className":3816,"code":17308,"language":71,"meta":1603,"style":1603},"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",[3590,17310,17311,17331,17359,17398],{"__ignoreMap":1603},[1115,17312,17313,17316,17318,17320,17322,17325,17327,17329],{"class":3822,"line":10},[1115,17314,17315],{"class":3833},"confint",[1115,17317,1994],{"class":3837},[1115,17319,786],{"class":3825},[1115,17321,1917],{"class":3829},[1115,17323,17324],{"class":3825}," level",[1115,17326,3918],{"class":3829},[1115,17328,10113],{"class":3845},[1115,17330,4022],{"class":3837},[1115,17332,17333,17336,17338,17341,17343,17345,17347,17349,17351,17353,17355,17357],{"class":3822,"line":27},[1115,17334,17335],{"class":3825},"nove",[1115,17337,3830],{"class":3829},[1115,17339,17340],{"class":3833}," data.frame",[1115,17342,1994],{"class":3837},[1115,17344,16884],{"class":3825},[1115,17346,3918],{"class":3829},[1115,17348,3956],{"class":3833},[1115,17350,1994],{"class":3837},[1115,17352,13444],{"class":3845},[1115,17354,1917],{"class":3829},[1115,17356,15370],{"class":3845},[1115,17358,9607],{"class":3837},[1115,17360,17361,17364,17366,17368,17370,17373,17375,17378,17380,17383,17385,17388,17390,17392,17394,17396],{"class":3822,"line":148},[1115,17362,17363],{"class":3833},"predict",[1115,17365,1994],{"class":3837},[1115,17367,786],{"class":3825},[1115,17369,1917],{"class":3829},[1115,17371,17372],{"class":3825}," newdata",[1115,17374,3918],{"class":3829},[1115,17376,17377],{"class":3825}," nove",[1115,17379,1917],{"class":3829},[1115,17381,17382],{"class":3825}," interval",[1115,17384,3918],{"class":3829},[1115,17386,17387],{"class":3961}," \"confidence\"",[1115,17389,1917],{"class":3829},[1115,17391,17324],{"class":3825},[1115,17393,3918],{"class":3829},[1115,17395,10113],{"class":3845},[1115,17397,4022],{"class":3837},[1115,17399,17400,17402,17404,17406,17408,17410,17412,17414,17416,17418,17420,17423,17425,17427,17429,17431],{"class":3822,"line":111},[1115,17401,17363],{"class":3833},[1115,17403,1994],{"class":3837},[1115,17405,786],{"class":3825},[1115,17407,1917],{"class":3829},[1115,17409,17372],{"class":3825},[1115,17411,3918],{"class":3829},[1115,17413,17377],{"class":3825},[1115,17415,1917],{"class":3829},[1115,17417,17382],{"class":3825},[1115,17419,3918],{"class":3829},[1115,17421,17422],{"class":3961}," \"prediction\"",[1115,17424,1917],{"class":3829},[1115,17426,17324],{"class":3825},[1115,17428,3918],{"class":3829},[1115,17430,10113],{"class":3845},[1115,17432,4022],{"class":3837},[3814,17434,17437],{"className":17435,"code":17436,"language":4044,"meta":1603},[4042],"                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",[3590,17438,17436],{"__ignoreMap":1603},[1110,17440,17441,17444,17445,1418,17448,17461,17462,3071,17475,17478,17479,17482],{},[3590,17442,17443],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1136,17446,17447],{},"střední hodnotu",[1115,17449,17451],{"className":17450},[1668],[1670,17452,17453],{"xmlns":1672},[1674,17454,17455,17459],{},[1677,17456,17457],{},[1683,17458,7244],{},[1691,17460,7244],{"encoding":1693}," při daném ",[1115,17463,17465],{"className":17464},[1668],[1670,17466,17467],{"xmlns":1672},[1674,17468,17469,17473],{},[1677,17470,17471],{},[1683,17472,6834],{},[1691,17474,6834],{"encoding":1693},[3590,17476,17477],{},"interval = \"prediction\""," širší interval pro ",[1136,17480,17481],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[16860,17484,17486],{"id":17485},"diagnostika-modelu","Diagnostika modelu",[1110,17488,17489,17490,3071,17493,5862,17496,17499],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1136,17491,17492],{},"absenci autokorelace",[1136,17494,17495],{},"stálosti rozptylu (homoskedasticitě)",[1136,17497,17498],{},"normalitě",". V R se ověřují takto:",[3814,17501,17503],{"className":3816,"code":17502,"language":71,"meta":1603,"style":1603},"library(lmtest)\ndwtest(model)\n",[3590,17504,17505,17517],{"__ignoreMap":1603},[1115,17506,17507,17510,17512,17515],{"class":3822,"line":10},[1115,17508,17509],{"class":3829},"library",[1115,17511,1994],{"class":3837},[1115,17513,17514],{"class":3825},"lmtest",[1115,17516,4022],{"class":3837},[1115,17518,17519,17522,17524,17526],{"class":3822,"line":27},[1115,17520,17521],{"class":3833},"dwtest",[1115,17523,1994],{"class":3837},[1115,17525,786],{"class":3825},[1115,17527,4022],{"class":3837},[3814,17529,17532],{"className":17530,"code":17531,"language":4044,"meta":1603},[4042],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3590,17533,17531],{"__ignoreMap":1603},[1110,17535,17536,17537,17554,17555,17572,17573,17590],{},"Durbinův–Watsonův test má ",[1115,17538,17540],{"className":17539},[1668],[1670,17541,17542],{"xmlns":1672},[1674,17543,17544,17552],{},[1677,17545,17546],{},[1680,17547,17548,17550],{},[1683,17549,1685],{},[1687,17551,1689],{},[1691,17553,1694],{"encoding":1693},": v modelu není problém s autokorelací, proti ",[1115,17556,17558],{"className":17557},[1668],[1670,17559,17560],{"xmlns":1672},[1674,17561,17562,17570],{},[1677,17563,17564],{},[1680,17565,17566,17568],{},[1683,17567,1685],{},[1687,17569,1914],{},[1691,17571,3116],{"encoding":1693},": 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, ",[1115,17574,17576],{"className":17575},[1668],[1670,17577,17578],{"xmlns":1672},[1674,17579,17580,17588],{},[1677,17581,17582],{},[1680,17583,17584,17586],{},[1683,17585,1685],{},[1687,17587,1689],{},[1691,17589,1694],{"encoding":1693}," se nezamítá.",[3814,17592,17594],{"className":3816,"code":17593,"language":71,"meta":1603,"style":1603},"library(whitestrap)\nwhite_test(model)\n",[3590,17595,17596,17607],{"__ignoreMap":1603},[1115,17597,17598,17600,17602,17605],{"class":3822,"line":10},[1115,17599,17509],{"class":3829},[1115,17601,1994],{"class":3837},[1115,17603,17604],{"class":3825},"whitestrap",[1115,17606,4022],{"class":3837},[1115,17608,17609,17612,17614,17616],{"class":3822,"line":27},[1115,17610,17611],{"class":3833},"white_test",[1115,17613,1994],{"class":3837},[1115,17615,786],{"class":3825},[1115,17617,4022],{"class":3837},[3814,17619,17622],{"className":17620,"code":17621,"language":4044,"meta":1603},[4042],"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",[3590,17623,17621],{"__ignoreMap":1603},[1110,17625,17626,17627,17644,17645,17662,17663,17590],{},"Whiteův test má ",[1115,17628,17630],{"className":17629},[1668],[1670,17631,17632],{"xmlns":1672},[1674,17633,17634,17642],{},[1677,17635,17636],{},[1680,17637,17638,17640],{},[1683,17639,1685],{},[1687,17641,1689],{},[1691,17643,1694],{"encoding":1693},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,17646,17648],{"className":17647},[1668],[1670,17649,17650],{"xmlns":1672},[1674,17651,17652,17660],{},[1677,17653,17654],{},[1680,17655,17656,17658],{},[1683,17657,1685],{},[1687,17659,1914],{},[1691,17661,3116],{"encoding":1693},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,17664,17666],{"className":17665},[1668],[1670,17667,17668],{"xmlns":1672},[1674,17669,17670,17678],{},[1677,17671,17672],{},[1680,17673,17674,17676],{},[1683,17675,1685],{},[1687,17677,1689],{},[1691,17679,1694],{"encoding":1693},[3814,17681,17683],{"className":3816,"code":17682,"language":71,"meta":1603,"style":1603},"shapiro.test(residuals(model))\n",[3590,17684,17685],{"__ignoreMap":1603},[1115,17686,17687,17690,17692,17694,17696,17698],{"class":3822,"line":10},[1115,17688,17689],{"class":3833},"shapiro.test",[1115,17691,1994],{"class":3837},[1115,17693,17157],{"class":3833},[1115,17695,1994],{"class":3837},[1115,17697,786],{"class":3825},[1115,17699,9607],{"class":3837},[3814,17701,17704],{"className":17702,"code":17703,"language":4044,"meta":1603},[4042],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3590,17705,17703],{"__ignoreMap":1603},[1110,17707,17708,17709,17726],{},"Shapiro–Wilkův test má ",[1115,17710,17712],{"className":17711},[1668],[1670,17713,17714],{"xmlns":1672},[1674,17715,17716,17724],{},[1677,17717,17718],{},[1680,17719,17720,17722],{},[1683,17721,1685],{},[1687,17723,1689],{},[1691,17725,1694],{"encoding":1693},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,17728,17729],{},[4504,17730],{"alt":17731,"className":17732,"src":17733},"mask-ra-diagnostika-rezidui",[1131,4508],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,17735,17736],{},"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.",[1103,17738,17740,17747,17778,17813,17878],{"className":17739,"dataCallout":3597},[1106,3596],[1110,17741,17743,17746],{"className":17742},[1113],[1115,17744],{"className":17745,"ariaHidden":1121},[1118,3604,1120],"Příklad: Regresní přímka",[1110,17748,17749,17750,17763,17764,17777],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,17751,17753],{"className":17752},[1668],[1670,17754,17755],{"xmlns":1672},[1674,17756,17757,17761],{},[1677,17758,17759],{},[1683,17760,7244],{},[1691,17762,7244],{"encoding":1693},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,17765,17767],{"className":17766},[1668],[1670,17768,17769],{"xmlns":1672},[1674,17770,17771,17775],{},[1677,17772,17773],{},[1683,17774,6834],{},[1691,17776,6834],{"encoding":1693},") 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.",[1110,17779,17780,17781,1497],{},"Výsledek: ",[1115,17782,17784],{"className":17783},[1668],[1670,17785,17786],{"xmlns":1672},[1674,17787,17788,17810],{},[1677,17789,17790,17796,17798,17801,17803,17806,17808],{},[2843,17791,17792,17794],{"accent":1121},[1683,17793,7244],{},[1811,17795,2849],{},[1811,17797,2101],{},[1687,17799,17800],{},"32,74",[1811,17802,5598],{},[1687,17804,17805],{},"2,15",[3028,17807,3030],{},[1683,17809,6834],{},[1691,17811,17812],{"encoding":1693},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,17814,16811,17815,17837,17838,17877],{},[1115,17816,17818],{"className":17817},[1668],[1670,17819,17820],{"xmlns":1672},[1674,17821,17822,17834],{},[1677,17823,17824,17830,17832],{},[1680,17825,17826,17828],{},[1683,17827,11618],{},[1687,17829,1914],{},[1811,17831,2101],{},[1687,17833,17805],{},[1691,17835,17836],{"encoding":1693},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,17839,17841],{"className":17840},[1668],[1670,17842,17843],{"xmlns":1672},[1674,17844,17845,17874],{},[1677,17846,17847,17849,17851,17853,17855,17857,17859,17861,17863,17865,17867,17870,17872],{},[1687,17848,17805],{},[1811,17850,8225],{},[1687,17852,1914],{},[3028,17854,3030],{},[1687,17856,11436],{},[3028,17858,3030],{},[1687,17860,11436],{},[1811,17862,2101],{},[1687,17864,1713],{},[3028,17866,3030],{},[1687,17868,17869],{},"150",[3028,17871,3030],{},[1687,17873,11436],{},[1691,17875,17876],{"encoding":1693},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,17879,17880,17881,4109,17900,17948,17949,1277],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,17882,17884],{"className":17883},[1668],[1670,17885,17886],{"xmlns":1672},[1674,17887,17888,17897],{},[1677,17889,17890,17892,17894],{},[1683,17891,6834],{},[1811,17893,2101],{},[1687,17895,17896],{},"34",[1691,17898,17899],{"encoding":1693},"x=34",[1115,17901,17903],{"className":17902},[1668],[1670,17904,17905],{"xmlns":1672},[1674,17906,17907,17945],{},[1677,17908,17909,17919,17921,17927,17929,17935,17937,17939,17942],{},[1680,17910,17911,17917],{},[2843,17912,17913,17915],{"accent":1121},[1683,17914,7244],{},[1811,17916,2849],{},[1687,17918,3665],{},[1811,17920,2101],{},[1680,17922,17923,17925],{},[1683,17924,11618],{},[1687,17926,1689],{},[1811,17928,5598],{},[1680,17930,17931,17933],{},[1683,17932,11618],{},[1687,17934,1914],{},[1811,17936,8225],{},[1687,17938,17896],{},[1811,17940,17941],{},"≐",[1687,17943,17944],{},"105,81",[1691,17946,17947],{"encoding":1693},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,17950,17952],{"className":17951},[1668],[1670,17953,17954],{"xmlns":1672},[1674,17955,17956,17973],{},[1677,17957,17958,17960,17962,17964,17966,17968,17970],{},[1687,17959,17800],{},[1811,17961,5598],{},[1687,17963,17805],{},[1811,17965,8225],{},[1687,17967,17896],{},[1811,17969,17941],{},[1687,17971,17972],{},"105,8",[1691,17974,17975],{"encoding":1693},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1153,17977,17979],{"id":17978},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,17981,17982,17983,17986,17987,18054,18055,18073,18074,18091],{},"Když přímka závislost nevystihuje, nabízí se další ",[1136,17984,17985],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,17988,17990],{"className":17989},[1668],[1670,17991,17992],{"xmlns":1672},[1674,17993,17994,18051],{},[1677,17995,17996,17998,18000,18006,18008,18014,18020,18022,18024,18026,18028,18031,18033,18039,18045,18047,18049],{},[1683,17997,16436],{},[1811,17999,2101],{},[1680,18001,18002,18004],{},[1683,18003,16451],{},[1687,18005,1689],{},[1811,18007,5598],{},[1680,18009,18010,18012],{},[1683,18011,16451],{},[1687,18013,1914],{},[1680,18015,18016,18018],{},[1683,18017,6885],{},[1687,18019,1914],{},[1811,18021,1994],{"stretchy":1993},[1683,18023,6834],{},[1811,18025,2005],{"stretchy":1993},[1811,18027,5598],{},[1811,18029,18030],{},"⋯",[1811,18032,5598],{},[1680,18034,18035,18037],{},[1683,18036,16451],{},[1683,18038,1110],{},[1680,18040,18041,18043],{},[1683,18042,6885],{},[1683,18044,1110],{},[1811,18046,1994],{"stretchy":1993},[1683,18048,6834],{},[1811,18050,2005],{"stretchy":1993},[1691,18052,18053],{"encoding":1693},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,18056,18058],{"className":18057},[1668],[1670,18059,18060],{"xmlns":1672},[1674,18061,18062,18070],{},[1677,18063,18064],{},[1680,18065,18066,18068],{},[1683,18067,6885],{},[1683,18069,1997],{},[1691,18071,18072],{"encoding":1693},"f_i"," a neznámými parametry ",[1115,18075,18077],{"className":18076},[1668],[1670,18078,18079],{"xmlns":1672},[1674,18080,18081,18089],{},[1677,18082,18083],{},[1680,18084,18085,18087],{},[1683,18086,16451],{},[1683,18088,1997],{},[1691,18090,16497],{"encoding":1693},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,18093,18095],{"className":18094},[1668],[1670,18096,18097],{"xmlns":1672,"display":2083},[1674,18098,18099,18409],{},[18100,18101,18104,18177,18290,18349],"mtable",{"rowspacing":18102,"columnalign":18103,"columnspacing":6873},"0.25em","right left",[18105,18106,18107,18131],"mtr",{},[18108,18109,18110],"mtd",{},[3361,18111,18112],{"scriptlevel":1689,"displaystyle":1121},[1677,18113,18114,18128],{},[1677,18115,18116,18119,18125],{},[3028,18117,18118],{},"parabolick",[2843,18120,18121,18123],{"accent":1121},[3028,18122,1127],{},[1811,18124,11615],{},[3028,18126,18127],{}," regrese: ",[2131,18129],{"width":18130},"1em",[18108,18132,18133],{},[3361,18134,18135],{"scriptlevel":1689,"displaystyle":1121},[1677,18136,18137,18139,18145,18147,18153,18155,18161,18163,18165,18171],{},[1677,18138],{},[2843,18140,18141,18143],{"accent":1121},[1683,18142,7244],{},[1811,18144,2849],{},[1811,18146,2101],{},[1680,18148,18149,18151],{},[1683,18150,11618],{},[1687,18152,1689],{},[1811,18154,5598],{},[1680,18156,18157,18159],{},[1683,18158,11618],{},[1687,18160,1914],{},[1683,18162,6834],{},[1811,18164,5598],{},[1680,18166,18167,18169],{},[1683,18168,11618],{},[1687,18170,1713],{},[1706,18172,18173,18175],{},[1683,18174,6834],{},[1687,18176,1713],{},[18105,18178,18179,18226],{},[18108,18180,18181],{},[3361,18182,18183],{"scriptlevel":1689,"displaystyle":1121},[1677,18184,18185,18224],{},[1677,18186,18187,18190,18196,18199,18203,18206,18212,18215,18221],{},[3028,18188,18189],{},"polynomick",[2843,18191,18192,18194],{"accent":1121},[3028,18193,1127],{},[1811,18195,11615],{},[3028,18197,18198],{}," regrese ",[3361,18200,18201],{"scriptlevel":1689,"displaystyle":1993},[1683,18202,1110],{},[3028,18204,18205],{},"-t",[2843,18207,18208,18210],{"accent":1121},[3028,18209,8706],{},[1811,18211,11615],{},[3028,18213,18214],{},"ho stupn",[2843,18216,18217,18219],{"accent":1121},[3028,18218,8706],{},[1811,18220,11625],{},[3028,18222,18223],{},": ",[2131,18225],{"width":18130},[18108,18227,18228],{},[3361,18229,18230],{"scriptlevel":1689,"displaystyle":1121},[1677,18231,18232,18234,18240,18242,18248,18250,18256,18258,18260,18266,18272,18274,18276,18278,18284],{},[1677,18233],{},[2843,18235,18236,18238],{"accent":1121},[1683,18237,7244],{},[1811,18239,2849],{},[1811,18241,2101],{},[1680,18243,18244,18246],{},[1683,18245,11618],{},[1687,18247,1689],{},[1811,18249,5598],{},[1680,18251,18252,18254],{},[1683,18253,11618],{},[1687,18255,1914],{},[1683,18257,6834],{},[1811,18259,5598],{},[1680,18261,18262,18264],{},[1683,18263,11618],{},[1687,18265,1713],{},[1706,18267,18268,18270],{},[1683,18269,6834],{},[1687,18271,1713],{},[1811,18273,5598],{},[1811,18275,18030],{},[1811,18277,5598],{},[1680,18279,18280,18282],{},[1683,18281,11618],{},[1683,18283,1110],{},[1706,18285,18286,18288],{},[1683,18287,6834],{},[1683,18289,1110],{},[18105,18291,18292,18313],{},[18108,18293,18294],{},[3361,18295,18296],{"scriptlevel":1689,"displaystyle":1121},[1677,18297,18298,18311],{},[1677,18299,18300,18303,18309],{},[3028,18301,18302],{},"hyperbolick",[2843,18304,18305,18307],{"accent":1121},[3028,18306,1127],{},[1811,18308,11615],{},[3028,18310,18127],{},[2131,18312],{"width":18130},[18108,18314,18315],{},[3361,18316,18317],{"scriptlevel":1689,"displaystyle":1121},[1677,18318,18319,18321,18327,18329,18335,18337,18343],{},[1677,18320],{},[2843,18322,18323,18325],{"accent":1121},[1683,18324,7244],{},[1811,18326,2849],{},[1811,18328,2101],{},[1680,18330,18331,18333],{},[1683,18332,11618],{},[1687,18334,1689],{},[1811,18336,5598],{},[1680,18338,18339,18341],{},[1683,18340,11618],{},[1687,18342,1914],{},[2859,18344,18345,18347],{},[1687,18346,1914],{},[1683,18348,6834],{},[18105,18350,18351,18372],{},[18108,18352,18353],{},[3361,18354,18355],{"scriptlevel":1689,"displaystyle":1121},[1677,18356,18357,18370],{},[1677,18358,18359,18362,18368],{},[3028,18360,18361],{},"logaritmick",[2843,18363,18364,18366],{"accent":1121},[3028,18365,1127],{},[1811,18367,11615],{},[3028,18369,18127],{},[2131,18371],{"width":18130},[18108,18373,18374],{},[3361,18375,18376],{"scriptlevel":1689,"displaystyle":1121},[1677,18377,18378,18380,18386,18388,18394,18396,18402,18405,18407],{},[1677,18379],{},[2843,18381,18382,18384],{"accent":1121},[1683,18383,7244],{},[1811,18385,2849],{},[1811,18387,2101],{},[1680,18389,18390,18392],{},[1683,18391,11618],{},[1687,18393,1689],{},[1811,18395,5598],{},[1680,18397,18398,18400],{},[1683,18399,11618],{},[1687,18401,1914],{},[1683,18403,18404],{},"ln",[1811,18406,4612],{},[1683,18408,6834],{},[1691,18410,18411],{"encoding":1693},"\\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}",[1110,18413,18414,18415,18418,18419,18465,18466,2077],{},"Naproti tomu ",[1136,18416,18417],{},"nelineární funkce"," nelze do tvaru ",[1115,18420,18422],{"className":18421},[1668],[1670,18423,18424],{"xmlns":1672},[1674,18425,18426,18462],{},[1677,18427,18428,18430,18432,18438,18440,18446,18452,18454,18456,18458,18460],{},[1683,18429,16436],{},[1811,18431,2101],{},[1680,18433,18434,18436],{},[1683,18435,16451],{},[1687,18437,1689],{},[1811,18439,5598],{},[1680,18441,18442,18444],{},[1683,18443,16451],{},[1687,18445,1914],{},[1680,18447,18448,18450],{},[1683,18449,6885],{},[1687,18451,1914],{},[1811,18453,1994],{"stretchy":1993},[1683,18455,6834],{},[1811,18457,2005],{"stretchy":1993},[1811,18459,5598],{},[1811,18461,1920],{},[1691,18463,18464],{"encoding":1693},"\\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 ",[1136,18467,18468],{},"exponenciální regrese",[1115,18470,18472],{"className":18471},[1668],[1670,18473,18474],{"xmlns":1672,"display":2083},[1674,18475,18476,18508],{},[1677,18477,18478,18484,18486,18492,18494,18506],{},[2843,18479,18480,18482],{"accent":1121},[1683,18481,7244],{},[1811,18483,2849],{},[1811,18485,2101],{},[1680,18487,18488,18490],{},[1683,18489,11618],{},[1687,18491,1689],{},[1811,18493,8225],{},[3473,18495,18496,18498,18500],{},[1683,18497,11618],{},[1687,18499,1914],{},[1677,18501,18502,18504],{},[3028,18503,3030],{},[1683,18505,6834],{},[1683,18507,1497],{"mathvariant":2240},[1691,18509,18510],{"encoding":1693},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,18512,18513],{},[4504,18514],{"alt":18515,"className":18516,"src":18517},"mask-ra-nelinearni-krivky",[1131,4508],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[16860,18519,18521],{"id":18520},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,18523,18524,18525,2077],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3590,18526,18527],{},"I(x^2)",[3814,18529,18531],{"className":3816,"code":18530,"language":71,"meta":1603,"style":1603},"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",[3590,18532,18533,18568,18608,18642],{"__ignoreMap":1603},[1115,18534,18535,18538,18540,18542,18544,18546,18548,18550,18552,18554,18556,18558,18560,18562,18564,18566],{"class":3822,"line":10},[1115,18536,18537],{"class":3825},"rok",[1115,18539,3830],{"class":3829},[1115,18541,3956],{"class":3833},[1115,18543,1994],{"class":3837},[1115,18545,1914],{"class":3845},[1115,18547,1917],{"class":3829},[1115,18549,4301],{"class":3845},[1115,18551,1917],{"class":3829},[1115,18553,10969],{"class":3845},[1115,18555,1917],{"class":3829},[1115,18557,3921],{"class":3845},[1115,18559,1917],{"class":3829},[1115,18561,10108],{"class":3845},[1115,18563,1917],{"class":3829},[1115,18565,12342],{"class":3845},[1115,18567,4022],{"class":3837},[1115,18569,18570,18572,18574,18576,18578,18581,18583,18586,18588,18591,18593,18596,18598,18601,18603,18606],{"class":3822,"line":27},[1115,18571,1088],{"class":3825},[1115,18573,3830],{"class":3829},[1115,18575,3956],{"class":3833},[1115,18577,1994],{"class":3837},[1115,18579,18580],{"class":3845},"112",[1115,18582,1917],{"class":3829},[1115,18584,18585],{"class":3845}," 149",[1115,18587,1917],{"class":3829},[1115,18589,18590],{"class":3845}," 238",[1115,18592,1917],{"class":3829},[1115,18594,18595],{"class":3845}," 354",[1115,18597,1917],{"class":3829},[1115,18599,18600],{"class":3845}," 580",[1115,18602,1917],{"class":3829},[1115,18604,18605],{"class":3845}," 867",[1115,18607,4022],{"class":3837},[1115,18609,18610,18613,18615,18617,18619,18621,18623,18626,18629,18632,18634,18636,18638,18640],{"class":3822,"line":148},[1115,18611,18612],{"class":3825},"model_parabola",[1115,18614,3830],{"class":3829},[1115,18616,16964],{"class":3833},[1115,18618,1994],{"class":3837},[1115,18620,1088],{"class":3825},[1115,18622,16971],{"class":3829},[1115,18624,18625],{"class":3825}," rok",[1115,18627,18628],{"class":3829}," +",[1115,18630,18631],{"class":3833}," I",[1115,18633,1994],{"class":3837},[1115,18635,18537],{"class":3825},[1115,18637,2849],{"class":3829},[1115,18639,1713],{"class":3845},[1115,18641,9607],{"class":3837},[1115,18643,18644,18646,18648,18650],{"class":3822,"line":111},[1115,18645,1626],{"class":3833},[1115,18647,1994],{"class":3837},[1115,18649,18612],{"class":3825},[1115,18651,4022],{"class":3837},[3814,18653,18656],{"className":18654,"code":18655,"language":4044,"meta":1603},[4042],"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",[3590,18657,18655],{"__ignoreMap":1603},[1110,18659,18660,18661,18706],{},"Odhadnutá parabola ",[1115,18662,18664],{"className":18663},[1668],[1670,18665,18666],{"xmlns":1672},[1674,18667,18668,18703],{},[1677,18669,18670,18676,18678,18681,18683,18686,18688,18690,18692,18695,18697],{},[2843,18671,18672,18674],{"accent":1121},[1683,18673,7244],{},[1811,18675,2849],{},[1811,18677,2101],{},[1687,18679,18680],{},"164,6",[1811,18682,3184],{},[1687,18684,18685],{},"76,6",[3028,18687,3030],{},[1683,18689,6834],{},[1811,18691,5598],{},[1687,18693,18694],{},"32,1",[3028,18696,3030],{},[1706,18698,18699,18701],{},[1683,18700,6834],{},[1687,18702,1713],{},[1691,18704,18705],{"encoding":1693},"\\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.",[16860,18708,18710],{"id":18709},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,18712,18713,18714,18716],{},"Nelineární funkce se v R odhadují funkcí ",[3590,18715,16222],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3814,18718,18720],{"className":3816,"code":18719,"language":71,"meta":1603,"style":1603},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3590,18721,18722,18732,18768],{"__ignoreMap":1603},[1115,18723,18724,18726,18728,18730],{"class":3822,"line":10},[1115,18725,17509],{"class":3829},[1115,18727,1994],{"class":3837},[1115,18729,16207],{"class":3825},[1115,18731,4022],{"class":3837},[1115,18733,18734,18737,18739,18742,18744,18746,18748,18751,18754,18757,18759,18762,18764,18766],{"class":3822,"line":27},[1115,18735,18736],{"class":3825},"model_exp",[1115,18738,3830],{"class":3829},[1115,18740,18741],{"class":3833}," nls2",[1115,18743,1994],{"class":3837},[1115,18745,1088],{"class":3825},[1115,18747,16971],{"class":3829},[1115,18749,18750],{"class":3825}," b1",[1115,18752,18753],{"class":3829}," *",[1115,18755,18756],{"class":3833}," exp",[1115,18758,1994],{"class":3837},[1115,18760,18761],{"class":3825},"b2",[1115,18763,18753],{"class":3829},[1115,18765,18625],{"class":3825},[1115,18767,9607],{"class":3837},[1115,18769,18770,18772,18774,18776],{"class":3822,"line":148},[1115,18771,1626],{"class":3833},[1115,18773,1994],{"class":3837},[1115,18775,18736],{"class":3825},[1115,18777,4022],{"class":3837},[3814,18779,18782],{"className":18780,"code":18781,"language":4044,"meta":1603},[4042],"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",[3590,18783,18781],{"__ignoreMap":1603},[1110,18785,18786,18787,2077],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,18788,18790],{"className":18789},[1668],[1670,18791,18792],{"xmlns":1672},[1674,18793,18794,18820],{},[1677,18795,18796,18802,18804,18810,18812],{},[2843,18797,18798,18800],{"accent":1121},[1683,18799,7244],{},[1811,18801,2849],{},[1811,18803,2101],{},[1680,18805,18806,18808],{},[1683,18807,11618],{},[1687,18809,1914],{},[1811,18811,8225],{},[3473,18813,18814,18816,18818],{},[1683,18815,11618],{},[1687,18817,1713],{},[1683,18819,6834],{},[1691,18821,18822],{"encoding":1693},"\\hat y=b_1\\cdot b_2^{x}",[3814,18824,18826],{"className":3816,"code":18825,"language":71,"meta":1603,"style":1603},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3590,18827,18828,18857],{"__ignoreMap":1603},[1115,18829,18830,18833,18835,18837,18839,18841,18843,18845,18847,18849,18851,18853,18855],{"class":3822,"line":10},[1115,18831,18832],{"class":3825},"model_pow",[1115,18834,3830],{"class":3829},[1115,18836,18741],{"class":3833},[1115,18838,1994],{"class":3837},[1115,18840,1088],{"class":3825},[1115,18842,16971],{"class":3829},[1115,18844,18750],{"class":3825},[1115,18846,18753],{"class":3829},[1115,18848,4728],{"class":3837},[1115,18850,18761],{"class":3825},[1115,18852,2849],{"class":3829},[1115,18854,18537],{"class":3825},[1115,18856,9607],{"class":3837},[1115,18858,18859,18861,18863,18865],{"class":3822,"line":27},[1115,18860,1626],{"class":3833},[1115,18862,1994],{"class":3837},[1115,18864,18832],{"class":3825},[1115,18866,4022],{"class":3837},[3814,18868,18871],{"className":18869,"code":18870,"language":4044,"meta":1603},[4042],"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",[3590,18872,18870],{"__ignoreMap":1603},[1110,18874,18875,18876,18940,18941,18965],{},"Obě varianty popisují stejnou křivku (",[1115,18877,18879],{"className":18878},[1668],[1670,18880,18881],{"xmlns":1672},[1674,18882,18883,18937],{},[1677,18884,18885,18902,18904],{},[3473,18886,18887,18889,18891],{},[1683,18888,11618],{},[1687,18890,1713],{},[1677,18892,18893,18896],{},[3028,18894,18895],{},"mocninn",[2843,18897,18898,18900],{"accent":1121},[3028,18899,7244],{},[1811,18901,11615],{},[1811,18903,2101],{},[1706,18905,18906,18908],{},[1683,18907,8706],{},[1677,18909,18910,18912],{},[3028,18911,3030],{},[3473,18913,18914,18916,18918],{},[1683,18915,11618],{},[1687,18917,1713],{},[1677,18919,18920,18923,18929,18931],{},[3028,18921,18922],{},"exponenci",[2843,18924,18925,18927],{"accent":1121},[3028,18926,1127],{},[1811,18928,11615],{},[3028,18930,18404],{},[2843,18932,18933,18935],{"accent":1121},[3028,18934,11865],{},[1811,18936,11615],{},[1691,18938,18939],{"encoding":1693},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,18942,18944],{"className":18943},[1668],[1670,18945,18946],{"xmlns":1672},[1674,18947,18948,18962],{},[1677,18949,18950,18957,18959],{},[1706,18951,18952,18954],{},[1683,18953,8706],{},[1687,18955,18956],{},"0,4316",[1811,18958,9554],{},[1687,18960,18961],{},"1,540",[1691,18963,18964],{"encoding":1693},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[16860,18967,18969],{"id":18968},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,18971,18972,18973,2077],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3590,18974,18975],{},"I(1\u002Fx)",[3814,18977,18979],{"className":3816,"code":18978,"language":71,"meta":1603,"style":1603},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3590,18980,18981,19008],{"__ignoreMap":1603},[1115,18982,18983,18986,18988,18990,18992,18994,18996,18998,19000,19002,19004,19006],{"class":3822,"line":10},[1115,18984,18985],{"class":3825},"model_hyperbola",[1115,18987,3830],{"class":3829},[1115,18989,16964],{"class":3833},[1115,18991,1994],{"class":3837},[1115,18993,16919],{"class":3825},[1115,18995,16971],{"class":3829},[1115,18997,18631],{"class":3833},[1115,18999,1994],{"class":3837},[1115,19001,1914],{"class":3845},[1115,19003,10189],{"class":3829},[1115,19005,16974],{"class":3825},[1115,19007,9607],{"class":3837},[1115,19009,19010,19012,19014,19016],{"class":3822,"line":27},[1115,19011,1626],{"class":3833},[1115,19013,1994],{"class":3837},[1115,19015,18985],{"class":3825},[1115,19017,4022],{"class":3837},[3814,19019,19022],{"className":19020,"code":19021,"language":4044,"meta":1603},[4042],"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",[3590,19023,19021],{"__ignoreMap":1603},[1110,19025,19026,19027,19061,19062,19083],{},"Model ",[1115,19028,19030],{"className":19029},[1668],[1670,19031,19032],{"xmlns":1672},[1674,19033,19034,19058],{},[1677,19035,19036,19042,19044,19047,19049],{},[2843,19037,19038,19040],{"accent":1121},[1683,19039,7244],{},[1811,19041,2849],{},[1811,19043,2101],{},[1687,19045,19046],{},"2180,7",[1811,19048,3184],{},[3361,19050,19051],{"scriptlevel":1689,"displaystyle":1121},[2859,19052,19053,19056],{},[1687,19054,19055],{},"1920,0",[1683,19057,6834],{},[1691,19059,19060],{"encoding":1693},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,19063,19065],{"className":19064},[1668],[1670,19066,19067],{"xmlns":1672},[1674,19068,19069,19081],{},[1677,19070,19071,19077,19079],{},[1706,19072,19073,19075],{},[1683,19074,10337],{},[1687,19076,1713],{},[1811,19078,2101],{},[1687,19080,17118],{},[1691,19082,17121],{"encoding":1693},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,19085,19087,19094,19125,19173],{"className":19086,"dataCallout":3597},[1106,3596],[1110,19088,19090,19093],{"className":19089},[1113],[1115,19091],{"className":19092,"ariaHidden":1121},[1118,3604,1120],"Příklad: Parabolická regrese",[1110,19095,19096,19097,19110,19111,19124],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,19098,19100],{"className":19099},[1668],[1670,19101,19102],{"xmlns":1672},[1674,19103,19104,19108],{},[1677,19105,19106],{},[1683,19107,6834],{},[1691,19109,6834],{"encoding":1693},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,19112,19114],{"className":19113},[1668],[1670,19115,19116],{"xmlns":1672},[1674,19117,19118,19122],{},[1677,19119,19120],{},[1683,19121,7244],{},[1691,19123,7244],{"encoding":1693},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,19126,17780,19127,1497],{},[1115,19128,19130],{"className":19129},[1668],[1670,19131,19132],{"xmlns":1672},[1674,19133,19134,19170],{},[1677,19135,19136,19142,19144,19146,19149,19151,19154,19156,19158,19160,19162,19164],{},[2843,19137,19138,19140],{"accent":1121},[1683,19139,7244],{},[1811,19141,2849],{},[1811,19143,2101],{},[1811,19145,3184],{},[1687,19147,19148],{},"60,3",[1811,19150,5598],{},[1687,19152,19153],{},"4,55",[3028,19155,3030],{},[1683,19157,6834],{},[1811,19159,3184],{},[1687,19161,4105],{},[3028,19163,3030],{},[1706,19165,19166,19168],{},[1683,19167,6834],{},[1687,19169,1713],{},[1691,19171,19172],{"encoding":1693},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,19174,19175,19176,19194],{},"Záporný koeficient ",[1115,19177,19179],{"className":19178},[1668],[1670,19180,19181],{"xmlns":1672},[1674,19182,19183,19191],{},[1677,19184,19185],{},[1680,19186,19187,19189],{},[1683,19188,11618],{},[1687,19190,1713],{},[1691,19192,19193],{"encoding":1693},"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.",[1103,19196,19198,19205,19235,19280],{"className":19197,"dataCallout":3597},[1106,3596],[1110,19199,19201,19204],{"className":19200},[1113],[1115,19202],{"className":19203,"ariaHidden":1121},[1118,3604,1120],"Příklad: Hyperbolická regrese",[1110,19206,19207,19208,19221,19222,1277],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,19209,19211],{"className":19210},[1668],[1670,19212,19213],{"xmlns":1672},[1674,19214,19215,19219],{},[1677,19216,19217],{},[1683,19218,7244],{},[1691,19220,7244],{"encoding":1693},") na objemu produkce v tisících kusů (proměnná ",[1115,19223,19225],{"className":19224},[1668],[1670,19226,19227],{"xmlns":1672},[1674,19228,19229,19233],{},[1677,19230,19231],{},[1683,19232,6834],{},[1691,19234,6834],{"encoding":1693},[1110,19236,17780,19237,1497],{},[1115,19238,19240],{"className":19239},[1668],[1670,19241,19242],{"xmlns":1672},[1674,19243,19244,19277],{},[1677,19245,19246,19252,19254,19256,19259,19261],{},[2843,19247,19248,19250],{"accent":1121},[1683,19249,7244],{},[1811,19251,2849],{},[1811,19253,2101],{},[1811,19255,3184],{},[1687,19257,19258],{},"96,78",[1811,19260,5598],{},[3361,19262,19263],{"scriptlevel":1689,"displaystyle":1121},[2859,19264,19265,19275],{},[1677,19266,19267,19270,19272],{},[1687,19268,19269],{},"250",[3028,19271,3030],{},[1687,19273,19274],{},"528,88",[1683,19276,6834],{},[1691,19278,19279],{"encoding":1693},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,19281,19282,19283,19300],{},"Záporná hodnota ",[1115,19284,19286],{"className":19285},[1668],[1670,19287,19288],{"xmlns":1672},[1674,19289,19290,19298],{},[1677,19291,19292],{},[1680,19293,19294,19296],{},[1683,19295,11618],{},[1687,19297,1914],{},[1691,19299,16829],{"encoding":1693}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1153,19302,19304],{"id":19303},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,19306,19307,19308,2077],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1136,19309,16121],{},[1115,19311,19313],{"className":19312},[1668],[1670,19314,19315],{"xmlns":1672,"display":2083},[1674,19316,19317,19385],{},[1677,19318,19319,19325,19327,19349,19351,19353,19355,19383],{},[1706,19320,19321,19323],{},[1683,19322,10337],{},[1687,19324,1713],{},[1811,19326,2101],{},[2859,19328,19329,19341],{},[3473,19330,19331,19333,19339],{},[1683,19332,1974],{},[2843,19334,19335,19337],{"accent":1121},[1683,19336,7244],{},[1811,19338,2849],{},[1687,19340,1713],{},[3473,19342,19343,19345,19347],{},[1683,19344,1974],{},[1683,19346,7244],{},[1687,19348,1713],{},[1811,19350,2101],{},[1687,19352,1914],{},[1811,19354,3184],{},[2859,19356,19357,19375],{},[3473,19358,19359,19361,19373],{},[1683,19360,1974],{},[1677,19362,19363,19365,19367],{},[1683,19364,7244],{},[1811,19366,3184],{},[2843,19368,19369,19371],{"accent":1121},[1683,19370,7244],{},[1811,19372,2849],{},[1687,19374,1713],{},[3473,19376,19377,19379,19381],{},[1683,19378,1974],{},[1683,19380,7244],{},[1687,19382,1713],{},[1683,19384,1497],{"mathvariant":2240},[1691,19386,19387],{"encoding":1693},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,19389,19390,19391,19408,19409,19422],{},"Čím blíž je ",[1115,19392,19394],{"className":19393},[1668],[1670,19395,19396],{"xmlns":1672},[1674,19397,19398,19406],{},[1677,19399,19400],{},[1706,19401,19402,19404],{},[1683,19403,10337],{},[1687,19405,1713],{},[1691,19407,16139],{"encoding":1693}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,19410,19412],{"className":19411},[1668],[1670,19413,19414],{"xmlns":1672},[1674,19415,19416,19420],{},[1677,19417,19418],{},[1683,19419,7244],{},[1691,19421,7244],{"encoding":1693}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,19424,19425,19426,1418,19428,19451,19452,2077],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1136,19427,16143],{},[1115,19429,19431],{"className":19430},[1668],[1670,19432,19433],{"xmlns":1672},[1674,19434,19435,19449],{},[1677,19436,19437,19439,19441],{},[1683,19438,11314],{},[1811,19440,2101],{},[4574,19442,19443],{},[1706,19444,19445,19447],{},[1683,19446,10337],{},[1687,19448,1713],{},[1691,19450,16167],{"encoding":1693},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1136,19453,16171],{},[1115,19455,19457],{"className":19456},[1668],[1670,19458,19459],{"xmlns":1672,"display":2083},[1674,19460,19461,19511],{},[1677,19462,19463,19473,19475,19509],{},[1680,19464,19465,19467],{},[1683,19466,71],{},[1677,19468,19469,19471],{},[1683,19470,6834],{},[1683,19472,7244],{},[1811,19474,2101],{},[2859,19476,19477,19487],{},[1680,19478,19479,19481],{},[1683,19480,1974],{},[1677,19482,19483,19485],{},[1683,19484,6834],{},[1683,19486,7244],{},[4574,19488,19489],{},[1677,19490,19491,19499,19501],{},[3473,19492,19493,19495,19497],{},[1683,19494,1974],{},[1683,19496,6834],{},[1687,19498,1713],{},[1811,19500,8225],{},[3473,19502,19503,19505,19507],{},[1683,19504,1974],{},[1683,19506,7244],{},[1687,19508,1713],{},[1683,19510,1497],{"mathvariant":2240},[1691,19512,19513],{"encoding":1693},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,19515,19516,19517,19533,19534,19550],{},"Koeficient korelace nabývá hodnot od ",[1115,19518,19520],{"className":19519},[1668],[1670,19521,19522],{"xmlns":1672},[1674,19523,19524,19530],{},[1677,19525,19526,19528],{},[1811,19527,3184],{},[1687,19529,1914],{},[1691,19531,19532],{"encoding":1693},"-1"," do ",[1115,19535,19537],{"className":19536},[1668],[1670,19538,19539],{"xmlns":1672},[1674,19540,19541,19547],{},[1677,19542,19543,19545],{},[1811,19544,5598],{},[1687,19546,1914],{},[1691,19548,19549],{"encoding":1693},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,19552,19553],{},[4504,19554],{"alt":19555,"className":19556,"src":19557},"mask-ra-korelace-sila",[1131,4508],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,19559,19560,19561,19574,19575,19593,19594,5862,19607,19620],{},"S rostoucí absolutní hodnotou ",[1115,19562,19564],{"className":19563},[1668],[1670,19565,19566],{"xmlns":1672},[1674,19567,19568,19572],{},[1677,19569,19570],{},[1683,19571,71],{},[1691,19573,71],{"encoding":1693}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,19576,19578],{"className":19577},[1668],[1670,19579,19580],{"xmlns":1672},[1674,19581,19582,19590],{},[1677,19583,19584,19586,19588],{},[1683,19585,71],{},[1811,19587,9554],{},[1687,19589,1689],{},[1691,19591,19592],{"encoding":1693},"r\\approx 0"," je mezi ",[1115,19595,19597],{"className":19596},[1668],[1670,19598,19599],{"xmlns":1672},[1674,19600,19601,19605],{},[1677,19602,19603],{},[1683,19604,6834],{},[1691,19606,6834],{"encoding":1693},[1115,19608,19610],{"className":19609},[1668],[1670,19611,19612],{"xmlns":1672},[1674,19613,19614,19618],{},[1677,19615,19616],{},[1683,19617,7244],{},[1691,19619,7244],{"encoding":1693}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[16860,19622,16863],{"id":19623},"v-r-1",[3814,19625,19627],{"className":3816,"code":19626,"language":71,"meta":1603,"style":1603},"cor(pocet_clenu, tydenni_vydaje)\n",[3590,19628,19629],{"__ignoreMap":1603},[1115,19630,19631,19634,19636,19638,19640,19643],{"class":3822,"line":10},[1115,19632,19633],{"class":3833},"cor",[1115,19635,1994],{"class":3837},[1115,19637,16884],{"class":3825},[1115,19639,1917],{"class":3829},[1115,19641,19642],{"class":3825}," tydenni_vydaje",[1115,19644,4022],{"class":3837},[3814,19646,19649],{"className":19647,"code":19648,"language":4044,"meta":1603},[4042],"[1] 0.9997441\n",[3590,19650,19648],{"__ignoreMap":1603},[1110,19652,19653,19654,19680],{},"Hodnota 0,9997 odpovídá ",[1115,19655,19657],{"className":19656},[1668],[1670,19658,19659],{"xmlns":1672},[1674,19660,19661,19677],{},[1677,19662,19663,19671,19673],{},[4574,19664,19665],{},[1706,19666,19667,19669],{},[1683,19668,10337],{},[1687,19670,1713],{},[1811,19672,2101],{},[4574,19674,19675],{},[1687,19676,17118],{},[1691,19678,19679],{"encoding":1693},"\\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.",[1103,19682,19684,19691,19694],{"className":19683,"dataCallout":3597},[1106,3596],[1110,19685,19687,19690],{"className":19686},[1113],[1115,19688],{"className":19689,"ariaHidden":1121},[1118,3604,1120],"Příklad: Koeficient korelace",[1110,19692,19693],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,19695,17780,19696,19723],{},[1115,19697,19699],{"className":19698},[1668],[1670,19700,19701],{"xmlns":1672},[1674,19702,19703,19720],{},[1677,19704,19705,19715,19717],{},[1680,19706,19707,19709],{},[1683,19708,71],{},[1677,19710,19711,19713],{},[1683,19712,6834],{},[1683,19714,7244],{},[1811,19716,2101],{},[1687,19718,19719],{},"0,739",[1691,19721,19722],{"encoding":1693},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1153,19725,19727],{"id":19726},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,19729,19730,19731,19744],{},"Pokud na závisle proměnnou ",[1115,19732,19734],{"className":19733},[1668],[1670,19735,19736],{"xmlns":1672},[1674,19737,19738,19742],{},[1677,19739,19740],{},[1683,19741,7244],{},[1691,19743,7244],{"encoding":1693}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,19746,19748],{"className":19747},[1668],[1670,19749,19750],{"xmlns":1672,"display":2083},[1674,19751,19752,19862],{},[1677,19753,19754,19756,19758,19764,19766,19772,19778,19780,19786,19792,19794,19796,19798,19804,19810,19812,19814,19820,19822,19828,19830,19836,19842,19844,19846,19848,19854,19860],{},[1683,19755,16436],{},[1811,19757,2101],{},[1680,19759,19760,19762],{},[1683,19761,16451],{},[1687,19763,1689],{},[1811,19765,5598],{},[1680,19767,19768,19770],{},[1683,19769,16451],{},[1687,19771,1914],{},[1680,19773,19774,19776],{},[1683,19775,6834],{},[1687,19777,1914],{},[1811,19779,5598],{},[1680,19781,19782,19784],{},[1683,19783,16451],{},[1687,19785,1713],{},[1680,19787,19788,19790],{},[1683,19789,6834],{},[1687,19791,1713],{},[1811,19793,5598],{},[1811,19795,18030],{},[1811,19797,5598],{},[1680,19799,19800,19802],{},[1683,19801,16451],{},[1683,19803,1110],{},[1680,19805,19806,19808],{},[1683,19807,6834],{},[1683,19809,1110],{},[1811,19811,1917],{"separator":1121},[2131,19813],{"width":2133},[2843,19815,19816,19818],{"accent":1121},[1683,19817,7244],{},[1811,19819,2849],{},[1811,19821,2101],{},[1680,19823,19824,19826],{},[1683,19825,11618],{},[1687,19827,1689],{},[1811,19829,5598],{},[1680,19831,19832,19834],{},[1683,19833,11618],{},[1687,19835,1914],{},[1680,19837,19838,19840],{},[1683,19839,6834],{},[1687,19841,1914],{},[1811,19843,5598],{},[1811,19845,18030],{},[1811,19847,5598],{},[1680,19849,19850,19852],{},[1683,19851,11618],{},[1683,19853,1110],{},[1680,19855,19856,19858],{},[1683,19857,6834],{},[1683,19859,1110],{},[1683,19861,1497],{"mathvariant":2240},[1691,19863,19864],{"encoding":1693},"\\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.",[16860,19866,19868],{"id":19867},"výběr-proměnných","Výběr proměnných",[1503,19870,19871,19877],{},[1265,19872,19873,19876],{},[1136,19874,19875],{},"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.",[1265,19878,19879,19882,19883,19886,19887,19890],{},[1136,19880,19881],{},"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 ",[1136,19884,19885],{},"forward"," proměnné postupně přidává, varianta ",[1136,19888,19889],{},"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.",[16860,19892,19894],{"id":19893},"postup-odhadu","Postup odhadu",[1262,19896,19897,19900,19903],{},[1265,19898,19899],{},"ověření předpokladů regresního modelu,",[1265,19901,19902],{},"samotný odhad parametrů,",[1265,19904,19905],{},"reziduální analýza výsledného modelu.",[1110,19907,19908,19909,19926,19927,4109,19929,19958,19959,19988,19989,20006],{},"Důležitost každého parametru ",[1115,19910,19912],{"className":19911},[1668],[1670,19913,19914],{"xmlns":1672},[1674,19915,19916,19924],{},[1677,19917,19918],{},[1680,19919,19920,19922],{},[1683,19921,11618],{},[1683,19923,1997],{},[1691,19925,16576],{"encoding":1693}," v modelu ověřuje ",[1136,19928,992],{},[1115,19930,19932],{"className":19931},[1668],[1670,19933,19934],{"xmlns":1672},[1674,19935,19936,19956],{},[1677,19937,19938,19944,19946,19952,19954],{},[1680,19939,19940,19942],{},[1683,19941,1685],{},[1687,19943,1689],{},[1811,19945,2077],{},[1680,19947,19948,19950],{},[1683,19949,16451],{},[1683,19951,1997],{},[1811,19953,2101],{},[1687,19955,1689],{},[1691,19957,17062],{"encoding":1693}," (proměnná je v modelu nevýznamná) proti ",[1115,19960,19962],{"className":19961},[1668],[1670,19963,19964],{"xmlns":1672},[1674,19965,19966,19986],{},[1677,19967,19968,19974,19976,19982,19984],{},[1680,19969,19970,19972],{},[1683,19971,1685],{},[1687,19973,1914],{},[1811,19975,2077],{},[1680,19977,19978,19980],{},[1683,19979,16451],{},[1683,19981,1997],{},[1811,19983,11070],{"mathvariant":2240},[1687,19985,1689],{},[1691,19987,17093],{"encoding":1693}," (proměnná je významná). Při nezamítnutí ",[1115,19990,19992],{"className":19991},[1668],[1670,19993,19994],{"xmlns":1672},[1674,19995,19996,20004],{},[1677,19997,19998],{},[1680,19999,20000,20002],{},[1683,20001,1685],{},[1687,20003,1689],{},[1691,20005,1694],{"encoding":1693}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[16860,20008,20010],{"id":20009},"předpoklady-modelu","Předpoklady modelu",[1262,20012,20013,20030,20063,20069,20072,20075],{},[1265,20014,20015,20016,20029],{},"Závisle proměnná ",[1115,20017,20019],{"className":20018},[1668],[1670,20020,20021],{"xmlns":1672},[1674,20022,20023,20027],{},[1677,20024,20025],{},[1683,20026,7244],{},[1691,20028,7244],{"encoding":1693}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1265,20031,20032,20033,20062],{},"Nezávislé proměnné ",[1115,20034,20036],{"className":20035},[1668],[1670,20037,20038],{"xmlns":1672},[1674,20039,20040,20060],{},[1677,20041,20042,20048,20050,20052,20054],{},[1680,20043,20044,20046],{},[1683,20045,6834],{},[1687,20047,1914],{},[1811,20049,1917],{"separator":1121},[1811,20051,1920],{},[1811,20053,1917],{"separator":1121},[1680,20055,20056,20058],{},[1683,20057,6834],{},[1683,20059,1110],{},[1691,20061,16400],{"encoding":1693}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1265,20064,20065,20066,1497],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1136,20067,20068],{},"multikolinearita",[1265,20070,20071],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1265,20073,20074],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1265,20076,20077,20078,20082],{},"Proměnné mají mít ",[1127,20079,20081],{"className":20080,"dataFsResolvedFilePath":1275,"href":1273},[1131],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,20084,20085,20086,20089],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1127,20087,1301],{"className":20088,"dataFsResolvedFilePath":1300,"href":1298},[1131],") — 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.",[16860,20091,20092],{"id":20068},"Multikolinearita",[1110,20094,20095],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1503,20097,20098,20101,20104],{},[1265,20099,20100],{},"výsledky regrese jsou pak nespolehlivé,",[1265,20102,20103],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1265,20105,20106],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,20108,20109,20110,20113,20114,20137,20138,20156,20157,20173],{},"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 ",[1136,20111,20112],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,20115,20117],{"className":20116},[1668],[1670,20118,20119],{"xmlns":1672},[1674,20120,20121,20134],{},[1677,20122,20123,20125,20127,20130,20132],{},[1687,20124,1914],{},[1811,20126,4453],{},[3028,20128,20129],{},"VIF",[1811,20131,4453],{},[1687,20133,10040],{},[1691,20135,20136],{"encoding":1693},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,20139,20141],{"className":20140},[1668],[1670,20142,20143],{"xmlns":1672},[1674,20144,20145,20153],{},[1677,20146,20147,20149,20151],{},[3028,20148,20129],{},[1811,20150,1813],{},[1687,20152,10040],{},[1691,20154,20155],{"encoding":1693},"\\text{VIF}>5"," (přísněji ",[1115,20158,20160],{"className":20159},[1668],[1670,20161,20162],{"xmlns":1672},[1674,20163,20164,20170],{},[1677,20165,20166,20168],{},[1811,20167,1813],{},[1687,20169,9147],{},[1691,20171,20172],{"encoding":1693},">10",") značí vysokou multikolinearitu.",[1110,20175,20176],{},"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.",[16860,20178,20180],{"id":20179},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1503,20182,20183,20189,20195],{},[1265,20184,20185,20188],{},[1136,20186,20187],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1265,20190,20191,20194],{},[1136,20192,20193],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1265,20196,20197,20200,20201,20204],{},[1136,20198,20199],{},"AIC"," (Akaikeho informační kritérium) a ",[1136,20202,20203],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[16860,20206,16863],{"id":20207},"v-r-2",[1110,20209,20210],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3814,20212,20214],{"className":3816,"code":20213,"language":71,"meta":1603,"style":1603},"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",[3590,20215,20216,20242,20286,20312,20322,20326,20337,20348,20352,20362,20372,20376,20386,20396,20401],{"__ignoreMap":1603},[1115,20217,20218,20221,20223,20226,20228,20231,20233,20236,20238,20240],{"class":3822,"line":10},[1115,20219,20220],{"class":3825},"data",[1115,20222,3830],{"class":3829},[1115,20224,20225],{"class":3833}," read.table",[1115,20227,1994],{"class":3837},[1115,20229,20230],{"class":3961},"\"4_4.txt\"",[1115,20232,1917],{"class":3829},[1115,20234,20235],{"class":3825}," header",[1115,20237,3918],{"class":3829},[1115,20239,3931],{"class":3845},[1115,20241,4022],{"class":3837},[1115,20243,20244,20247,20249,20251,20253,20255,20257,20260,20262,20265,20267,20270,20272,20275,20277,20280,20282,20284],{"class":3822,"line":27},[1115,20245,20246],{"class":3825},"model_plny",[1115,20248,3830],{"class":3829},[1115,20250,16964],{"class":3833},[1115,20252,1994],{"class":3837},[1115,20254,7244],{"class":3825},[1115,20256,16971],{"class":3829},[1115,20258,20259],{"class":3825}," x1",[1115,20261,18628],{"class":3829},[1115,20263,20264],{"class":3825}," x2",[1115,20266,18628],{"class":3829},[1115,20268,20269],{"class":3825}," x3",[1115,20271,18628],{"class":3829},[1115,20273,20274],{"class":3825}," x4",[1115,20276,1917],{"class":3829},[1115,20278,20279],{"class":3825}," data",[1115,20281,3918],{"class":3829},[1115,20283,20279],{"class":3825},[1115,20285,4022],{"class":3837},[1115,20287,20288,20291,20293,20296,20298,20300,20302,20305,20307,20310],{"class":3822,"line":148},[1115,20289,20290],{"class":3825},"model_krok",[1115,20292,3830],{"class":3829},[1115,20294,20295],{"class":3833}," step",[1115,20297,1994],{"class":3837},[1115,20299,20246],{"class":3825},[1115,20301,1917],{"class":3829},[1115,20303,20304],{"class":3825}," direction",[1115,20306,3918],{"class":3829},[1115,20308,20309],{"class":3961}," \"both\"",[1115,20311,4022],{"class":3837},[1115,20313,20314,20316,20318,20320],{"class":3822,"line":111},[1115,20315,1626],{"class":3833},[1115,20317,1994],{"class":3837},[1115,20319,20290],{"class":3825},[1115,20321,4022],{"class":3837},[1115,20323,20324],{"class":3822,"line":96},[1115,20325,10155],{"emptyLinePlaceholder":1618},[1115,20327,20328,20330,20332,20335],{"class":3822,"line":89},[1115,20329,17509],{"class":3829},[1115,20331,1994],{"class":3837},[1115,20333,20334],{"class":3825},"car",[1115,20336,4022],{"class":3837},[1115,20338,20339,20342,20344,20346],{"class":3822,"line":82},[1115,20340,20341],{"class":3833},"vif",[1115,20343,1994],{"class":3837},[1115,20345,20290],{"class":3825},[1115,20347,4022],{"class":3837},[1115,20349,20350],{"class":3822,"line":75},[1115,20351,10155],{"emptyLinePlaceholder":1618},[1115,20353,20354,20356,20358,20360],{"class":3822,"line":4012},[1115,20355,17509],{"class":3829},[1115,20357,1994],{"class":3837},[1115,20359,17514],{"class":3825},[1115,20361,4022],{"class":3837},[1115,20363,20364,20366,20368,20370],{"class":3822,"line":72},[1115,20365,17521],{"class":3833},[1115,20367,1994],{"class":3837},[1115,20369,20290],{"class":3825},[1115,20371,4022],{"class":3837},[1115,20373,20374],{"class":3822,"line":25},[1115,20375,10155],{"emptyLinePlaceholder":1618},[1115,20377,20378,20380,20382,20384],{"class":3822,"line":65},[1115,20379,17509],{"class":3829},[1115,20381,1994],{"class":3837},[1115,20383,17604],{"class":3825},[1115,20385,4022],{"class":3837},[1115,20387,20388,20390,20392,20394],{"class":3822,"line":63},[1115,20389,17611],{"class":3833},[1115,20391,1994],{"class":3837},[1115,20393,20290],{"class":3825},[1115,20395,4022],{"class":3837},[1115,20397,20399],{"class":3822,"line":20398},14,[1115,20400,10155],{"emptyLinePlaceholder":1618},[1115,20402,20403,20405,20407,20409,20411,20413],{"class":3822,"line":60},[1115,20404,17689],{"class":3833},[1115,20406,1994],{"class":3837},[1115,20408,17157],{"class":3833},[1115,20410,1994],{"class":3837},[1115,20412,20290],{"class":3825},[1115,20414,9607],{"class":3837},[1110,20416,20417,20419,20420,20423],{},[3590,20418,16234],{}," provádí stepwise výběr podle AIC, ",[3590,20421,20422],{},"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.",[1103,20425,20427,20434,20437,20440],{"className":20426,"dataCallout":3597},[1106,3596],[1110,20428,20430,20433],{"className":20429},[1113],[1115,20431],{"className":20432,"ariaHidden":1121},[1118,3604,1120],"Příklad: Vícenásobná regrese",[1110,20435,20436],{},"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.",[1110,20438,20439],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,20441,20442,20443,20446,20447,20449,20450,20453],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1136,20444,20445],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1136,20448,20068],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1136,20451,20452],{},"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.",[1153,20455,6529],{"id":6528},[1103,20457,20459,20466],{"className":20458,"dataCallout":6534},[1106,6533],[1110,20460,20462,20465],{"className":20461},[1113],[1115,20463],{"className":20464,"ariaHidden":1121},[1118,6541,1120],"Koeficient korelace jen pro přímku",[1110,20467,20468,20469,20525,20526,20543,20544,20564,20565,5862,20578,1497],{},"Vzorec ",[1115,20470,20472],{"className":20471},[1668],[1670,20473,20474],{"xmlns":1672},[1674,20475,20476,20522],{},[1677,20477,20478,20488,20490,20500,20502],{},[1680,20479,20480,20482],{},[1683,20481,71],{},[1677,20483,20484,20486],{},[1683,20485,6834],{},[1683,20487,7244],{},[1811,20489,2101],{},[1680,20491,20492,20494],{},[1683,20493,1974],{},[1677,20495,20496,20498],{},[1683,20497,6834],{},[1683,20499,7244],{},[1683,20501,4725],{"mathvariant":2240},[4574,20503,20504],{},[1677,20505,20506,20514],{},[3473,20507,20508,20510,20512],{},[1683,20509,1974],{},[1683,20511,6834],{},[1687,20513,1713],{},[3473,20515,20516,20518,20520],{},[1683,20517,1974],{},[1683,20519,7244],{},[1687,20521,1713],{},[1691,20523,20524],{"encoding":1693},"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 ",[1115,20527,20529],{"className":20528},[1668],[1670,20530,20531],{"xmlns":1672},[1674,20532,20533,20541],{},[1677,20534,20535],{},[1706,20536,20537,20539],{},[1683,20538,10337],{},[1687,20540,1713],{},[1691,20542,16139],{"encoding":1693},", případně obecným indexem korelace ",[1115,20545,20547],{"className":20546},[1668],[1670,20548,20549],{"xmlns":1672},[1674,20550,20551,20561],{},[1677,20552,20553],{},[4574,20554,20555],{},[1706,20556,20557,20559],{},[1683,20558,10337],{},[1687,20560,1713],{},[1691,20562,20563],{"encoding":1693},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,20566,20568],{"className":20567},[1668],[1670,20569,20570],{"xmlns":1672},[1674,20571,20572,20576],{},[1677,20573,20574],{},[1683,20575,6834],{},[1691,20577,6834],{"encoding":1693},[1115,20579,20581],{"className":20580},[1668],[1670,20582,20583],{"xmlns":1672},[1674,20584,20585,20589],{},[1677,20586,20587],{},[1683,20588,7244],{},[1691,20590,7244],{"encoding":1693},[1103,20592,20594,20601],{"className":20593,"dataCallout":6534},[1106,6533],[1110,20595,20597,20600],{"className":20596},[1113],[1115,20598],{"className":20599,"ariaHidden":1121},[1118,6541,1120],"Významný F-test, nevýznamné t-testy",[1110,20602,20603],{},"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.",[1103,20605,20607,20614],{"className":20606,"dataCallout":6534},[1106,6533],[1110,20608,20610,20613],{"className":20609},[1113],[1115,20611],{"className":20612,"ariaHidden":1121},[1118,6541,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,20615,20616],{},"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.",[1103,20618,20620,20627],{"className":20619,"dataCallout":6534},[1106,6533],[1110,20621,20623,20626],{"className":20622},[1113],[1115,20624],{"className":20625,"ariaHidden":1121},[1118,6541,1120],"Nízký počet pozorování při stepwise výběru",[1110,20628,20629],{},"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.",[1153,20631,1501],{"id":1500},[1503,20633,20634,20639,20644,20649,20654,20659,20664],{},[1265,20635,20636],{},[1127,20637,1133],{"className":20638,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,20640,20641],{},[1127,20642,1515],{"className":20643,"dataFsResolvedFilePath":1275,"href":1273},[1131],[1265,20645,20646],{},[1127,20647,1521],{"className":20648,"dataFsResolvedFilePath":1288,"href":1286},[1131],[1265,20650,20651],{},[1127,20652,1527],{"className":20653,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1265,20655,20656],{},[1127,20657,1318],{"className":20658,"dataFsResolvedFilePath":1324,"href":1322},[1131],[1265,20660,20661],{},[1127,20662,1543],{"className":20663,"dataFsResolvedFilePath":1336,"href":1334},[1131],[1265,20665,20666],{},[1127,20667,6753],{"className":20668,"dataFsResolvedFilePath":1550,"href":1548},[1131],[1153,20670,1554],{"id":934},[1110,20672,1557,20673,1561],{},[1420,20674,1560],{},[6761,20676,20677],{},"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.",[1265,20736,20737,20738,3071,20764,5862,20790,1497],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,20739,20741],{"className":20740},[1668],[1670,20742,20743],{"xmlns":1672},[1674,20744,20745,20761],{},[1677,20746,20747,20749,20755,20757,20759],{},[1811,20748,1994],{"stretchy":1993},[2843,20750,20751,20753],{"accent":1121},[1683,20752,6834],{},[1811,20754,11573],{},[1811,20756,1917],{"separator":1121},[1683,20758,10337],{},[1811,20760,2005],{"stretchy":1993},[1691,20762,20763],{"encoding":1693},"(\\bar{x}, R)",[1115,20765,20767],{"className":20766},[1668],[1670,20768,20769],{"xmlns":1672},[1674,20770,20771,20787],{},[1677,20772,20773,20775,20781,20783,20785],{},[1811,20774,1994],{"stretchy":1993},[2843,20776,20777,20779],{"accent":1121},[1683,20778,6834],{},[1811,20780,11573],{},[1811,20782,1917],{"separator":1121},[1683,20784,1974],{},[1811,20786,2005],{"stretchy":1993},[1691,20788,20789],{"encoding":1693},"(\\bar{x}, s)",[1115,20791,20793],{"className":20792},[1668],[1670,20794,20795],{"xmlns":1672},[1674,20796,20797,20826],{},[1677,20798,20799,20801,20807,20809,20824],{},[1811,20800,1994],{"stretchy":1993},[1680,20802,20803,20805],{},[1683,20804,6834],{},[1683,20806,1997],{},[1811,20808,1917],{"separator":1121},[1680,20810,20811,20813],{},[1683,20812,10337],{},[1677,20814,20815,20817,20820,20822],{},[1683,20816,7374],{},[1683,20818,20819],{},"l",[1811,20821,1917],{"separator":1121},[1683,20823,1997],{},[1811,20825,2005],{"stretchy":1993},[1691,20827,20828],{"encoding":1693},"(x_i, R_{kl,i})",[1265,20830,20831,20832,20845,20846,20859,20860,20876,20877,20890],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,20833,20835],{"className":20834},[1668],[1670,20836,20837],{"xmlns":1672},[1674,20838,20839,20843],{},[1677,20840,20841],{},[1683,20842,3840],{},[1691,20844,3840],{"encoding":1693}," (konstantní rozsah) a ",[1115,20847,20849],{"className":20848},[1668],[1670,20850,20851],{"xmlns":1672},[1674,20852,20853,20857],{},[1677,20854,20855],{},[1683,20856,11642],{},[1691,20858,11642],{"encoding":1693}," (nekonstantní rozsah), počet neshodných produktů ",[1115,20861,20863],{"className":20862},[1668],[1670,20864,20865],{"xmlns":1672},[1674,20866,20867,20873],{},[1677,20868,20869,20871],{},[1683,20870,1809],{},[1683,20872,1110],{},[1691,20874,20875],{"encoding":1693},"np"," (konstantní rozsah) a jejich podíl ",[1115,20878,20880],{"className":20879},[1668],[1670,20881,20882],{"xmlns":1672},[1674,20883,20884,20888],{},[1677,20885,20886],{},[1683,20887,1110],{},[1691,20889,1110],{"encoding":1693}," (nekonstantní rozsah).",[1265,20892,20893],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1265,20895,20896,20897,3071,20915,3071,20937,3071,20959,20983,20984,21005],{},"Indexy způsobilosti ",[1115,20898,20900],{"className":20899},[1668],[1670,20901,20902],{"xmlns":1672},[1674,20903,20904,20912],{},[1677,20905,20906],{},[1680,20907,20908,20910],{},[1683,20909,1379],{},[1683,20911,1110],{},[1691,20913,20914],{"encoding":1693},"C_p",[1115,20916,20918],{"className":20917},[1668],[1670,20919,20920],{"xmlns":1672},[1674,20921,20922,20934],{},[1677,20923,20924],{},[1680,20925,20926,20928],{},[1683,20927,1379],{},[1677,20929,20930,20932],{},[1683,20931,1110],{},[1683,20933,7374],{},[1691,20935,20936],{"encoding":1693},"C_{pk}",[1115,20938,20940],{"className":20939},[1668],[1670,20941,20942],{"xmlns":1672},[1674,20943,20944,20956],{},[1677,20945,20946],{},[1680,20947,20948,20950],{},[1683,20949,1379],{},[1677,20951,20952,20954],{},[1683,20953,1110],{},[1683,20955,4592],{},[1691,20957,20958],{"encoding":1693},"C_{pm}",[1115,20960,20962],{"className":20961},[1668],[1670,20963,20964],{"xmlns":1672},[1674,20965,20966,20980],{},[1677,20967,20968],{},[1680,20969,20970,20972],{},[1683,20971,1379],{},[1677,20973,20974,20976,20978],{},[1683,20975,1110],{},[1683,20977,4592],{},[1683,20979,7374],{},[1691,20981,20982],{"encoding":1693},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,20985,20987],{"className":20986},[1668],[1670,20988,20989],{"xmlns":1672},[1674,20990,20991,21003],{},[1677,20992,20993],{},[1680,20994,20995,20997],{},[1683,20996,1379],{},[1677,20998,20999,21001],{},[1683,21000,1110],{},[1683,21002,7374],{},[1691,21004,20936],{"encoding":1693}," navíc zohledňuje vychýlení střední hodnoty.",[1265,21007,21008,21009,1497],{},"V R diagramy i indexy počítá balíček ",[3590,21010,360],{},[1153,21012,1330],{"id":21013},"statistická-regulace-procesu",[1110,21015,21016,21017,21019,21020,1497],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1136,21018,1330],{}," 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 ",[1136,21021,21022],{},"statisticky zvládnutém stavu",[1110,21024,21025,21026,21029],{},"Teorie regulace vychází z ",[1136,21027,21028],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1158,21031,21032,21044],{},[1161,21033,21034],{},[1164,21035,21036,21038,21041],{},[1167,21037],{},[1167,21039,21040],{},"Náhodné příčiny",[1167,21042,21043],{},"Vymezitelné příčiny",[1174,21045,21046,21057,21068],{},[1164,21047,21048,21051,21054],{},[1179,21049,21050],{},"Povaha",[1179,21052,21053],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1179,21055,21056],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1164,21058,21059,21062,21065],{},[1179,21060,21061],{},"Stav procesu",[1179,21063,21064],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1179,21066,21067],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1164,21069,21070,21073,21076],{},[1179,21071,21072],{},"Příklady",[1179,21074,21075],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1179,21077,21078],{},"změna materiálu, nezaškolená obsluha",[1110,21080,21081,21082,21085,21086,21089],{},"Vymezitelné příčiny jsou ",[1136,21083,21084],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1136,21087,21088],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,21091,21092],{},[4504,21093],{"alt":21094,"className":21095,"src":21096},"mask-ilu-pricin-variability",[1131,4508],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,21098,21099],{},"Regulace probíhá ve třech fázích:",[1262,21101,21102,21112,21118],{},[1265,21103,21104,21107,21108,21111],{},[1136,21105,21106],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1136,21109,21110],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1265,21113,21114,21117],{},[1136,21115,21116],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1265,21119,21120,21123],{},[1136,21121,21122],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1153,21125,21127],{"id":21126},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,21129,21130,21133],{},[1136,21131,21132],{},"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.",[1503,21135,21136,21142,21148],{},[1265,21137,21138,21141],{},[1136,21139,21140],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1265,21143,21144,21147],{},[1136,21145,21146],{},"UCL"," — horní akční regulační mez,",[1265,21149,21150,21153],{},[1136,21151,21152],{},"LCL"," — dolní akční regulační mez.",[1110,21155,21156],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,21158,21159],{},[4504,21160],{"alt":21161,"className":21162,"src":21163},"mask-rd-schema",[1131,4508],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,21165,21166,21169],{},[1136,21167,21168],{},"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.",[1110,21171,21172,21173,21176,21177,21180],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1136,21174,21175],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1136,21178,21179],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,21182,21183],{},"Postup při konstrukci regulačního diagramu:",[1262,21185,21186,21189,21192,21195,21198,21201,21204,21207,21210],{},[1265,21187,21188],{},"volba regulované veličiny,",[1265,21190,21191],{},"sběr a záznam dat,",[1265,21193,21194],{},"ověření požadovaných předpokladů o datech,",[1265,21196,21197],{},"volba rozsahu logických podskupin,",[1265,21199,21200],{},"volba vhodného regulačního diagramu,",[1265,21202,21203],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1265,21205,21206],{},"ověření a zajištění statistické zvládnutosti procesu,",[1265,21208,21209],{},"ověření způsobilosti procesu,",[1265,21211,21212],{},"vlastní regulace procesu.",[1153,21214,21216],{"id":21215},"regulace-měřením","Regulace měřením",[1110,21218,21219],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1503,21221,21222,21225],{},[1265,21223,21224],{},"jednotlivá měření byla vzájemně nezávislá,",[1265,21226,21227,21228,21241,21242,21255,21256,21269,21270,21283],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,21229,21231],{"className":21230},[1668],[1670,21232,21233],{"xmlns":1672},[1674,21234,21235,21239],{},[1677,21236,21237],{},[1683,21238,7005],{},[1691,21240,8910],{"encoding":1693}," a směrodatnou odchylkou ",[1115,21243,21245],{"className":21244},[1668],[1670,21246,21247],{"xmlns":1672},[1674,21248,21249,21253],{},[1677,21250,21251],{},[1683,21252,7013],{},[1691,21254,7045],{"encoding":1693}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,21257,21259],{"className":21258},[1668],[1670,21260,21261],{"xmlns":1672},[1674,21262,21263,21267],{},[1677,21264,21265],{},[1683,21266,7005],{},[1691,21268,8910],{"encoding":1693}," je hodnota, na niž je proces nastaven, ",[1115,21271,21273],{"className":21272},[1668],[1670,21274,21275],{"xmlns":1672},[1674,21276,21277,21281],{},[1677,21278,21279],{},[1683,21280,7013],{},[1691,21282,7045],{"encoding":1693}," charakterizuje jeho přesnost.",[1110,21285,21286,21287,3071,21312,5862,21337,21374],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,21288,21290],{"className":21289},[1668],[1670,21291,21292],{"xmlns":1672},[1674,21293,21294,21310],{},[1677,21295,21296,21298,21304,21306,21308],{},[1811,21297,1994],{"stretchy":1993},[2843,21299,21300,21302],{"accent":1121},[1683,21301,6834],{},[1811,21303,11573],{},[1811,21305,1917],{"separator":1121},[1683,21307,10337],{},[1811,21309,2005],{"stretchy":1993},[1691,21311,20763],{"encoding":1693},[1115,21313,21315],{"className":21314},[1668],[1670,21316,21317],{"xmlns":1672},[1674,21318,21319,21335],{},[1677,21320,21321,21323,21329,21331,21333],{},[1811,21322,1994],{"stretchy":1993},[2843,21324,21325,21327],{"accent":1121},[1683,21326,6834],{},[1811,21328,11573],{},[1811,21330,1917],{"separator":1121},[1683,21332,1974],{},[1811,21334,2005],{"stretchy":1993},[1691,21336,20789],{"encoding":1693},[1115,21338,21340],{"className":21339},[1668],[1670,21341,21342],{"xmlns":1672},[1674,21343,21344,21372],{},[1677,21345,21346,21348,21354,21356,21370],{},[1811,21347,1994],{"stretchy":1993},[1680,21349,21350,21352],{},[1683,21351,6834],{},[1683,21353,1997],{},[1811,21355,1917],{"separator":1121},[1680,21357,21358,21360],{},[1683,21359,10337],{},[1677,21361,21362,21364,21366,21368],{},[1683,21363,7374],{},[1683,21365,20819],{},[1811,21367,1917],{"separator":1121},[1683,21369,1997],{},[1811,21371,2005],{"stretchy":1993},[1691,21373,20828],{"encoding":1693},". Výsledkem jsou vždy dva diagramy.",[16860,21376,21378,21379],{"id":21377},"diagram-xˉrbarx-r","Diagram ",[1115,21380,21382],{"className":21381},[1668],[1670,21383,21384],{"xmlns":1672},[1674,21385,21386,21402],{},[1677,21387,21388,21390,21396,21398,21400],{},[1811,21389,1994],{"stretchy":1993},[2843,21391,21392,21394],{"accent":1121},[1683,21393,6834],{},[1811,21395,11573],{},[1811,21397,1917],{"separator":1121},[1683,21399,10337],{},[1811,21401,2005],{"stretchy":1993},[1691,21403,20763],{"encoding":1693},[1110,21405,21406,21407,21429,21430,21448],{},"Regulované veličiny jsou výběrové průměry ",[1115,21408,21410],{"className":21409},[1668],[1670,21411,21412],{"xmlns":1672},[1674,21413,21414,21426],{},[1677,21415,21416],{},[1680,21417,21418,21424],{},[2843,21419,21420,21422],{"accent":1121},[1683,21421,6834],{},[1811,21423,11573],{},[1683,21425,1997],{},[1691,21427,21428],{"encoding":1693},"\\bar{x}_i"," a výběrová rozpětí ",[1115,21431,21433],{"className":21432},[1668],[1670,21434,21435],{"xmlns":1672},[1674,21436,21437,21445],{},[1677,21438,21439],{},[1680,21440,21441,21443],{},[1683,21442,10337],{},[1683,21444,1997],{},[1691,21446,21447],{"encoding":1693},"R_i"," v logických podskupinách:",[1115,21450,21452],{"className":21451},[1668],[1670,21453,21454],{"xmlns":1672,"display":2083},[1674,21455,21456,21557],{},[1677,21457,21458,21468,21470,21476,21490,21500,21502,21504,21510,21512,21523,21533,21535,21545,21555],{},[1680,21459,21460,21466],{},[2843,21461,21462,21464],{"accent":1121},[1683,21463,6834],{},[1811,21465,11573],{},[1683,21467,1997],{},[1811,21469,2101],{},[2859,21471,21472,21474],{},[1687,21473,1914],{},[1683,21475,1809],{},[2103,21477,21478,21480,21488],{},[1811,21479,2107],{},[1677,21481,21482,21484,21486],{},[1683,21483,2002],{},[1811,21485,2101],{},[1687,21487,1914],{},[1683,21489,1809],{},[1680,21491,21492,21494],{},[1683,21493,6834],{},[1677,21495,21496,21498],{},[1683,21497,1997],{},[1683,21499,2002],{},[1811,21501,1917],{"separator":1121},[2131,21503],{"width":2133},[1680,21505,21506,21508],{},[1683,21507,10337],{},[1683,21509,1997],{},[1811,21511,2101],{},[21513,21514,21515,21521],"munder",{},[1677,21516,21517,21519],{},[1683,21518,11833],{},[1811,21520,4612],{},[1683,21522,2002],{},[1680,21524,21525,21527],{},[1683,21526,6834],{},[1677,21528,21529,21531],{},[1683,21530,1997],{},[1683,21532,2002],{},[1811,21534,3184],{},[21513,21536,21537,21543],{},[1677,21538,21539,21541],{},[1683,21540,4609],{},[1811,21542,4612],{},[1683,21544,2002],{},[1680,21546,21547,21549],{},[1683,21548,6834],{},[1677,21550,21551,21553],{},[1683,21552,1997],{},[1683,21554,2002],{},[1683,21556,1497],{"mathvariant":2240},[1691,21558,21559],{"encoding":1693},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,21561,21562],{},"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.",[1110,21564,21565,21566,21592,21593,21606,21607,5862,21628,21645,21646,21659,21660,21678,21679,1497],{},"Data se zapisují do tabulky: řádek ",[1115,21567,21569],{"className":21568},[1668],[1670,21570,21571],{"xmlns":1672},[1674,21572,21573,21589],{},[1677,21574,21575,21577,21579,21581,21583,21585,21587],{},[1683,21576,1997],{},[1811,21578,2101],{},[1687,21580,1914],{},[1811,21582,1917],{"separator":1121},[1811,21584,1920],{},[1811,21586,1917],{"separator":1121},[1683,21588,7374],{},[1691,21590,21591],{"encoding":1693},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,21594,21596],{"className":21595},[1668],[1670,21597,21598],{"xmlns":1672},[1674,21599,21600,21604],{},[1677,21601,21602],{},[1683,21603,1809],{},[1691,21605,1809],{"encoding":1693}," naměřených hodnot a poslední dva sloupce ",[1115,21608,21610],{"className":21609},[1668],[1670,21611,21612],{"xmlns":1672},[1674,21613,21614,21626],{},[1677,21615,21616],{},[1680,21617,21618,21624],{},[2843,21619,21620,21622],{"accent":1121},[1683,21621,6834],{},[1811,21623,11573],{},[1683,21625,1997],{},[1691,21627,21428],{"encoding":1693},[1115,21629,21631],{"className":21630},[1668],[1670,21632,21633],{"xmlns":1672},[1674,21634,21635,21643],{},[1677,21636,21637],{},[1680,21638,21639,21641],{},[1683,21640,10337],{},[1683,21642,1997],{},[1691,21644,21447],{"encoding":1693},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,21647,21649],{"className":21648},[1668],[1670,21650,21651],{"xmlns":1672},[1674,21652,21653,21657],{},[1677,21654,21655],{},[1683,21656,10337],{},[1691,21658,10337],{"encoding":1693},", potom diagram ",[1115,21661,21663],{"className":21662},[1668],[1670,21664,21665],{"xmlns":1672},[1674,21666,21667,21675],{},[1677,21668,21669],{},[2843,21670,21671,21673],{"accent":1121},[1683,21672,6834],{},[1811,21674,11573],{},[1691,21676,21677],{"encoding":1693},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3590,21680,21681],{},"qcc()",[1103,21683,21685,21692],{"className":21684,"dataCallout":3597},[1106,3596],[1110,21686,21688,21691],{"className":21687},[1113],[1115,21689],{"className":21690,"ariaHidden":1121},[1118,3604,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,21693,21694,21695,21708,21709,3071,21727,21745,21746,1497],{},"Naměřená data znaku jakosti ",[1115,21696,21698],{"className":21697},[1668],[1670,21699,21700],{"xmlns":1672},[1674,21701,21702,21706],{},[1677,21703,21704],{},[1683,21705,6846],{},[1691,21707,6846],{"encoding":1693}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,21710,21712],{"className":21711},[1668],[1670,21713,21714],{"xmlns":1672},[1674,21715,21716,21724],{},[1677,21717,21718,21720,21722],{},[1683,21719,7374],{},[1811,21721,2101],{},[1687,21723,4166],{},[1691,21725,21726],{"encoding":1693},"k=20",[1115,21728,21730],{"className":21729},[1668],[1670,21731,21732],{"xmlns":1672},[1674,21733,21734,21742],{},[1677,21735,21736,21738,21740],{},[1683,21737,1809],{},[1811,21739,2101],{},[1687,21741,3662],{},[1691,21743,21744],{"encoding":1693},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,21747,21749],{"className":21748},[1668],[1670,21750,21751],{"xmlns":1672},[1674,21752,21753,21769],{},[1677,21754,21755,21757,21763,21765,21767],{},[1811,21756,1994],{"stretchy":1993},[2843,21758,21759,21761],{"accent":1121},[1683,21760,6834],{},[1811,21762,11573],{},[1811,21764,1917],{"separator":1121},[1683,21766,10337],{},[1811,21768,2005],{"stretchy":1993},[1691,21770,20763],{"encoding":1693},[1158,21772,21773,21888],{},[1161,21774,21775],{},[1164,21776,21777,21792,21816,21840,21864],{},[1167,21778,21779],{},[1115,21780,21782],{"className":21781},[1668],[1670,21783,21784],{"xmlns":1672},[1674,21785,21786,21790],{},[1677,21787,21788],{},[1683,21789,1997],{},[1691,21791,1997],{"encoding":1693},[1167,21793,21794],{},[1115,21795,21797],{"className":21796},[1668],[1670,21798,21799],{"xmlns":1672},[1674,21800,21801,21813],{},[1677,21802,21803],{},[1680,21804,21805,21807],{},[1683,21806,6834],{},[1677,21808,21809,21811],{},[1683,21810,1997],{},[1687,21812,1914],{},[1691,21814,21815],{"encoding":1693},"x_{i1}",[1167,21817,21818],{},[1115,21819,21821],{"className":21820},[1668],[1670,21822,21823],{"xmlns":1672},[1674,21824,21825,21837],{},[1677,21826,21827],{},[1680,21828,21829,21831],{},[1683,21830,6834],{},[1677,21832,21833,21835],{},[1683,21834,1997],{},[1687,21836,1713],{},[1691,21838,21839],{"encoding":1693},"x_{i2}",[1167,21841,21842],{},[1115,21843,21845],{"className":21844},[1668],[1670,21846,21847],{"xmlns":1672},[1674,21848,21849,21861],{},[1677,21850,21851],{},[1680,21852,21853,21855],{},[1683,21854,6834],{},[1677,21856,21857,21859],{},[1683,21858,1997],{},[1687,21860,3712],{},[1691,21862,21863],{"encoding":1693},"x_{i3}",[1167,21865,21866],{},[1115,21867,21869],{"className":21868},[1668],[1670,21870,21871],{"xmlns":1672},[1674,21872,21873,21885],{},[1677,21874,21875],{},[1680,21876,21877,21879],{},[1683,21878,6834],{},[1677,21880,21881,21883],{},[1683,21882,1997],{},[1687,21884,3662],{},[1691,21886,21887],{"encoding":1693},"x_{i4}",[1174,21889,21890,21904,21919,21935,21950,21962,21976,21988,22001],{},[1164,21891,21892,21894,21897,21900,21902],{},[1179,21893,1914],{},[1179,21895,21896],{},"106",[1179,21898,21899],{},"98",[1179,21901,14199],{},[1179,21903,14199],{},[1164,21905,21906,21908,21911,21914,21917],{},[1179,21907,1713],{},[1179,21909,21910],{},"95",[1179,21912,21913],{},"94",[1179,21915,21916],{},"108",[1179,21918,6245],{},[1164,21920,21921,21923,21926,21929,21932],{},[1179,21922,3712],{},[1179,21924,21925],{},"122",[1179,21927,21928],{},"105",[1179,21930,21931],{},"103",[1179,21933,21934],{},"133",[1164,21936,21937,21939,21942,21944,21947],{},[1179,21938,3662],{},[1179,21940,21941],{},"113",[1179,21943,3684],{},[1179,21945,21946],{},"128",[1179,21948,21949],{},"135",[1164,21951,21952,21954,21956,21958,21960],{},[1179,21953,10040],{},[1179,21955,14199],{},[1179,21957,6245],{},[1179,21959,21931],{},[1179,21961,6245],{},[1164,21963,21964,21966,21968,21970,21973],{},[1179,21965,4085],{},[1179,21967,21899],{},[1179,21969,21931],{},[1179,21971,21972],{},"97",[1179,21974,21975],{},"99",[1164,21977,21978,21980,21982,21984,21986],{},[1179,21979,1920],{},[1179,21981,1920],{},[1179,21983,1920],{},[1179,21985,1920],{},[1179,21987,1920],{},[1164,21989,21990,21992,21994,21996,21999],{},[1179,21991,14833],{},[1179,21993,21946],{},[1179,21995,21934],{},[1179,21997,21998],{},"120",[1179,22000,14861],{},[1164,22002,22003,22005,22007,22009,22011],{},[1179,22004,4166],{},[1179,22006,21899],{},[1179,22008,21931],{},[1179,22010,21972],{},[1179,22012,21975],{},[1110,22014,22015,22016,22037,22038,2077],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,22017,22019],{"className":22018},[1668],[1670,22020,22021],{"xmlns":1672},[1674,22022,22023,22035],{},[1677,22024,22025],{},[1680,22026,22027,22033],{},[2843,22028,22029,22031],{"accent":1121},[1683,22030,6834],{},[1811,22032,11573],{},[1683,22034,1997],{},[1691,22036,21428],{"encoding":1693}," a rozpětí ",[1115,22039,22041],{"className":22040},[1668],[1670,22042,22043],{"xmlns":1672},[1674,22044,22045,22053],{},[1677,22046,22047],{},[1680,22048,22049,22051],{},[1683,22050,10337],{},[1683,22052,1997],{},[1691,22054,21447],{"encoding":1693},[1158,22056,22057,22118],{},[1161,22058,22059],{},[1164,22060,22061,22076,22099],{},[1167,22062,22063],{},[1115,22064,22066],{"className":22065},[1668],[1670,22067,22068],{"xmlns":1672},[1674,22069,22070,22074],{},[1677,22071,22072],{},[1683,22073,1997],{},[1691,22075,1997],{"encoding":1693},[1167,22077,22078],{},[1115,22079,22081],{"className":22080},[1668],[1670,22082,22083],{"xmlns":1672},[1674,22084,22085,22097],{},[1677,22086,22087],{},[1680,22088,22089,22095],{},[2843,22090,22091,22093],{"accent":1121},[1683,22092,6834],{},[1811,22094,11573],{},[1683,22096,1997],{},[1691,22098,21428],{"encoding":1693},[1167,22100,22101],{},[1115,22102,22104],{"className":22103},[1668],[1670,22105,22106],{"xmlns":1672},[1674,22107,22108,22116],{},[1677,22109,22110],{},[1680,22111,22112,22114],{},[1683,22113,10337],{},[1683,22115,1997],{},[1691,22117,21447],{"encoding":1693},[1174,22119,22120,22129,22139,22149,22159,22168,22177,22185,22194],{},[1164,22121,22122,22124,22127],{},[1179,22123,1914],{},[1179,22125,22126],{},"101,50",[1179,22128,14928],{},[1164,22130,22131,22133,22136],{},[1179,22132,1713],{},[1179,22134,22135],{},"97,25",[1179,22137,22138],{},"16",[1164,22140,22141,22143,22146],{},[1179,22142,3712],{},[1179,22144,22145],{},"115,75",[1179,22147,22148],{},"30",[1164,22150,22151,22153,22156],{},[1179,22152,3662],{},[1179,22154,22155],{},"111,75",[1179,22157,22158],{},"64",[1164,22160,22161,22163,22166],{},[1179,22162,10040],{},[1179,22164,22165],{},"97,00",[1179,22167,2374],{},[1164,22169,22170,22172,22175],{},[1179,22171,4085],{},[1179,22173,22174],{},"99,25",[1179,22176,4085],{},[1164,22178,22179,22181,22183],{},[1179,22180,1920],{},[1179,22182,1920],{},[1179,22184,1920],{},[1164,22186,22187,22189,22192],{},[1179,22188,14833],{},[1179,22190,22191],{},"126,50",[1179,22193,3665],{},[1164,22195,22196,22198,22200],{},[1179,22197,4166],{},[1179,22199,22174],{},[1179,22201,4085],{},[1110,22203,22204,22205,22218,22219,3071,22247,3071,22277,22305,22306,22328,22329,3071,22356,3071,22385,22412,22413,1497],{},"Nejprve se posoudí diagram ",[1115,22206,22208],{"className":22207},[1668],[1670,22209,22210],{"xmlns":1672},[1674,22211,22212,22216],{},[1677,22213,22214],{},[1683,22215,10337],{},[1691,22217,10337],{"encoding":1693}," na všech 20 podskupinách: ",[1115,22220,22222],{"className":22221},[1668],[1670,22223,22224],{"xmlns":1672},[1674,22225,22226,22244],{},[1677,22227,22228,22230,22233,22235,22237,22239,22241],{},[1683,22229,1379],{},[1683,22231,22232],{},"L",[1811,22234,1994],{"stretchy":1993},[1683,22236,10337],{},[1811,22238,2005],{"stretchy":1993},[1811,22240,2101],{},[1687,22242,22243],{},"15,8",[1691,22245,22246],{"encoding":1693},"CL(R)=15{,}8",[1115,22248,22250],{"className":22249},[1668],[1670,22251,22252],{"xmlns":1672},[1674,22253,22254,22274],{},[1677,22255,22256,22259,22261,22263,22265,22267,22269,22271],{},[1683,22257,22258],{},"U",[1683,22260,1379],{},[1683,22262,22232],{},[1811,22264,1994],{"stretchy":1993},[1683,22266,10337],{},[1811,22268,2005],{"stretchy":1993},[1811,22270,2101],{},[1687,22272,22273],{},"36,06",[1691,22275,22276],{"encoding":1693},"UCL(R)=36{,}06",[1115,22278,22280],{"className":22279},[1668],[1670,22281,22282],{"xmlns":1672},[1674,22283,22284,22302],{},[1677,22285,22286,22288,22290,22292,22294,22296,22298,22300],{},[1683,22287,22232],{},[1683,22289,1379],{},[1683,22291,22232],{},[1811,22293,1994],{"stretchy":1993},[1683,22295,10337],{},[1811,22297,2005],{"stretchy":1993},[1811,22299,2101],{},[1687,22301,1689],{},[1691,22303,22304],{"encoding":1693},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,22307,22309],{"className":22308},[1668],[1670,22310,22311],{"xmlns":1672},[1674,22312,22313,22325],{},[1677,22314,22315,22321,22323],{},[1680,22316,22317,22319],{},[1683,22318,10337],{},[1687,22320,3662],{},[1811,22322,2101],{},[1687,22324,22158],{},[1691,22326,22327],{"encoding":1693},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,22330,22332],{"className":22331},[1668],[1670,22333,22334],{"xmlns":1672},[1674,22335,22336,22353],{},[1677,22337,22338,22340,22342,22344,22346,22348,22350],{},[1683,22339,1379],{},[1683,22341,22232],{},[1811,22343,1994],{"stretchy":1993},[1683,22345,10337],{},[1811,22347,2005],{"stretchy":1993},[1811,22349,2101],{},[1687,22351,22352],{},"13,26",[1691,22354,22355],{"encoding":1693},"CL(R)=13{,}26",[1115,22357,22359],{"className":22358},[1668],[1670,22360,22361],{"xmlns":1672},[1674,22362,22363,22382],{},[1677,22364,22365,22367,22369,22371,22373,22375,22377,22379],{},[1683,22366,22258],{},[1683,22368,1379],{},[1683,22370,22232],{},[1811,22372,1994],{"stretchy":1993},[1683,22374,10337],{},[1811,22376,2005],{"stretchy":1993},[1811,22378,2101],{},[1687,22380,22381],{},"30,27",[1691,22383,22384],{"encoding":1693},"UCL(R)=30{,}27",[1115,22386,22388],{"className":22387},[1668],[1670,22389,22390],{"xmlns":1672},[1674,22391,22392,22410],{},[1677,22393,22394,22396,22398,22400,22402,22404,22406,22408],{},[1683,22395,22232],{},[1683,22397,1379],{},[1683,22399,22232],{},[1811,22401,1994],{"stretchy":1993},[1683,22403,10337],{},[1811,22405,2005],{"stretchy":1993},[1811,22407,2101],{},[1687,22409,1689],{},[1691,22411,22304],{"encoding":1693},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,22414,22416],{"className":22415},[1668],[1670,22417,22418],{"xmlns":1672},[1674,22419,22420,22428],{},[1677,22421,22422],{},[2843,22423,22424,22426],{"accent":1121},[1683,22425,6834],{},[1811,22427,11573],{},[1691,22429,21677],{"encoding":1693},[1110,22431,21378,22432,22449,22450,3071,22481,3071,22514,22547,22548,22561,22562,3071,22589,3071,22618,22645],{},[1115,22433,22435],{"className":22434},[1668],[1670,22436,22437],{"xmlns":1672},[1674,22438,22439,22447],{},[1677,22440,22441],{},[2843,22442,22443,22445],{"accent":1121},[1683,22444,6834],{},[1811,22446,11573],{},[1691,22448,21677],{"encoding":1693}," bez čtvrté podskupiny dává ",[1115,22451,22453],{"className":22452},[1668],[1670,22454,22455],{"xmlns":1672},[1674,22456,22457,22478],{},[1677,22458,22459,22461,22463,22465,22471,22473,22475],{},[1683,22460,1379],{},[1683,22462,22232],{},[1811,22464,1994],{"stretchy":1993},[2843,22466,22467,22469],{"accent":1121},[1683,22468,6834],{},[1811,22470,11573],{},[1811,22472,2005],{"stretchy":1993},[1811,22474,2101],{},[1687,22476,22477],{},"102,01",[1691,22479,22480],{"encoding":1693},"CL(\\bar{x})=102{,}01",[1115,22482,22484],{"className":22483},[1668],[1670,22485,22486],{"xmlns":1672},[1674,22487,22488,22511],{},[1677,22489,22490,22492,22494,22496,22498,22504,22506,22508],{},[1683,22491,22258],{},[1683,22493,1379],{},[1683,22495,22232],{},[1811,22497,1994],{"stretchy":1993},[2843,22499,22500,22502],{"accent":1121},[1683,22501,6834],{},[1811,22503,11573],{},[1811,22505,2005],{"stretchy":1993},[1811,22507,2101],{},[1687,22509,22510],{},"111,68",[1691,22512,22513],{"encoding":1693},"UCL(\\bar{x})=111{,}68",[1115,22515,22517],{"className":22516},[1668],[1670,22518,22519],{"xmlns":1672},[1674,22520,22521,22544],{},[1677,22522,22523,22525,22527,22529,22531,22537,22539,22541],{},[1683,22524,22232],{},[1683,22526,1379],{},[1683,22528,22232],{},[1811,22530,1994],{"stretchy":1993},[2843,22532,22533,22535],{"accent":1121},[1683,22534,6834],{},[1811,22536,11573],{},[1811,22538,2005],{"stretchy":1993},[1811,22540,2101],{},[1687,22542,22543],{},"92,34",[1691,22545,22546],{"encoding":1693},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,22549,22551],{"className":22550},[1668],[1670,22552,22553],{"xmlns":1672},[1674,22554,22555,22559],{},[1677,22556,22557],{},[1683,22558,10337],{},[1691,22560,10337],{"encoding":1693}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,22563,22565],{"className":22564},[1668],[1670,22566,22567],{"xmlns":1672},[1674,22568,22569,22586],{},[1677,22570,22571,22573,22575,22577,22579,22581,22583],{},[1683,22572,1379],{},[1683,22574,22232],{},[1811,22576,1994],{"stretchy":1993},[1683,22578,10337],{},[1811,22580,2005],{"stretchy":1993},[1811,22582,2101],{},[1687,22584,22585],{},"12,29",[1691,22587,22588],{"encoding":1693},"CL(R)=12{,}29",[1115,22590,22592],{"className":22591},[1668],[1670,22593,22594],{"xmlns":1672},[1674,22595,22596,22615],{},[1677,22597,22598,22600,22602,22604,22606,22608,22610,22612],{},[1683,22599,22258],{},[1683,22601,1379],{},[1683,22603,22232],{},[1811,22605,1994],{"stretchy":1993},[1683,22607,10337],{},[1811,22609,2005],{"stretchy":1993},[1811,22611,2101],{},[1687,22613,22614],{},"28,06",[1691,22616,22617],{"encoding":1693},"UCL(R)=28{,}06",[1115,22619,22621],{"className":22620},[1668],[1670,22622,22623],{"xmlns":1672},[1674,22624,22625,22643],{},[1677,22626,22627,22629,22631,22633,22635,22637,22639,22641],{},[1683,22628,22232],{},[1683,22630,1379],{},[1683,22632,22232],{},[1811,22634,1994],{"stretchy":1993},[1683,22636,10337],{},[1811,22638,2005],{"stretchy":1993},[1811,22640,2101],{},[1687,22642,1689],{},[1691,22644,22304],{"encoding":1693}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,22647,22648,22649,22666,22667,3071,22698,3071,22731,22764],{},"Konečný diagram ",[1115,22650,22652],{"className":22651},[1668],[1670,22653,22654],{"xmlns":1672},[1674,22655,22656,22664],{},[1677,22657,22658],{},[2843,22659,22660,22662],{"accent":1121},[1683,22661,6834],{},[1811,22663,11573],{},[1691,22665,21677],{"encoding":1693}," na stejných 17 podskupinách má ",[1115,22668,22670],{"className":22669},[1668],[1670,22671,22672],{"xmlns":1672},[1674,22673,22674,22695],{},[1677,22675,22676,22678,22680,22682,22688,22690,22692],{},[1683,22677,1379],{},[1683,22679,22232],{},[1811,22681,1994],{"stretchy":1993},[2843,22683,22684,22686],{"accent":1121},[1683,22685,6834],{},[1811,22687,11573],{},[1811,22689,2005],{"stretchy":1993},[1811,22691,2101],{},[1687,22693,22694],{},"99,76",[1691,22696,22697],{"encoding":1693},"CL(\\bar{x})=99{,}76",[1115,22699,22701],{"className":22700},[1668],[1670,22702,22703],{"xmlns":1672},[1674,22704,22705,22728],{},[1677,22706,22707,22709,22711,22713,22715,22721,22723,22725],{},[1683,22708,22258],{},[1683,22710,1379],{},[1683,22712,22232],{},[1811,22714,1994],{"stretchy":1993},[2843,22716,22717,22719],{"accent":1121},[1683,22718,6834],{},[1811,22720,11573],{},[1811,22722,2005],{"stretchy":1993},[1811,22724,2101],{},[1687,22726,22727],{},"108,73",[1691,22729,22730],{"encoding":1693},"UCL(\\bar{x})=108{,}73",[1115,22732,22734],{"className":22733},[1668],[1670,22735,22736],{"xmlns":1672},[1674,22737,22738,22761],{},[1677,22739,22740,22742,22744,22746,22748,22754,22756,22758],{},[1683,22741,22232],{},[1683,22743,1379],{},[1683,22745,22232],{},[1811,22747,1994],{"stretchy":1993},[2843,22749,22750,22752],{"accent":1121},[1683,22751,6834],{},[1811,22753,11573],{},[1811,22755,2005],{"stretchy":1993},[1811,22757,2101],{},[1687,22759,22760],{},"90,80",[1691,22762,22763],{"encoding":1693},"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.",[1110,22766,22767],{},[4504,22768],{"alt":22769,"className":22770,"src":22771},"mask-rd-priklad1-meze",[1131,4508],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,22773,22774,22775,22777,22778,22780],{},"V R se diagramy sestrojí funkcí ",[3590,22776,21681],{}," z balíčku ",[3590,22779,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3814,22782,22784],{"className":3816,"code":22783,"language":71,"meta":1603,"style":1603},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3590,22785,22786,22796,22819,22842],{"__ignoreMap":1603},[1115,22787,22788,22790,22792,22794],{"class":3822,"line":10},[1115,22789,17509],{"class":3829},[1115,22791,1994],{"class":3837},[1115,22793,360],{"class":3825},[1115,22795,4022],{"class":3837},[1115,22797,22798,22800,22802,22804,22806,22809,22811,22813,22815,22817],{"class":3822,"line":27},[1115,22799,20220],{"class":3825},[1115,22801,3830],{"class":3829},[1115,22803,20225],{"class":3833},[1115,22805,1994],{"class":3837},[1115,22807,22808],{"class":3961},"\"3_2.txt\"",[1115,22810,1917],{"class":3829},[1115,22812,20235],{"class":3825},[1115,22814,3918],{"class":3829},[1115,22816,3931],{"class":3845},[1115,22818,4022],{"class":3837},[1115,22820,22821,22823,22825,22827,22829,22831,22833,22836,22839],{"class":3822,"line":148},[1115,22822,360],{"class":3833},[1115,22824,1994],{"class":3837},[1115,22826,20220],{"class":3825},[1115,22828,1917],{"class":3829},[1115,22830,12337],{"class":3825},[1115,22832,3918],{"class":3829},[1115,22834,22835],{"class":3961}," \"R\"",[1115,22837,22838],{"class":3837},")      ",[1115,22840,22841],{"class":12147},"# diagram R\n",[1115,22843,22844,22846,22848,22850,22852,22854,22856,22859,22861],{"class":3822,"line":111},[1115,22845,360],{"class":3833},[1115,22847,1994],{"class":3837},[1115,22849,20220],{"class":3825},[1115,22851,1917],{"class":3829},[1115,22853,12337],{"class":3825},[1115,22855,3918],{"class":3829},[1115,22857,22858],{"class":3961}," \"xbar\"",[1115,22860,12144],{"class":3837},[1115,22862,22863],{"class":12147},"# diagram x̄\n",[1110,22865,22866,22867,22870],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3590,22868,22869],{},"data[-4, ]",") a diagram se sestrojí znovu.",[16860,22872,21378,22874],{"id":22873},"diagram-xˉsbarx-s",[1115,22875,22877],{"className":22876},[1668],[1670,22878,22879],{"xmlns":1672},[1674,22880,22881,22897],{},[1677,22882,22883,22885,22891,22893,22895],{},[1811,22884,1994],{"stretchy":1993},[2843,22886,22887,22889],{"accent":1121},[1683,22888,6834],{},[1811,22890,11573],{},[1811,22892,1917],{"separator":1121},[1683,22894,1974],{},[1811,22896,2005],{"stretchy":1993},[1691,22898,20789],{"encoding":1693},[1110,22900,21406,22901,22922,22923,22941,22942,22967],{},[1115,22902,22904],{"className":22903},[1668],[1670,22905,22906],{"xmlns":1672},[1674,22907,22908,22920],{},[1677,22909,22910],{},[1680,22911,22912,22918],{},[2843,22913,22914,22916],{"accent":1121},[1683,22915,6834],{},[1811,22917,11573],{},[1683,22919,1997],{},[1691,22921,21428],{"encoding":1693}," a výběrové směrodatné odchylky ",[1115,22924,22926],{"className":22925},[1668],[1670,22927,22928],{"xmlns":1672},[1674,22929,22930,22938],{},[1677,22931,22932],{},[1680,22933,22934,22936],{},[1683,22935,1974],{},[1683,22937,1997],{},[1691,22939,22940],{"encoding":1693},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,22943,22945],{"className":22944},[1668],[1670,22946,22947],{"xmlns":1672},[1674,22948,22949,22965],{},[1677,22950,22951,22953,22959,22961,22963],{},[1811,22952,1994],{"stretchy":1993},[2843,22954,22955,22957],{"accent":1121},[1683,22956,6834],{},[1811,22958,11573],{},[1811,22960,1917],{"separator":1121},[1683,22962,10337],{},[1811,22964,2005],{"stretchy":1993},[1691,22966,20763],{"encoding":1693},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3814,22969,22971],{"className":3816,"code":22970,"language":71,"meta":1603,"style":1603},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3590,22972,22973,22995,23017],{"__ignoreMap":1603},[1115,22974,22975,22977,22979,22981,22983,22985,22987,22989,22991,22993],{"class":3822,"line":10},[1115,22976,20220],{"class":3825},[1115,22978,3830],{"class":3829},[1115,22980,20225],{"class":3833},[1115,22982,1994],{"class":3837},[1115,22984,22808],{"class":3961},[1115,22986,1917],{"class":3829},[1115,22988,20235],{"class":3825},[1115,22990,3918],{"class":3829},[1115,22992,3931],{"class":3845},[1115,22994,4022],{"class":3837},[1115,22996,22997,22999,23001,23003,23005,23007,23009,23012,23014],{"class":3822,"line":27},[1115,22998,360],{"class":3833},[1115,23000,1994],{"class":3837},[1115,23002,20220],{"class":3825},[1115,23004,1917],{"class":3829},[1115,23006,12337],{"class":3825},[1115,23008,3918],{"class":3829},[1115,23010,23011],{"class":3961}," \"S\"",[1115,23013,22838],{"class":3837},[1115,23015,23016],{"class":12147},"# diagram s\n",[1115,23018,23019,23021,23023,23025,23027,23029,23031,23033,23035],{"class":3822,"line":148},[1115,23020,360],{"class":3833},[1115,23022,1994],{"class":3837},[1115,23024,20220],{"class":3825},[1115,23026,1917],{"class":3829},[1115,23028,12337],{"class":3825},[1115,23030,3918],{"class":3829},[1115,23032,22858],{"class":3961},[1115,23034,12144],{"class":3837},[1115,23036,22863],{"class":12147},[16860,23038,21378,23040],{"id":23039},"diagram-xirklix_i-r_kli",[1115,23041,23043],{"className":23042},[1668],[1670,23044,23045],{"xmlns":1672},[1674,23046,23047,23075],{},[1677,23048,23049,23051,23057,23059,23073],{},[1811,23050,1994],{"stretchy":1993},[1680,23052,23053,23055],{},[1683,23054,6834],{},[1683,23056,1997],{},[1811,23058,1917],{"separator":1121},[1680,23060,23061,23063],{},[1683,23062,10337],{},[1677,23064,23065,23067,23069,23071],{},[1683,23066,7374],{},[1683,23068,20819],{},[1811,23070,1917],{"separator":1121},[1683,23072,1997],{},[1811,23074,2005],{"stretchy":1993},[1691,23076,20828],{"encoding":1693},[1110,23078,23079,23080,23105,23106,2077],{},"Používá se za stejných podmínek jako ",[1115,23081,23083],{"className":23082},[1668],[1670,23084,23085],{"xmlns":1672},[1674,23086,23087,23103],{},[1677,23088,23089,23091,23097,23099,23101],{},[1811,23090,1994],{"stretchy":1993},[2843,23092,23093,23095],{"accent":1121},[1683,23094,6834],{},[1811,23096,11573],{},[1811,23098,1917],{"separator":1121},[1683,23100,10337],{},[1811,23102,2005],{"stretchy":1993},[1691,23104,20763],{"encoding":1693},", 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 ",[1136,23107,23108],{},"klouzavé rozpětí",[1115,23110,23112],{"className":23111},[1668],[1670,23113,23114],{"xmlns":1672,"display":2083},[1674,23115,23116,23243],{},[1677,23117,23118,23132,23134,23137,23143,23145,23157,23159,23161,23163,23165,23167,23169,23171,23173,23175,23177,23179,23181,23183,23185,23199,23201,23213,23227,23241],{},[1680,23119,23120,23122],{},[1683,23121,10337],{},[1677,23123,23124,23126,23128,23130],{},[1683,23125,7374],{},[1683,23127,20819],{},[1811,23129,1917],{"separator":1121},[1683,23131,1997],{},[1811,23133,2101],{},[1683,23135,23136],{"mathvariant":2240},"∣",[1680,23138,23139,23141],{},[1683,23140,6834],{},[1683,23142,1997],{},[1811,23144,3184],{},[1680,23146,23147,23149],{},[1683,23148,6834],{},[1677,23150,23151,23153,23155],{},[1683,23152,1997],{},[1811,23154,3184],{},[1687,23156,1914],{},[1683,23158,23136],{"mathvariant":2240},[1811,23160,1917],{"separator":1121},[2131,23162],{"width":18130},[1683,23164,1997],{},[1811,23166,2101],{},[1687,23168,1713],{},[1811,23170,1917],{"separator":1121},[1687,23172,3712],{},[1811,23174,1917],{"separator":1121},[1811,23176,1920],{},[1811,23178,1917],{"separator":1121},[1683,23180,7374],{},[1811,23182,1917],{"separator":1121},[2131,23184],{"width":2133},[1680,23186,23187,23193],{},[2843,23188,23189,23191],{"accent":1121},[1683,23190,10337],{},[1811,23192,11573],{},[1677,23194,23195,23197],{},[1683,23196,7374],{},[1683,23198,20819],{},[1811,23200,2101],{},[2859,23202,23203,23205],{},[1687,23204,1914],{},[1677,23206,23207,23209,23211],{},[1683,23208,7374],{},[1811,23210,3184],{},[1687,23212,1914],{},[2103,23214,23215,23217,23225],{},[1811,23216,2107],{},[1677,23218,23219,23221,23223],{},[1683,23220,1997],{},[1811,23222,2101],{},[1687,23224,1713],{},[1683,23226,7374],{},[1680,23228,23229,23231],{},[1683,23230,10337],{},[1677,23232,23233,23235,23237,23239],{},[1683,23234,7374],{},[1683,23236,20819],{},[1811,23238,1917],{"separator":1121},[1683,23240,1997],{},[1683,23242,1497],{"mathvariant":2240},[1691,23244,23245],{"encoding":1693},"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}.",[1110,23247,23248,23249,5862,23266,23292,23293,23318,23319,23336],{},"Regulované veličiny jsou hodnoty ",[1115,23250,23252],{"className":23251},[1668],[1670,23253,23254],{"xmlns":1672},[1674,23255,23256,23264],{},[1677,23257,23258],{},[1680,23259,23260,23262],{},[1683,23261,6834],{},[1683,23263,1997],{},[1691,23265,17246],{"encoding":1693},[1115,23267,23269],{"className":23268},[1668],[1670,23270,23271],{"xmlns":1672},[1674,23272,23273,23289],{},[1677,23274,23275],{},[1680,23276,23277,23279],{},[1683,23278,10337],{},[1677,23280,23281,23283,23285,23287],{},[1683,23282,7374],{},[1683,23284,20819],{},[1811,23286,1917],{"separator":1121},[1683,23288,1997],{},[1691,23290,23291],{"encoding":1693},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,23294,23296],{"className":23295},[1668],[1670,23297,23298],{"xmlns":1672},[1674,23299,23300,23316],{},[1677,23301,23302],{},[1680,23303,23304,23306],{},[1683,23305,10337],{},[1677,23307,23308,23310,23312,23314],{},[1683,23309,7374],{},[1683,23311,20819],{},[1811,23313,1917],{"separator":1121},[1683,23315,1997],{},[1691,23317,23291],{"encoding":1693},", potom diagramu ",[1115,23320,23322],{"className":23321},[1668],[1670,23323,23324],{"xmlns":1672},[1674,23325,23326,23334],{},[1677,23327,23328],{},[1680,23329,23330,23332],{},[1683,23331,6834],{},[1683,23333,1997],{},[1691,23335,17246],{"encoding":1693},". Data jsou jeden vektor naměřených hodnot:",[3814,23338,23340],{"className":3816,"code":23339,"language":71,"meta":1603,"style":1603},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3590,23341,23342,23365],{"__ignoreMap":1603},[1115,23343,23344,23346,23348,23350,23352,23355,23357,23359,23361,23363],{"class":3822,"line":10},[1115,23345,20220],{"class":3825},[1115,23347,3830],{"class":3829},[1115,23349,20225],{"class":3833},[1115,23351,1994],{"class":3837},[1115,23353,23354],{"class":3961},"\"3_3.txt\"",[1115,23356,1917],{"class":3829},[1115,23358,20235],{"class":3825},[1115,23360,3918],{"class":3829},[1115,23362,3931],{"class":3845},[1115,23364,4022],{"class":3837},[1115,23366,23367,23369,23371,23373,23375,23377,23379,23381,23383,23385,23387,23390],{"class":3822,"line":27},[1115,23368,360],{"class":3833},[1115,23370,1994],{"class":3837},[1115,23372,20220],{"class":3825},[1115,23374,8289],{"class":3837},[1115,23376,1917],{"class":3829},[1115,23378,4762],{"class":3845},[1115,23380,8306],{"class":3837},[1115,23382,1917],{"class":3829},[1115,23384,12337],{"class":3825},[1115,23386,3918],{"class":3829},[1115,23388,23389],{"class":3961}," \"xbar.one\"",[1115,23391,4022],{"class":3837},[1153,23393,23395],{"id":23394},"regulace-srovnáváním","Regulace srovnáváním",[1110,23397,23398],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1158,23400,23401,23414],{},[1161,23402,23403],{},[1164,23404,23405,23408,23411],{},[1167,23406,23407],{},"Sleduje se",[1167,23409,23410],{},"Konstantní rozsah podskupin",[1167,23412,23413],{},"Nekonstantní rozsah podskupin",[1174,23415,23416,23451],{},[1164,23417,23418,23421,23436],{},[1179,23419,23420],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1179,23422,23423],{},[1115,23424,23426],{"className":23425},[1668],[1670,23427,23428],{"xmlns":1672},[1674,23429,23430,23434],{},[1677,23431,23432],{},[1683,23433,3840],{},[1691,23435,3840],{"encoding":1693},[1179,23437,23438],{},[1115,23439,23441],{"className":23440},[1668],[1670,23442,23443],{"xmlns":1672},[1674,23444,23445,23449],{},[1677,23446,23447],{},[1683,23448,11642],{},[1691,23450,11642],{"encoding":1693},[1164,23452,23453,23456,23473],{},[1179,23454,23455],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1179,23457,23458],{},[1115,23459,23461],{"className":23460},[1668],[1670,23462,23463],{"xmlns":1672},[1674,23464,23465,23471],{},[1677,23466,23467,23469],{},[1683,23468,1809],{},[1683,23470,1110],{},[1691,23472,20875],{"encoding":1693},[1179,23474,23475],{},[1115,23476,23478],{"className":23477},[1668],[1670,23479,23480],{"xmlns":1672},[1674,23481,23482,23486],{},[1677,23483,23484],{},[1683,23485,1110],{},[1691,23487,1110],{"encoding":1693},[16860,23489,21378,23491],{"id":23490},"diagram-cc",[1115,23492,23494],{"className":23493},[1668],[1670,23495,23496],{"xmlns":1672},[1674,23497,23498,23502],{},[1677,23499,23500],{},[1683,23501,3840],{},[1691,23503,3840],{"encoding":1693},[1110,23505,23506,23507,23525,23526,23539,23540,23565,23566,23579],{},"Regulovanou veličinou ",[1115,23508,23510],{"className":23509},[1668],[1670,23511,23512],{"xmlns":1672},[1674,23513,23514,23522],{},[1677,23515,23516],{},[1680,23517,23518,23520],{},[1683,23519,3840],{},[1683,23521,1997],{},[1691,23523,23524],{"encoding":1693},"c_i"," je počet neshod na produktech v ",[1115,23527,23529],{"className":23528},[1668],[1670,23530,23531],{"xmlns":1672},[1674,23532,23533,23537],{},[1677,23534,23535],{},[1683,23536,1997],{},[1691,23538,1997],{"encoding":1693},"-té logické podskupině, ",[1115,23541,23543],{"className":23542},[1668],[1670,23544,23545],{"xmlns":1672},[1674,23546,23547,23563],{},[1677,23548,23549,23551,23553,23555,23557,23559,23561],{},[1683,23550,1997],{},[1811,23552,2101],{},[1687,23554,1914],{},[1811,23556,1917],{"separator":1121},[1811,23558,1920],{},[1811,23560,1917],{"separator":1121},[1683,23562,7374],{},[1691,23564,21591],{"encoding":1693},"; v každé podskupině je stejný počet ",[1115,23567,23569],{"className":23568},[1668],[1670,23570,23571],{"xmlns":1672},[1674,23572,23573,23577],{},[1677,23574,23575],{},[1683,23576,1809],{},[1691,23578,1809],{"encoding":1693}," 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.",[1103,23581,23583,23590],{"className":23582,"dataCallout":3597},[1106,3596],[1110,23584,23586,23589],{"className":23585},[1113],[1115,23587],{"className":23588,"ariaHidden":1121},[1118,3604,1120],"Příklad: bodové vady na pásech látky",[1110,23591,23592,23593,23610,23611,1497],{},"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 ",[1115,23594,23596],{"className":23595},[1668],[1670,23597,23598],{"xmlns":1672},[1674,23599,23600,23608],{},[1677,23601,23602],{},[1680,23603,23604,23606],{},[1683,23605,3840],{},[1683,23607,1997],{},[1691,23609,23524],{"encoding":1693},". Sestrojte regulační diagram ",[1115,23612,23614],{"className":23613},[1668],[1670,23615,23616],{"xmlns":1672},[1674,23617,23618,23622],{},[1677,23619,23620],{},[1683,23621,3840],{},[1691,23623,3840],{"encoding":1693},[3814,23625,23627],{"className":3816,"code":23626,"language":71,"meta":1603,"style":1603},"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",[3590,23628,23629,23719,23723,23748],{"__ignoreMap":1603},[1115,23630,23631,23633,23635,23637,23639,23641,23643,23645,23647,23649,23651,23653,23655,23657,23659,23661,23663,23665,23667,23669,23671,23673,23675,23677,23679,23681,23683,23685,23687,23689,23691,23693,23695,23697,23699,23701,23703,23705,23707,23709,23711,23713,23715,23717],{"class":3822,"line":10},[1115,23632,23524],{"class":3825},[1115,23634,3830],{"class":3829},[1115,23636,3956],{"class":3833},[1115,23638,1994],{"class":3837},[1115,23640,13444],{"class":3845},[1115,23642,1917],{"class":3829},[1115,23644,4762],{"class":3845},[1115,23646,1917],{"class":3829},[1115,23648,4301],{"class":3845},[1115,23650,1917],{"class":3829},[1115,23652,10108],{"class":3845},[1115,23654,1917],{"class":3829},[1115,23656,10084],{"class":3845},[1115,23658,1917],{"class":3829},[1115,23660,12342],{"class":3845},[1115,23662,1917],{"class":3829},[1115,23664,4301],{"class":3845},[1115,23666,1917],{"class":3829},[1115,23668,10084],{"class":3845},[1115,23670,1917],{"class":3829},[1115,23672,3921],{"class":3845},[1115,23674,1917],{"class":3829},[1115,23676,3921],{"class":3845},[1115,23678,1917],{"class":3829},[1115,23680,12342],{"class":3845},[1115,23682,1917],{"class":3829},[1115,23684,10969],{"class":3845},[1115,23686,1917],{"class":3829},[1115,23688,10969],{"class":3845},[1115,23690,1917],{"class":3829},[1115,23692,10969],{"class":3845},[1115,23694,1917],{"class":3829},[1115,23696,4762],{"class":3845},[1115,23698,1917],{"class":3829},[1115,23700,12342],{"class":3845},[1115,23702,1917],{"class":3829},[1115,23704,10969],{"class":3845},[1115,23706,1917],{"class":3829},[1115,23708,4762],{"class":3845},[1115,23710,1917],{"class":3829},[1115,23712,10108],{"class":3845},[1115,23714,1917],{"class":3829},[1115,23716,12342],{"class":3845},[1115,23718,4022],{"class":3837},[1115,23720,23721],{"class":3822,"line":27},[1115,23722,10155],{"emptyLinePlaceholder":1618},[1115,23724,23725,23728,23730,23733,23735,23737,23739,23741,23743,23746],{"class":3822,"line":148},[1115,23726,23727],{"class":3825},"q_c",[1115,23729,3830],{"class":3829},[1115,23731,23732],{"class":3833}," qcc",[1115,23734,1994],{"class":3837},[1115,23736,23524],{"class":3825},[1115,23738,1917],{"class":3829},[1115,23740,12337],{"class":3825},[1115,23742,3918],{"class":3829},[1115,23744,23745],{"class":3961}," \"c\"",[1115,23747,4022],{"class":3837},[1115,23749,23750,23752,23754,23756],{"class":3822,"line":111},[1115,23751,1626],{"class":3833},[1115,23753,1994],{"class":3837},[1115,23755,23727],{"class":3825},[1115,23757,4022],{"class":3837},[3814,23759,23762],{"className":23760,"code":23761,"language":4044,"meta":1603},[4042],"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",[3590,23763,23761],{"__ignoreMap":1603},[1110,23765,23766,23767,23796,23797,23820,23821,23843],{},"Průměrný počet vad na pás je ",[1115,23768,23770],{"className":23769},[1668],[1670,23771,23772],{"xmlns":1672},[1674,23773,23774,23793],{},[1677,23775,23776,23778,23780,23782,23788,23790],{},[1683,23777,1379],{},[1683,23779,22232],{},[1811,23781,2101],{},[2843,23783,23784,23786],{"accent":1121},[1683,23785,3840],{},[1811,23787,11573],{},[1811,23789,2101],{},[1687,23791,23792],{},"3,4",[1691,23794,23795],{"encoding":1693},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,23798,23800],{"className":23799},[1668],[1670,23801,23802],{"xmlns":1672},[1674,23803,23804,23817],{},[1677,23805,23806,23808,23810,23812,23814],{},[1683,23807,22258],{},[1683,23809,1379],{},[1683,23811,22232],{},[1811,23813,2101],{},[1687,23815,23816],{},"8,93",[1691,23818,23819],{"encoding":1693},"UCL = 8{,}93"," a dolní mez ",[1115,23822,23824],{"className":23823},[1668],[1670,23825,23826],{"xmlns":1672},[1674,23827,23828,23840],{},[1677,23829,23830,23832,23834,23836,23838],{},[1683,23831,22232],{},[1683,23833,1379],{},[1683,23835,22232],{},[1811,23837,2101],{},[1687,23839,1689],{},[1691,23841,23842],{"encoding":1693},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,23845,23846],{},[4504,23847],{"alt":23848,"className":23849,"src":23850},"mask-rd-priklad2-c",[1131,4508],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[16860,23852,21378,23854],{"id":23853},"diagram-uu",[1115,23855,23857],{"className":23856},[1668],[1670,23858,23859],{"xmlns":1672},[1674,23860,23861,23865],{},[1677,23862,23863],{},[1683,23864,11642],{},[1691,23866,11642],{"encoding":1693},[1110,23868,23506,23869,23903,23904,23922],{},[1115,23870,23872],{"className":23871},[1668],[1670,23873,23874],{"xmlns":1672},[1674,23875,23876,23900],{},[1677,23877,23878,23884,23886,23892,23894],{},[1680,23879,23880,23882],{},[1683,23881,11642],{},[1683,23883,1997],{},[1811,23885,2101],{},[1680,23887,23888,23890],{},[1683,23889,3840],{},[1683,23891,1997],{},[1683,23893,4725],{"mathvariant":2240},[1680,23895,23896,23898],{},[1683,23897,1809],{},[1683,23899,1997],{},[1691,23901,23902],{"encoding":1693},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,23905,23907],{"className":23906},[1668],[1670,23908,23909],{"xmlns":1672},[1674,23910,23911,23919],{},[1677,23912,23913],{},[1680,23914,23915,23917],{},[1683,23916,1809],{},[1683,23918,1997],{},[1691,23920,23921],{"encoding":1693},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,23924,23925,23926,23929],{},"Za ",[3590,23927,23928],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3814,23931,23933],{"className":3816,"code":23932,"language":71,"meta":1603,"style":1603},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3590,23934,23935,23961],{"__ignoreMap":1603},[1115,23936,23937,23939,23941,23943,23945,23948,23950,23952,23954,23956,23958],{"class":3822,"line":10},[1115,23938,20220],{"class":3825},[1115,23940,3830],{"class":3829},[1115,23942,20225],{"class":3833},[1115,23944,1994],{"class":3837},[1115,23946,23947],{"class":3961},"\"3_4.txt\"",[1115,23949,1917],{"class":3829},[1115,23951,20235],{"class":3825},[1115,23953,3918],{"class":3829},[1115,23955,3931],{"class":3845},[1115,23957,12144],{"class":3837},[1115,23959,23960],{"class":12147},"# počty suků a rozměry prken\n",[1115,23962,23963,23965,23967,23969,23971,23973,23975,23977,23979,23981,23983,23986,23988,23991,23993,23995,23997,23999,24001],{"class":3822,"line":27},[1115,23964,360],{"class":3833},[1115,23966,1994],{"class":3837},[1115,23968,20220],{"class":3825},[1115,23970,8289],{"class":3837},[1115,23972,1917],{"class":3829},[1115,23974,4762],{"class":3845},[1115,23976,8306],{"class":3837},[1115,23978,1917],{"class":3829},[1115,23980,12337],{"class":3825},[1115,23982,3918],{"class":3829},[1115,23984,23985],{"class":3961}," \"u\"",[1115,23987,1917],{"class":3829},[1115,23989,23990],{"class":3825}," sizes",[1115,23992,3918],{"class":3829},[1115,23994,20279],{"class":3825},[1115,23996,8289],{"class":3837},[1115,23998,1917],{"class":3829},[1115,24000,4301],{"class":3845},[1115,24002,24003],{"class":3837},"])\n",[16860,24005,21378,24007],{"id":24006},"diagram-npnp",[1115,24008,24010],{"className":24009},[1668],[1670,24011,24012],{"xmlns":1672},[1674,24013,24014,24020],{},[1677,24015,24016,24018],{},[1683,24017,1809],{},[1683,24019,1110],{},[1691,24021,20875],{"encoding":1693},[1110,24023,24024,24025,6895,24040,24053],{},"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 ",[1115,24026,24028],{"className":24027},[1668],[1670,24029,24030],{"xmlns":1672},[1674,24031,24032,24038],{},[1677,24033,24034,24036],{},[1683,24035,1809],{},[1683,24037,1110],{},[1691,24039,20875],{"encoding":1693},[1115,24041,24043],{"className":24042},[1668],[1670,24044,24045],{"xmlns":1672},[1674,24046,24047,24051],{},[1677,24048,24049],{},[1683,24050,1110],{},[1691,24052,1110],{"encoding":1693}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,24055,24056,24057,2077],{},"Pro konstantní rozsah ",[1115,24058,24060],{"className":24059},[1668],[1670,24061,24062],{"xmlns":1672},[1674,24063,24064,24068],{},[1677,24065,24066],{},[1683,24067,1809],{},[1691,24069,1809],{"encoding":1693},[3814,24071,24073],{"className":3816,"code":24072,"language":71,"meta":1603,"style":1603},"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",[3590,24074,24075,24101],{"__ignoreMap":1603},[1115,24076,24077,24079,24081,24083,24085,24088,24090,24092,24094,24096,24098],{"class":3822,"line":10},[1115,24078,20220],{"class":3825},[1115,24080,3830],{"class":3829},[1115,24082,20225],{"class":3833},[1115,24084,1994],{"class":3837},[1115,24086,24087],{"class":3961},"\"3_7.txt\"",[1115,24089,1917],{"class":3829},[1115,24091,20235],{"class":3825},[1115,24093,3918],{"class":3829},[1115,24095,3931],{"class":3845},[1115,24097,12144],{"class":3837},[1115,24099,24100],{"class":12147},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,24102,24103,24105,24107,24109,24111,24113,24115,24117,24119,24121,24123,24126,24128,24130,24132,24134],{"class":3822,"line":27},[1115,24104,360],{"class":3833},[1115,24106,1994],{"class":3837},[1115,24108,20220],{"class":3825},[1115,24110,8289],{"class":3837},[1115,24112,1917],{"class":3829},[1115,24114,4762],{"class":3845},[1115,24116,8306],{"class":3837},[1115,24118,1917],{"class":3829},[1115,24120,12337],{"class":3825},[1115,24122,3918],{"class":3829},[1115,24124,24125],{"class":3961}," \"np\"",[1115,24127,1917],{"class":3829},[1115,24129,23990],{"class":3825},[1115,24131,3918],{"class":3829},[1115,24133,15453],{"class":3845},[1115,24135,4022],{"class":3837},[16860,24137,21378,24139],{"id":24138},"diagram-pp",[1115,24140,24142],{"className":24141},[1668],[1670,24143,24144],{"xmlns":1672},[1674,24145,24146,24150],{},[1677,24147,24148],{},[1683,24149,1110],{},[1691,24151,1110],{"encoding":1693},[1110,24153,24154,24155,24191],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,24156,24158],{"className":24157},[1668],[1670,24159,24160],{"xmlns":1672},[1674,24161,24162,24188],{},[1677,24163,24164,24170,24172,24174,24180,24182],{},[1680,24165,24166,24168],{},[1683,24167,1110],{},[1683,24169,1997],{},[1811,24171,2101],{},[1683,24173,1809],{},[1680,24175,24176,24178],{},[1683,24177,1110],{},[1683,24179,1997],{},[1683,24181,4725],{"mathvariant":2240},[1680,24183,24184,24186],{},[1683,24185,1809],{},[1683,24187,1997],{},[1691,24189,24190],{"encoding":1693},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,24193,23925,24194,24196],{},[3590,24195,23928],{}," se dosadí vektor rozsahů logických podskupin:",[3814,24198,24200],{"className":3816,"code":24199,"language":71,"meta":1603,"style":1603},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3590,24201,24202,24228],{"__ignoreMap":1603},[1115,24203,24204,24206,24208,24210,24212,24215,24217,24219,24221,24223,24225],{"class":3822,"line":10},[1115,24205,20220],{"class":3825},[1115,24207,3830],{"class":3829},[1115,24209,20225],{"class":3833},[1115,24211,1994],{"class":3837},[1115,24213,24214],{"class":3961},"\"3_6.txt\"",[1115,24216,1917],{"class":3829},[1115,24218,20235],{"class":3825},[1115,24220,3918],{"class":3829},[1115,24222,3931],{"class":3845},[1115,24224,12144],{"class":3837},[1115,24226,24227],{"class":12147},"# počty vadných tabletů a rozsahy sérií\n",[1115,24229,24230,24232,24234,24236,24238,24240,24242,24244,24246,24248,24250,24253,24255,24257,24259,24261,24263,24265,24267],{"class":3822,"line":27},[1115,24231,360],{"class":3833},[1115,24233,1994],{"class":3837},[1115,24235,20220],{"class":3825},[1115,24237,8289],{"class":3837},[1115,24239,1917],{"class":3829},[1115,24241,4762],{"class":3845},[1115,24243,8306],{"class":3837},[1115,24245,1917],{"class":3829},[1115,24247,12337],{"class":3825},[1115,24249,3918],{"class":3829},[1115,24251,24252],{"class":3961}," \"p\"",[1115,24254,1917],{"class":3829},[1115,24256,23990],{"class":3825},[1115,24258,3918],{"class":3829},[1115,24260,20279],{"class":3825},[1115,24262,8289],{"class":3837},[1115,24264,1917],{"class":3829},[1115,24266,4301],{"class":3845},[1115,24268,24003],{"class":3837},[1153,24270,24272],{"id":24271},"indexy-způsobilosti","Indexy způsobilosti",[1110,24274,24275,24276,24295,24296,24314],{},"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 ",[1115,24277,24279],{"className":24278},[1668],[1670,24280,24281],{"xmlns":1672},[1674,24282,24283,24292],{},[1677,24284,24285,24287,24290],{},[1683,24286,22232],{},[1683,24288,24289],{},"S",[1683,24291,22232],{},[1691,24293,24294],{"encoding":1693},"LSL"," a horní meze ",[1115,24297,24299],{"className":24298},[1668],[1670,24300,24301],{"xmlns":1672},[1674,24302,24303,24311],{},[1677,24304,24305,24307,24309],{},[1683,24306,22258],{},[1683,24308,24289],{},[1683,24310,22232],{},[1691,24312,24313],{"encoding":1693},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[16860,24316,24318,24335],{"id":24317},"cpc_p-index-způsobilosti",[1115,24319,24321],{"className":24320},[1668],[1670,24322,24323],{"xmlns":1672},[1674,24324,24325,24333],{},[1677,24326,24327],{},[1680,24328,24329,24331],{},[1683,24330,1379],{},[1683,24332,1110],{},[1691,24334,20914],{"encoding":1693}," — index způsobilosti",[1110,24337,24338,24339,2077],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,24340,24342],{"className":24341},[1668],[1670,24343,24344],{"xmlns":1672},[1674,24345,24346,24352],{},[1677,24347,24348,24350],{},[1687,24349,4085],{},[1683,24351,7013],{},[1691,24353,24354],{"encoding":1693},"6\\sigma",[1115,24356,24358],{"className":24357},[1668],[1670,24359,24360],{"xmlns":1672,"display":2083},[1674,24361,24362,24398],{},[1677,24363,24364,24370,24372,24396],{},[1680,24365,24366,24368],{},[1683,24367,1379],{},[1683,24369,1110],{},[1811,24371,2101],{},[2859,24373,24374,24390],{},[1677,24375,24376,24378,24380,24382,24384,24386,24388],{},[1683,24377,22258],{},[1683,24379,24289],{},[1683,24381,22232],{},[1811,24383,3184],{},[1683,24385,22232],{},[1683,24387,24289],{},[1683,24389,22232],{},[1677,24391,24392,24394],{},[1687,24393,4085],{},[1683,24395,7013],{},[1683,24397,1497],{"mathvariant":2240},[1691,24399,24400],{"encoding":1693},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,24402,24403,24420,24421,24434,24435,1497],{},[1115,24404,24406],{"className":24405},[1668],[1670,24407,24408],{"xmlns":1672},[1674,24409,24410,24418],{},[1677,24411,24412],{},[1680,24413,24414,24416],{},[1683,24415,1379],{},[1683,24417,1110],{},[1691,24419,20914],{"encoding":1693}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,24422,24424],{"className":24423},[1668],[1670,24425,24426],{"xmlns":1672},[1674,24427,24428,24432],{},[1677,24429,24430],{},[1683,24431,7013],{},[1691,24433,7045],{"encoding":1693}," mají stejné ",[1115,24436,24438],{"className":24437},[1668],[1670,24439,24440],{"xmlns":1672},[1674,24441,24442,24450],{},[1677,24443,24444],{},[1680,24445,24446,24448],{},[1683,24447,1379],{},[1683,24449,1110],{},[1691,24451,20914],{"encoding":1693},[1110,24453,24454],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1503,24456,24457,24491,24579],{},[1265,24458,24459,4109,24462,24490],{},[1136,24460,24461],{},"míra využití tolerančního intervalu",[1115,24463,24465],{"className":24464},[1668],[1670,24466,24467],{"xmlns":1672},[1674,24468,24469,24487],{},[1677,24470,24471,24483,24485],{},[3361,24472,24473],{"scriptlevel":1689,"displaystyle":1121},[2859,24474,24475,24477],{},[1687,24476,11932],{},[1680,24478,24479,24481],{},[1683,24480,1379],{},[1683,24482,1110],{},[3028,24484,3030],{},[1683,24486,11939],{"mathvariant":2240},[1691,24488,24489],{"encoding":1693},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1265,24492,24493,24496,24497,24514,24515,5862,24547,1917],{},[1136,24494,24495],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,24498,24500],{"className":24499},[1668],[1670,24501,24502],{"xmlns":1672},[1674,24503,24504,24512],{},[1677,24505,24506],{},[1680,24507,24508,24510],{},[1683,24509,1379],{},[1683,24511,1110],{},[1691,24513,20914],{"encoding":1693}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,24516,24518],{"className":24517},[1668],[1670,24519,24520],{"xmlns":1672},[1674,24521,24522,24544],{},[1677,24523,24524,24526,24528,24530,24532,24534,24536,24538,24540,24542],{},[1683,24525,22258],{},[1683,24527,24289],{},[1683,24529,22232],{},[1811,24531,3184],{},[1811,24533,1994],{"stretchy":1993},[1683,24535,7005],{},[1811,24537,5598],{},[1687,24539,3712],{},[1683,24541,7013],{},[1811,24543,2005],{"stretchy":1993},[1691,24545,24546],{"encoding":1693},"USL-(\\mu+3\\sigma)",[1115,24548,24550],{"className":24549},[1668],[1670,24551,24552],{"xmlns":1672},[1674,24553,24554,24576],{},[1677,24555,24556,24558,24560,24562,24564,24566,24568,24570,24572,24574],{},[1811,24557,1994],{"stretchy":1993},[1683,24559,7005],{},[1811,24561,3184],{},[1687,24563,3712],{},[1683,24565,7013],{},[1811,24567,2005],{"stretchy":1993},[1811,24569,3184],{},[1683,24571,22232],{},[1683,24573,24289],{},[1683,24575,22232],{},[1691,24577,24578],{"encoding":1693},"(\\mu-3\\sigma)-LSL",[1265,24580,24581,4109,24584,6895,24624,24638],{},[1136,24582,24583],{},"podíl zmetků",[1115,24585,24587],{"className":24586},[1668],[1670,24588,24589],{"xmlns":1672},[1674,24590,24591,24621],{},[1677,24592,24593,24600,24602,24604,24607,24609,24611,24613,24619],{},[1680,24594,24595,24597],{},[1683,24596,6841],{},[1683,24598,24599],{},"z",[1811,24601,2101],{},[1687,24603,1713],{},[1683,24605,24606],{"mathvariant":2240},"Φ",[1811,24608,1994],{"stretchy":1993},[1811,24610,3184],{},[1687,24612,3712],{},[1680,24614,24615,24617],{},[1683,24616,1379],{},[1683,24618,1110],{},[1811,24620,2005],{"stretchy":1993},[1691,24622,24623],{"encoding":1693},"P_z = 2\\Phi(-3C_p)",[1115,24625,24627],{"className":24626},[1668],[1670,24628,24629],{"xmlns":1672},[1674,24630,24631,24635],{},[1677,24632,24633],{},[1683,24634,24606],{"mathvariant":2240},[1691,24636,24637],{"encoding":1693},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[16860,24640,24642,24663],{"id":24641},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,24643,24645],{"className":24644},[1668],[1670,24646,24647],{"xmlns":1672},[1674,24648,24649,24661],{},[1677,24650,24651],{},[1680,24652,24653,24655],{},[1683,24654,1379],{},[1677,24656,24657,24659],{},[1683,24658,1110],{},[1683,24660,7374],{},[1691,24662,20936],{"encoding":1693}," — index způsobilosti s ohledem na vychýlení",[1110,24665,24666],{},"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:",[1115,24668,24670],{"className":24669},[1668],[1670,24671,24672],{"xmlns":1672,"display":2083},[1674,24673,24674,24744],{},[1677,24675,24676,24686,24688,24690,24692,24742],{},[1680,24677,24678,24680],{},[1683,24679,1379],{},[1677,24681,24682,24684],{},[1683,24683,1110],{},[1683,24685,7374],{},[1811,24687,2101],{},[1683,24689,4609],{},[1811,24691,4612],{},[1677,24693,24694,24696,24716,24718,24720,24740],{},[1811,24695,1994],{"fence":1121},[2859,24697,24698,24710],{},[1677,24699,24700,24702,24704,24706,24708],{},[1683,24701,22258],{},[1683,24703,24289],{},[1683,24705,22232],{},[1811,24707,3184],{},[1683,24709,7005],{},[1677,24711,24712,24714],{},[1687,24713,3712],{},[1683,24715,7013],{},[1811,24717,1917],{"separator":1121},[3028,24719,11428],{},[2859,24721,24722,24734],{},[1677,24723,24724,24726,24728,24730,24732],{},[1683,24725,7005],{},[1811,24727,3184],{},[1683,24729,22232],{},[1683,24731,24289],{},[1683,24733,22232],{},[1677,24735,24736,24738],{},[1687,24737,3712],{},[1683,24739,7013],{},[1811,24741,2005],{"fence":1121},[1683,24743,1497],{"mathvariant":2240},[1691,24745,24746],{"encoding":1693},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,24748,24749,24750,24763,24764,24794,24795,24816,24817,1497],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,24751,24753],{"className":24752},[1668],[1670,24754,24755],{"xmlns":1672},[1674,24756,24757,24761],{},[1677,24758,24759],{},[1683,24760,7005],{},[1691,24762,8910],{"encoding":1693}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,24765,24767],{"className":24766},[1668],[1670,24768,24769],{"xmlns":1672},[1674,24770,24771,24791],{},[1677,24772,24773,24783,24785],{},[1680,24774,24775,24777],{},[1683,24776,1379],{},[1677,24778,24779,24781],{},[1683,24780,1110],{},[1683,24782,7374],{},[1811,24784,2101],{},[1680,24786,24787,24789],{},[1683,24788,1379],{},[1683,24790,1110],{},[1691,24792,24793],{"encoding":1693},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,24796,24798],{"className":24797},[1668],[1670,24799,24800],{"xmlns":1672},[1674,24801,24802,24814],{},[1677,24803,24804],{},[1680,24805,24806,24808],{},[1683,24807,1379],{},[1677,24809,24810,24812],{},[1683,24811,1110],{},[1683,24813,7374],{},[1691,24815,20936],{"encoding":1693}," menší než ",[1115,24818,24820],{"className":24819},[1668],[1670,24821,24822],{"xmlns":1672},[1674,24823,24824,24832],{},[1677,24825,24826],{},[1680,24827,24828,24830],{},[1683,24829,1379],{},[1683,24831,1110],{},[1691,24833,20914],{"encoding":1693},[16860,24835,24837,5862,24858,24881],{"id":24836},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,24838,24840],{"className":24839},[1668],[1670,24841,24842],{"xmlns":1672},[1674,24843,24844,24856],{},[1677,24845,24846],{},[1680,24847,24848,24850],{},[1683,24849,1379],{},[1677,24851,24852,24854],{},[1683,24853,1110],{},[1683,24855,4592],{},[1691,24857,20958],{"encoding":1693},[1115,24859,24861],{"className":24860},[1668],[1670,24862,24863],{"xmlns":1672},[1674,24864,24865,24879],{},[1677,24866,24867],{},[1680,24868,24869,24871],{},[1683,24870,1379],{},[1677,24872,24873,24875,24877],{},[1683,24874,1110],{},[1683,24876,4592],{},[1683,24878,7374],{},[1691,24880,20982],{"encoding":1693}," — indexy vztažené k cíli",[1110,24883,24884,24885,24898,24899,24912,24913,24956,24957,2077],{},"Pokud má proces zadaný cílový střed ",[1115,24886,24888],{"className":24887},[1668],[1670,24889,24890],{"xmlns":1672},[1674,24891,24892,24896],{},[1677,24893,24894],{},[1683,24895,7216],{},[1691,24897,7216],{"encoding":1693}," (ne nutně střed tolerance), nahradí se ",[1115,24900,24902],{"className":24901},[1668],[1670,24903,24904],{"xmlns":1672},[1674,24905,24906,24910],{},[1677,24907,24908],{},[1683,24909,7013],{},[1691,24911,7045],{"encoding":1693}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,24914,24916],{"className":24915},[1668],[1670,24917,24918],{"xmlns":1672},[1674,24919,24920,24953],{},[1677,24921,24922,24925,24927],{},[1683,24923,24924],{},"τ",[1811,24926,2101],{},[4574,24928,24929],{},[1677,24930,24931,24937,24939,24941,24943,24945,24947],{},[1706,24932,24933,24935],{},[1683,24934,7013],{},[1687,24936,1713],{},[1811,24938,5598],{},[1811,24940,1994],{"stretchy":1993},[1683,24942,7005],{},[1811,24944,3184],{},[1683,24946,7216],{},[1706,24948,24949,24951],{},[1811,24950,2005],{"stretchy":1993},[1687,24952,1713],{},[1691,24954,24955],{"encoding":1693},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,24958,24960],{"className":24959},[1668],[1670,24961,24962],{"xmlns":1672},[1674,24963,24964,24968],{},[1677,24965,24966],{},[1683,24967,7216],{},[1691,24969,7216],{"encoding":1693},[1115,24971,24973],{"className":24972},[1668],[1670,24974,24975],{"xmlns":1672,"display":2083},[1674,24976,24977,25089],{},[1677,24978,24979,24989,24991,25015,25017,25019,25031,25033,25035,25037,25087],{},[1680,24980,24981,24983],{},[1683,24982,1379],{},[1677,24984,24985,24987],{},[1683,24986,1110],{},[1683,24988,4592],{},[1811,24990,2101],{},[2859,24992,24993,25009],{},[1677,24994,24995,24997,24999,25001,25003,25005,25007],{},[1683,24996,22258],{},[1683,24998,24289],{},[1683,25000,22232],{},[1811,25002,3184],{},[1683,25004,22232],{},[1683,25006,24289],{},[1683,25008,22232],{},[1677,25010,25011,25013],{},[1687,25012,4085],{},[1683,25014,24924],{},[1811,25016,1917],{"separator":1121},[2131,25018],{"width":2133},[1680,25020,25021,25023],{},[1683,25022,1379],{},[1677,25024,25025,25027,25029],{},[1683,25026,1110],{},[1683,25028,4592],{},[1683,25030,7374],{},[1811,25032,2101],{},[1683,25034,4609],{},[1811,25036,4612],{},[1677,25038,25039,25041,25061,25063,25065,25085],{},[1811,25040,1994],{"fence":1121},[2859,25042,25043,25055],{},[1677,25044,25045,25047,25049,25051,25053],{},[1683,25046,22258],{},[1683,25048,24289],{},[1683,25050,22232],{},[1811,25052,3184],{},[1683,25054,7005],{},[1677,25056,25057,25059],{},[1687,25058,3712],{},[1683,25060,24924],{},[1811,25062,1917],{"separator":1121},[3028,25064,11428],{},[2859,25066,25067,25079],{},[1677,25068,25069,25071,25073,25075,25077],{},[1683,25070,7005],{},[1811,25072,3184],{},[1683,25074,22232],{},[1683,25076,24289],{},[1683,25078,22232],{},[1677,25080,25081,25083],{},[1687,25082,3712],{},[1683,25084,24924],{},[1811,25086,2005],{"fence":1121},[1683,25088,1497],{"mathvariant":2240},[1691,25090,25091],{"encoding":1693},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[16860,25093,25095],{"id":25094},"interpretace","Interpretace",[1158,25097,25098,25125],{},[1161,25099,25100],{},[1164,25101,25102,25122],{},[1167,25103,25104,25105],{},"Hodnota ",[1115,25106,25108],{"className":25107},[1668],[1670,25109,25110],{"xmlns":1672},[1674,25111,25112,25120],{},[1677,25113,25114],{},[1680,25115,25116,25118],{},[1683,25117,1379],{},[1683,25119,1110],{},[1691,25121,20914],{"encoding":1693},[1167,25123,25124],{},"Způsobilost procesu",[1174,25126,25127,25156,25199],{},[1164,25128,25129,25153],{},[1179,25130,25131],{},[1115,25132,25134],{"className":25133},[1668],[1670,25135,25136],{"xmlns":1672},[1674,25137,25138,25150],{},[1677,25139,25140,25146,25148],{},[1680,25141,25142,25144],{},[1683,25143,1379],{},[1683,25145,1110],{},[1811,25147,4453],{},[1687,25149,1914],{},[1691,25151,25152],{"encoding":1693},"C_p \u003C 1",[1179,25154,25155],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1164,25157,25158,25182],{},[1179,25159,25160],{},[1115,25161,25163],{"className":25162},[1668],[1670,25164,25165],{"xmlns":1672},[1674,25166,25167,25179],{},[1677,25168,25169,25175,25177],{},[1680,25170,25171,25173],{},[1683,25172,1379],{},[1683,25174,1110],{},[1811,25176,2101],{},[1687,25178,1914],{},[1691,25180,25181],{"encoding":1693},"C_p = 1",[1179,25183,25184,25185,25198],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,25186,25188],{"className":25187},[1668],[1670,25189,25190],{"xmlns":1672},[1674,25191,25192,25196],{},[1677,25193,25194],{},[1683,25195,7013],{},[1691,25197,7045],{"encoding":1693}," jej posune na nezpůsobilý",[1164,25200,25201,25225],{},[1179,25202,25203],{},[1115,25204,25206],{"className":25205},[1668],[1670,25207,25208],{"xmlns":1672},[1674,25209,25210,25222],{},[1677,25211,25212,25218,25220],{},[1680,25213,25214,25216],{},[1683,25215,1379],{},[1683,25217,1110],{},[1811,25219,1813],{},[1687,25221,1914],{},[1691,25223,25224],{"encoding":1693},"C_p > 1",[1179,25226,25227],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,25229,25230,25231,25252,25253,1497],{},"U indexu ",[1115,25232,25234],{"className":25233},[1668],[1670,25235,25236],{"xmlns":1672},[1674,25237,25238,25250],{},[1677,25239,25240],{},[1680,25241,25242,25244],{},[1683,25243,1379],{},[1677,25245,25246,25248],{},[1683,25247,1110],{},[1683,25249,7374],{},[1691,25251,20936],{"encoding":1693}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,25254,25256],{"className":25255},[1668],[1670,25257,25258],{"xmlns":1672},[1674,25259,25260,25265],{},[1677,25261,25262],{},[1687,25263,25264],{},"1,5",[1691,25266,25267],{"encoding":1693},"1{,}5",[1110,25269,25270],{},[4504,25271],{"alt":25272,"className":25273,"src":25274},"mask-rd-cp-panely",[1131,4508],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,25276,25277],{},[4504,25278],{"alt":25279,"className":25280,"src":25281},"mask-rd-cpk-off-centre",[1131,4508],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[16860,25283,25285],{"id":25284},"výpočet-v-r","Výpočet v R",[1110,25287,25288,25289,25292,25293,25296,25297,25300,25301,5862,25318,3071,25335,25338,25339,25352],{},"Indexy způsobilosti počítá ",[3590,25290,25291],{},"process.capability()"," z výstupu regulačního diagramu ",[3590,25294,25295],{},"q","; ",[3590,25298,25299],{},"spec.limits"," jsou toleranční meze ",[1115,25302,25304],{"className":25303},[1668],[1670,25305,25306],{"xmlns":1672},[1674,25307,25308,25316],{},[1677,25309,25310,25312,25314],{},[1683,25311,22232],{},[1683,25313,24289],{},[1683,25315,22232],{},[1691,25317,24294],{"encoding":1693},[1115,25319,25321],{"className":25320},[1668],[1670,25322,25323],{"xmlns":1672},[1674,25324,25325,25333],{},[1677,25326,25327,25329,25331],{},[1683,25328,22258],{},[1683,25330,24289],{},[1683,25332,22232],{},[1691,25334,24313],{"encoding":1693},[3590,25336,25337],{},"target"," cílová hodnota ",[1115,25340,25342],{"className":25341},[1668],[1670,25343,25344],{"xmlns":1672},[1674,25345,25346,25350],{},[1677,25347,25348],{},[1683,25349,7216],{},[1691,25351,7216],{"encoding":1693},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3814,25354,25356],{"className":3816,"code":25355,"language":71,"meta":1603,"style":1603},"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",[3590,25357,25358,25368,25391,25406,25428],{"__ignoreMap":1603},[1115,25359,25360,25362,25364,25366],{"class":3822,"line":10},[1115,25361,17509],{"class":3829},[1115,25363,1994],{"class":3837},[1115,25365,360],{"class":3825},[1115,25367,4022],{"class":3837},[1115,25369,25370,25372,25374,25376,25378,25381,25383,25385,25387,25389],{"class":3822,"line":27},[1115,25371,20220],{"class":3825},[1115,25373,3830],{"class":3829},[1115,25375,20225],{"class":3833},[1115,25377,1994],{"class":3837},[1115,25379,25380],{"class":3961},"\"3_8.txt\"",[1115,25382,1917],{"class":3829},[1115,25384,20235],{"class":3825},[1115,25386,3918],{"class":3829},[1115,25388,3931],{"class":3845},[1115,25390,4022],{"class":3837},[1115,25392,25393,25395,25397,25400,25402,25404],{"class":3822,"line":148},[1115,25394,6834],{"class":3825},[1115,25396,3830],{"class":3829},[1115,25398,25399],{"class":3833}," as.matrix",[1115,25401,1994],{"class":3837},[1115,25403,20220],{"class":3825},[1115,25405,4022],{"class":3837},[1115,25407,25408,25410,25412,25414,25416,25418,25420,25422,25424,25426],{"class":3822,"line":111},[1115,25409,25295],{"class":3825},[1115,25411,3830],{"class":3829},[1115,25413,23732],{"class":3833},[1115,25415,1994],{"class":3837},[1115,25417,6834],{"class":3825},[1115,25419,1917],{"class":3829},[1115,25421,12337],{"class":3825},[1115,25423,3918],{"class":3829},[1115,25425,22858],{"class":3961},[1115,25427,4022],{"class":3837},[1115,25429,25430,25433,25435,25437,25439,25442,25444,25446,25448,25450,25452,25454,25456,25458,25461,25463,25466,25468,25471,25473,25475,25477,25479],{"class":3822,"line":96},[1115,25431,25432],{"class":3833},"process.capability",[1115,25434,1994],{"class":3837},[1115,25436,25295],{"class":3825},[1115,25438,1917],{"class":3829},[1115,25440,25441],{"class":3825}," spec.limits",[1115,25443,3918],{"class":3829},[1115,25445,3956],{"class":3833},[1115,25447,1994],{"class":3837},[1115,25449,11932],{"class":3845},[1115,25451,1917],{"class":3829},[1115,25453,14382],{"class":3845},[1115,25455,2005],{"class":3837},[1115,25457,1917],{"class":3829},[1115,25459,25460],{"class":3825}," target",[1115,25462,3918],{"class":3829},[1115,25464,25465],{"class":3845}," 105",[1115,25467,1917],{"class":3829},[1115,25469,25470],{"class":3825}," std.dev",[1115,25472,3918],{"class":3829},[1115,25474,9355],{"class":3833},[1115,25476,1994],{"class":3837},[1115,25478,6834],{"class":3825},[1115,25480,9607],{"class":3837},[1110,25482,25483,25484,3071,25487,3071,25490,3071,25493,5862,25496,25499,25500,5862,25502,25504,25505,25526,25527,25550],{},"Výpis obsahuje řádky ",[3590,25485,25486],{},"Cp",[3590,25488,25489],{},"Cp_l",[3590,25491,25492],{},"Cp_u",[3590,25494,25495],{},"Cp_k",[3590,25497,25498],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3590,25501,25489],{},[3590,25503,25492],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,25506,25508],{"className":25507},[1668],[1670,25509,25510],{"xmlns":1672},[1674,25511,25512,25524],{},[1677,25513,25514],{},[1680,25515,25516,25518],{},[1683,25517,1379],{},[1677,25519,25520,25522],{},[1683,25521,1110],{},[1683,25523,7374],{},[1691,25525,20936],{"encoding":1693},". Index ",[1115,25528,25530],{"className":25529},[1668],[1670,25531,25532],{"xmlns":1672},[1674,25533,25534,25548],{},[1677,25535,25536],{},[1680,25537,25538,25540],{},[1683,25539,1379],{},[1677,25541,25542,25544,25546],{},[1683,25543,1110],{},[1683,25545,4592],{},[1683,25547,7374],{},[1691,25549,20982],{"encoding":1693}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3814,25552,25554],{"className":3816,"code":25553,"language":71,"meta":1603,"style":1603},"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",[3590,25555,25556,25583,25608,25645,25675,25733,25747,25798],{"__ignoreMap":1603},[1115,25557,25558,25561,25563,25565,25567,25569,25571,25573,25575,25577,25579,25581],{"class":3822,"line":10},[1115,25559,25560],{"class":3825},"mu",[1115,25562,3830],{"class":3829},[1115,25564,9345],{"class":3833},[1115,25566,1994],{"class":3837},[1115,25568,6834],{"class":3825},[1115,25570,12291],{"class":3837},[1115,25572,380],{"class":3825},[1115,25574,3830],{"class":3829},[1115,25576,9355],{"class":3833},[1115,25578,1994],{"class":3837},[1115,25580,6834],{"class":3825},[1115,25582,4022],{"class":3837},[1115,25584,25585,25587,25589,25591,25593,25595,25597,25599,25601,25603,25605],{"class":3822,"line":27},[1115,25586,24294],{"class":3825},[1115,25588,3830],{"class":3829},[1115,25590,15453],{"class":3845},[1115,25592,25296],{"class":3837},[1115,25594,24313],{"class":3825},[1115,25596,3830],{"class":3829},[1115,25598,14382],{"class":3845},[1115,25600,25296],{"class":3837},[1115,25602,7216],{"class":3825},[1115,25604,3830],{"class":3829},[1115,25606,25607],{"class":3845}," 105\n",[1115,25609,25610,25613,25615,25617,25619,25621,25623,25625,25627,25629,25631,25634,25637,25639,25641,25643],{"class":3822,"line":148},[1115,25611,25612],{"class":3825},"tau",[1115,25614,3830],{"class":3829},[1115,25616,4699],{"class":3833},[1115,25618,1994],{"class":3837},[1115,25620,380],{"class":3825},[1115,25622,2849],{"class":3829},[1115,25624,1713],{"class":3845},[1115,25626,18628],{"class":3829},[1115,25628,4728],{"class":3837},[1115,25630,25560],{"class":3825},[1115,25632,25633],{"class":3829}," -",[1115,25635,25636],{"class":3825}," T",[1115,25638,2005],{"class":3837},[1115,25640,2849],{"class":3829},[1115,25642,1713],{"class":3845},[1115,25644,4022],{"class":3837},[1115,25646,25647,25649,25651,25653,25655,25657,25660,25662,25664,25666,25668,25670,25673],{"class":3822,"line":111},[1115,25648,25486],{"class":3825},[1115,25650,3830],{"class":3829},[1115,25652,4728],{"class":3837},[1115,25654,24313],{"class":3825},[1115,25656,25633],{"class":3829},[1115,25658,25659],{"class":3825}," LSL",[1115,25661,4722],{"class":3837},[1115,25663,4725],{"class":3829},[1115,25665,4728],{"class":3837},[1115,25667,4085],{"class":3845},[1115,25669,18753],{"class":3829},[1115,25671,25672],{"class":3825}," sigma",[1115,25674,4022],{"class":3837},[1115,25676,25677,25680,25682,25684,25687,25689,25691,25694,25696,25698,25700,25702,25704,25707,25709,25711,25713,25715,25717,25719,25721,25723,25725,25727,25729,25731],{"class":3822,"line":96},[1115,25678,25679],{"class":3825},"Cpmk",[1115,25681,3830],{"class":3829},[1115,25683,12312],{"class":3833},[1115,25685,25686],{"class":3837},"((",[1115,25688,24313],{"class":3825},[1115,25690,25633],{"class":3829},[1115,25692,25693],{"class":3825}," mu",[1115,25695,4722],{"class":3837},[1115,25697,4725],{"class":3829},[1115,25699,4728],{"class":3837},[1115,25701,3712],{"class":3845},[1115,25703,18753],{"class":3829},[1115,25705,25706],{"class":3825}," tau",[1115,25708,2005],{"class":3837},[1115,25710,1917],{"class":3829},[1115,25712,4728],{"class":3837},[1115,25714,25560],{"class":3825},[1115,25716,25633],{"class":3829},[1115,25718,25659],{"class":3825},[1115,25720,4722],{"class":3837},[1115,25722,4725],{"class":3829},[1115,25724,4728],{"class":3837},[1115,25726,3712],{"class":3845},[1115,25728,18753],{"class":3829},[1115,25730,25706],{"class":3825},[1115,25732,9607],{"class":3837},[1115,25734,25735,25738,25740,25742,25744],{"class":3822,"line":89},[1115,25736,25737],{"class":3825},"miravyuziti",[1115,25739,3830],{"class":3829},[1115,25741,15453],{"class":3845},[1115,25743,10189],{"class":3829},[1115,25745,25746],{"class":3825}," Cp\n",[1115,25748,25749,25752,25754,25756,25758,25760,25762,25764,25766,25768,25770,25772,25774,25776,25778,25780,25782,25784,25786,25788,25790,25792,25794,25796],{"class":3822,"line":82},[1115,25750,25751],{"class":3825},"robustnost",[1115,25753,3830],{"class":3829},[1115,25755,12312],{"class":3833},[1115,25757,1994],{"class":3837},[1115,25759,24313],{"class":3825},[1115,25761,25633],{"class":3829},[1115,25763,4728],{"class":3837},[1115,25765,25560],{"class":3825},[1115,25767,18628],{"class":3829},[1115,25769,10969],{"class":3845},[1115,25771,18753],{"class":3829},[1115,25773,25672],{"class":3825},[1115,25775,2005],{"class":3837},[1115,25777,1917],{"class":3829},[1115,25779,4728],{"class":3837},[1115,25781,25560],{"class":3825},[1115,25783,25633],{"class":3829},[1115,25785,10969],{"class":3845},[1115,25787,18753],{"class":3829},[1115,25789,25672],{"class":3825},[1115,25791,4722],{"class":3837},[1115,25793,4759],{"class":3829},[1115,25795,25659],{"class":3825},[1115,25797,4022],{"class":3837},[1115,25799,25800,25803,25805,25807,25809,25811,25813,25815,25817,25819,25822],{"class":3822,"line":75},[1115,25801,25802],{"class":3825},"Pz",[1115,25804,3830],{"class":3829},[1115,25806,4301],{"class":3845},[1115,25808,18753],{"class":3829},[1115,25810,9465],{"class":3833},[1115,25812,1994],{"class":3837},[1115,25814,4759],{"class":3829},[1115,25816,3712],{"class":3845},[1115,25818,18753],{"class":3829},[1115,25820,25821],{"class":3825}," Cp",[1115,25823,4022],{"class":3837},[1153,25825,6529],{"id":6528},[1503,25827,25828,25831,25891,25982,26048],{},[1265,25829,25830],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1265,25832,25833,25834,25851,25852,25869,25870,1497],{},"Posuzovat jen ",[1115,25835,25837],{"className":25836},[1668],[1670,25838,25839],{"xmlns":1672},[1674,25840,25841,25849],{},[1677,25842,25843],{},[1680,25844,25845,25847],{},[1683,25846,1379],{},[1683,25848,1110],{},[1691,25850,20914],{"encoding":1693}," u vychýleného procesu — ",[1115,25853,25855],{"className":25854},[1668],[1670,25856,25857],{"xmlns":1672},[1674,25858,25859,25867],{},[1677,25860,25861],{},[1680,25862,25863,25865],{},[1683,25864,1379],{},[1683,25866,1110],{},[1691,25868,20914],{"encoding":1693}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,25871,25873],{"className":25872},[1668],[1670,25874,25875],{"xmlns":1672},[1674,25876,25877,25889],{},[1677,25878,25879],{},[1680,25880,25881,25883],{},[1683,25882,1379],{},[1677,25884,25885,25887],{},[1683,25886,1110],{},[1683,25888,7374],{},[1691,25890,20936],{"encoding":1693},[1265,25892,25893,25894,25907,25908,25921,25922,25907,25937,25950,25951,25964,25965,25978,25979,25981],{},"Zaměnit diagram ",[1115,25895,25897],{"className":25896},[1668],[1670,25898,25899],{"xmlns":1672},[1674,25900,25901,25905],{},[1677,25902,25903],{},[1683,25904,3840],{},[1691,25906,3840],{"encoding":1693}," s diagramem ",[1115,25909,25911],{"className":25910},[1668],[1670,25912,25913],{"xmlns":1672},[1674,25914,25915,25919],{},[1677,25916,25917],{},[1683,25918,11642],{},[1691,25920,11642],{"encoding":1693}," nebo diagram ",[1115,25923,25925],{"className":25924},[1668],[1670,25926,25927],{"xmlns":1672},[1674,25928,25929,25935],{},[1677,25930,25931,25933],{},[1683,25932,1809],{},[1683,25934,1110],{},[1691,25936,20875],{"encoding":1693},[1115,25938,25940],{"className":25939},[1668],[1670,25941,25942],{"xmlns":1672},[1674,25943,25944,25948],{},[1677,25945,25946],{},[1683,25947,1110],{},[1691,25949,1110],{"encoding":1693}," — při nekonstantním rozsahu podskupin se volí ",[1115,25952,25954],{"className":25953},[1668],[1670,25955,25956],{"xmlns":1672},[1674,25957,25958,25962],{},[1677,25959,25960],{},[1683,25961,11642],{},[1691,25963,11642],{"encoding":1693},", resp. ",[1115,25966,25968],{"className":25967},[1668],[1670,25969,25970],{"xmlns":1672},[1674,25971,25972,25976],{},[1677,25973,25974],{},[1683,25975,1110],{},[1691,25977,1110],{"encoding":1693},", a do ",[3590,25980,23928],{}," se zadává vektor rozsahů.",[1265,25983,25984,25985,26002,26003,26016,26017,26030,26031,1497],{},"Posuzovat diagram ",[1115,25986,25988],{"className":25987},[1668],[1670,25989,25990],{"xmlns":1672},[1674,25991,25992,26000],{},[1677,25993,25994],{},[2843,25995,25996,25998],{"accent":1121},[1683,25997,6834],{},[1811,25999,11573],{},[1691,26001,21677],{"encoding":1693}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,26004,26006],{"className":26005},[1668],[1670,26007,26008],{"xmlns":1672},[1674,26009,26010,26014],{},[1677,26011,26012],{},[1683,26013,10337],{},[1691,26015,10337],{"encoding":1693}," (resp. ",[1115,26018,26020],{"className":26019},[1668],[1670,26021,26022],{"xmlns":1672},[1674,26023,26024,26028],{},[1677,26025,26026],{},[1683,26027,1974],{},[1691,26029,1974],{"encoding":1693},"), potom diagram ",[1115,26032,26034],{"className":26033},[1668],[1670,26035,26036],{"xmlns":1672},[1674,26037,26038,26046],{},[1677,26039,26040],{},[2843,26041,26042,26044],{"accent":1121},[1683,26043,6834],{},[1811,26045,11573],{},[1691,26047,21677],{"encoding":1693},[1265,26049,26050],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1153,26052,1501],{"id":1500},[1503,26054,26055,26060,26065,26071,26076,26081,26086],{},[1265,26056,26057],{},[1127,26058,1133],{"className":26059,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,26061,26062],{},[1127,26063,886],{"className":26064,"dataFsResolvedFilePath":1288,"href":1286},[1131],[1265,26066,26067],{},[1127,26068,26070],{"className":26069,"dataFsResolvedFilePath":1275,"href":1273},[1131],"nahodne-veliciny-a-rozdeleni",[1265,26072,26073],{},[1127,26074,141],{"className":26075,"dataFsResolvedFilePath":1300,"href":1298},[1131],[1265,26077,26078],{},[1127,26079,11199],{"className":26080,"dataFsResolvedFilePath":1312,"href":1310},[1131],[1265,26082,26083],{},[1127,26084,716],{"className":26085,"dataFsResolvedFilePath":1324,"href":1322},[1131],[1265,26087,26088],{},[1127,26089,6753],{"className":26090,"dataFsResolvedFilePath":1550,"href":1548},[1131],[1153,26092,1554],{"id":934},[1110,26094,1557,26095,1561],{},[1420,26096,1560],{},[1110,26098,1590,26099,1594],{},[1420,26100,1593],{},[1110,26102,1583,26103,1587],{},[1420,26104,1586],{},[1110,26106,1576,26107,1580],{},[1420,26108,1579],{},[6761,26110,26111],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: 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.shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":1603,"searchDepth":27,"depth":27,"links":26113},[26114,26115,26116,26124,26134,26144,26145,26146],{"id":21013,"depth":27,"text":1330},{"id":21126,"depth":27,"text":21127},{"id":21215,"depth":27,"text":21216,"children":26117},[26118,26120,26122],{"id":21377,"depth":148,"text":26119},"Diagram (xˉ,R)(\\bar{x}, R)",{"id":22873,"depth":148,"text":26121},"Diagram (xˉ,s)(\\bar{x}, s)",{"id":23039,"depth":148,"text":26123},"Diagram (xi,Rkl,i)(x_i, R_{kl,i})",{"id":23394,"depth":27,"text":23395,"children":26125},[26126,26128,26130,26132],{"id":23490,"depth":148,"text":26127},"Diagram cc",{"id":23853,"depth":148,"text":26129},"Diagram uu",{"id":24006,"depth":148,"text":26131},"Diagram npnp",{"id":24138,"depth":148,"text":26133},"Diagram pp",{"id":24271,"depth":27,"text":24272,"children":26135},[26136,26138,26140,26142,26143],{"id":24317,"depth":148,"text":26137},"CpC_p — index způsobilosti",{"id":24641,"depth":148,"text":26139},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":24836,"depth":148,"text":26141},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":25094,"depth":148,"text":25095},{"id":25284,"depth":148,"text":25285},{"id":6528,"depth":27,"text":6529},{"id":1500,"depth":27,"text":1501},{"id":934,"depth":27,"text":1554},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":1543,"description":1603},[26151,26152,26153,26154],"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":26159,"title":1527,"body":26160,"course":23,"courses":1614,"created":1615,"description":1603,"extension":1616,"meta":35970,"navigation":1618,"path":35971,"seo":35972,"sources":35973,"stem":35979,"tags":35980,"type":6782,"updated":1615,"__hash__":35981},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":26161,"toc":35943},[26162,26165,26364,26408,26412,26421,26424,26490,26540,26693,26697,26700,26794,26944,26963,26970,27059,27063,27098,27135,27173,27208,27212,27219,27437,27556,27560,27692,27746,27768,28110,28117,28205,28211,28252,28537,28546,28661,28667,28674,28679,28685,28779,28785,28811,28817,28909,28915,28965,28969,29165,29225,29587,29926,30025,30031,30259,30263,30529,30533,30536,30602,30649,31105,31109,31112,31299,31332,31554,31873,31912,31919,32576,32715,32721,32877,32883,32890,32943,32949,33122,33128,33192,33197,33382,33388,33433,33437,33440,33444,33491,33719,33735,33824,33830,33856,33860,33863,33935,34028,34097,34103,34126,34573,34580,34584,34614,34618,34868,34887,34948,34957,35113,35119,35145,35320,35324,35345,35376,35380,35404,35434,35438,35498,35556,35560,35567,35740,35742,35895,35897,35934,35936,35940],[1099,26163,1527],{"id":26164},"testování-statistických-hypotéz",[1103,26166,26168,26174],{"className":26167,"dataCallout":1641},[1106,1640],[1110,26169,26171,1649],{"className":26170},[1113],[1115,26172],{"className":26173,"ariaHidden":1121},[1118,1648,1120],[1503,26175,26176,26246,26328,26331,26334],{},[1265,26177,26178,26179,26196,26197,26214,26215,3071,26228,26245],{},"Test porovnává tvrzení ",[1115,26180,26182],{"className":26181},[1668],[1670,26183,26184],{"xmlns":1672},[1674,26185,26186,26194],{},[1677,26187,26188],{},[1680,26189,26190,26192],{},[1683,26191,1685],{},[1687,26193,1689],{},[1691,26195,1694],{"encoding":1693}," s alternativou ",[1115,26198,26200],{"className":26199},[1668],[1670,26201,26202],{"xmlns":1672},[1674,26203,26204,26212],{},[1677,26205,26206],{},[1680,26207,26208,26210],{},[1683,26209,1685],{},[1687,26211,1914],{},[1691,26213,3116],{"encoding":1693}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,26216,26218],{"className":26217},[1668],[1670,26219,26220],{"xmlns":1672},[1674,26221,26222,26226],{},[1677,26223,26224],{},[1683,26225,1729],{},[1691,26227,1729],{"encoding":1693},[1115,26229,26231],{"className":26230},[1668],[1670,26232,26233],{"xmlns":1672},[1674,26234,26235,26243],{},[1677,26236,26237],{},[1680,26238,26239,26241],{},[1683,26240,1685],{},[1687,26242,1689],{},[1691,26244,1694],{"encoding":1693}," zamítáme.",[1265,26247,26248,26249,26262,26263,26280,26281,26295,26296,26313,26314,26327],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,26250,26252],{"className":26251},[1668],[1670,26253,26254],{"xmlns":1672},[1674,26255,26256,26260],{},[1677,26257,26258],{},[1683,26259,3485],{},[1691,26261,3548],{"encoding":1693},", zamítnutí platné ",[1115,26264,26266],{"className":26265},[1668],[1670,26267,26268],{"xmlns":1672},[1674,26269,26270,26278],{},[1677,26271,26272],{},[1680,26273,26274,26276],{},[1683,26275,1685],{},[1687,26277,1689],{},[1691,26279,1694],{"encoding":1693},") a chybu II. druhu (",[1115,26282,26284],{"className":26283},[1668],[1670,26285,26286],{"xmlns":1672},[1674,26287,26288,26292],{},[1677,26289,26290],{},[1683,26291,16451],{},[1691,26293,26294],{"encoding":1693},"\\beta",", přijetí neplatné ",[1115,26297,26299],{"className":26298},[1668],[1670,26300,26301],{"xmlns":1672},[1674,26302,26303,26311],{},[1677,26304,26305],{},[1680,26306,26307,26309],{},[1683,26308,1685],{},[1687,26310,1689],{},[1691,26312,1694],{"encoding":1693},"). Hladina významnosti ",[1115,26315,26317],{"className":26316},[1668],[1670,26318,26319],{"xmlns":1672},[1674,26320,26321,26325],{},[1677,26322,26323],{},[1683,26324,3485],{},[1691,26326,3548],{"encoding":1693}," se volí předem, obvykle 0,05.",[1265,26329,26330],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1265,26332,26333],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1265,26335,26336,26337,26350,26351,1497],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,26338,26340],{"className":26339},[1668],[1670,26341,26342],{"xmlns":1672},[1674,26343,26344,26348],{},[1677,26345,26346],{},[1683,26347,1729],{},[1691,26349,1729],{"encoding":1693},", nebo podle p-hodnoty vůči ",[1115,26352,26354],{"className":26353},[1668],[1670,26355,26356],{"xmlns":1672},[1674,26357,26358,26362],{},[1677,26359,26360],{},[1683,26361,3485],{},[1691,26363,3548],{"encoding":1693},[1110,26365,26366,26367,26371,26372,26376,26377,26381,26382,3071,26395,1277],{},"Testy statistických hypotéz jsou nástroj ",[1127,26368,26370],{"className":26369,"dataFsResolvedFilePath":1132,"href":1129},[1131],"Metod aplikované statistiky"," pro rozhodování o parametrech nebo tvaru rozdělení na základě náhodného výběru, nikoli vyčerpávajícího šetření celého základního souboru. Vycházejí z charakteristik, které lze předem spočítat jako ",[1127,26373,26375],{"className":26374,"dataFsResolvedFilePath":1288,"href":1286},[1131],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1127,26378,26380],{"className":26379,"dataFsResolvedFilePath":1275,"href":1273},[1131],"náhodných veličin"," (normální, ",[1115,26383,26385],{"className":26384},[1668],[1670,26386,26387],{"xmlns":1672},[1674,26388,26389,26393],{},[1677,26390,26391],{},[1683,26392,7258],{},[1691,26394,7258],{"encoding":1693},[1115,26396,26398],{"className":26397},[1668],[1670,26399,26400],{"xmlns":1672},[1674,26401,26402,26406],{},[1677,26403,26404],{},[1683,26405,1403],{},[1691,26407,1403],{"encoding":1693},[1153,26409,26411],{"id":26410},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,26413,26414,26417,26418,26420],{},[1136,26415,26416],{},"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. ",[1136,26419,1294],{}," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,26422,26423],{},"Proti sobě stojí dvě hypotézy:",[1503,26425,26426,26449],{},[1265,26427,26428,26448],{},[1136,26429,26430,26431],{},"Nulová hypotéza ",[1115,26432,26434],{"className":26433},[1668],[1670,26435,26436],{"xmlns":1672},[1674,26437,26438,26446],{},[1677,26439,26440],{},[1680,26441,26442,26444],{},[1683,26443,1685],{},[1687,26445,1689],{},[1691,26447,1694],{"encoding":1693}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1265,26450,26451,26471,26472,26489],{},[1136,26452,26453,26454],{},"Alternativní hypotéza ",[1115,26455,26457],{"className":26456},[1668],[1670,26458,26459],{"xmlns":1672},[1674,26460,26461,26469],{},[1677,26462,26463],{},[1680,26464,26465,26467],{},[1683,26466,1685],{},[1687,26468,1914],{},[1691,26470,3116],{"encoding":1693}," — staví se proti ",[1115,26473,26475],{"className":26474},[1668],[1670,26476,26477],{"xmlns":1672},[1674,26478,26479,26487],{},[1677,26480,26481],{},[1680,26482,26483,26485],{},[1683,26484,1685],{},[1687,26486,1689],{},[1691,26488,1694],{"encoding":1693}," a určitým způsobem popírá její tvrzení.",[1110,26491,1822,26492,26522,26523,2077],{},[1115,26493,26495],{"className":26494},[1668],[1670,26496,26497],{"xmlns":1672},[1674,26498,26499,26519],{},[1677,26500,26501,26507,26509,26511,26513],{},[1680,26502,26503,26505],{},[1683,26504,1685],{},[1687,26506,1689],{},[1811,26508,2077],{},[1683,26510,7005],{},[1811,26512,2101],{},[1680,26514,26515,26517],{},[1683,26516,7005],{},[1687,26518,1689],{},[1691,26520,26521],{"encoding":1693},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,26524,26526],{"className":26525},[1668],[1670,26527,26528],{"xmlns":1672},[1674,26529,26530,26538],{},[1677,26531,26532],{},[1680,26533,26534,26536],{},[1683,26535,1685],{},[1687,26537,1914],{},[1691,26539,3116],{"encoding":1693},[1158,26541,26542,26572],{},[1161,26543,26544],{},[1164,26545,26546,26566,26569],{},[1167,26547,26548,26549],{},"Tvar ",[1115,26550,26552],{"className":26551},[1668],[1670,26553,26554],{"xmlns":1672},[1674,26555,26556,26564],{},[1677,26557,26558],{},[1680,26559,26560,26562],{},[1683,26561,1685],{},[1687,26563,1914],{},[1691,26565,3116],{"encoding":1693},[1167,26567,26568],{},"Zápis",[1167,26570,26571],{},"Typ",[1174,26573,26574,26614,26654],{},[1164,26575,26576,26579,26611],{},[1179,26577,26578],{},"nerovnost",[1179,26580,26581],{},[1115,26582,26584],{"className":26583},[1668],[1670,26585,26586],{"xmlns":1672},[1674,26587,26588,26608],{},[1677,26589,26590,26596,26598,26600,26602],{},[1680,26591,26592,26594],{},[1683,26593,1685],{},[1687,26595,1914],{},[1811,26597,2077],{},[1683,26599,7005],{},[1811,26601,11070],{"mathvariant":2240},[1680,26603,26604,26606],{},[1683,26605,7005],{},[1687,26607,1689],{},[1691,26609,26610],{"encoding":1693},"H_1: \\mu \\neq \\mu_0",[1179,26612,26613],{},"dvoustranná",[1164,26615,26616,26619,26651],{},[1179,26617,26618],{},"větší",[1179,26620,26621],{},[1115,26622,26624],{"className":26623},[1668],[1670,26625,26626],{"xmlns":1672},[1674,26627,26628,26648],{},[1677,26629,26630,26636,26638,26640,26642],{},[1680,26631,26632,26634],{},[1683,26633,1685],{},[1687,26635,1914],{},[1811,26637,2077],{},[1683,26639,7005],{},[1811,26641,1813],{},[1680,26643,26644,26646],{},[1683,26645,7005],{},[1687,26647,1689],{},[1691,26649,26650],{"encoding":1693},"H_1: \\mu > \\mu_0",[1179,26652,26653],{},"jednostranná",[1164,26655,26656,26659,26691],{},[1179,26657,26658],{},"menší",[1179,26660,26661],{},[1115,26662,26664],{"className":26663},[1668],[1670,26665,26666],{"xmlns":1672},[1674,26667,26668,26688],{},[1677,26669,26670,26676,26678,26680,26682],{},[1680,26671,26672,26674],{},[1683,26673,1685],{},[1687,26675,1914],{},[1811,26677,2077],{},[1683,26679,7005],{},[1811,26681,4453],{},[1680,26683,26684,26686],{},[1683,26685,7005],{},[1687,26687,1689],{},[1691,26689,26690],{"encoding":1693},"H_1: \\mu \u003C \\mu_0",[1179,26692,26653],{},[16860,26694,26696],{"id":26695},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,26698,26699],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1503,26701,26702,26739],{},[1265,26703,26704,26707,26708,26725,26726,1497],{},[1136,26705,26706],{},"Chyba I. druhu"," — zamítnutí ",[1115,26709,26711],{"className":26710},[1668],[1670,26712,26713],{"xmlns":1672},[1674,26714,26715,26723],{},[1677,26716,26717],{},[1680,26718,26719,26721],{},[1683,26720,1685],{},[1687,26722,1689],{},[1691,26724,1694],{"encoding":1693},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,26727,26729],{"className":26728},[1668],[1670,26730,26731],{"xmlns":1672},[1674,26732,26733,26737],{},[1677,26734,26735],{},[1683,26736,3485],{},[1691,26738,3548],{"encoding":1693},[1265,26740,26741,26744,26745,26762,26763,26780,26781,1497],{},[1136,26742,26743],{},"Chyba II. druhu"," — přijetí ",[1115,26746,26748],{"className":26747},[1668],[1670,26749,26750],{"xmlns":1672},[1674,26751,26752,26760],{},[1677,26753,26754],{},[1680,26755,26756,26758],{},[1683,26757,1685],{},[1687,26759,1689],{},[1691,26761,1694],{"encoding":1693},", ačkoliv platí ",[1115,26764,26766],{"className":26765},[1668],[1670,26767,26768],{"xmlns":1672},[1674,26769,26770,26778],{},[1677,26771,26772],{},[1680,26773,26774,26776],{},[1683,26775,1685],{},[1687,26777,1914],{},[1691,26779,3116],{"encoding":1693},". Pravděpodobnost ",[1115,26782,26784],{"className":26783},[1668],[1670,26785,26786],{"xmlns":1672},[1674,26787,26788,26792],{},[1677,26789,26790],{},[1683,26791,16451],{},[1691,26793,26294],{"encoding":1693},[1158,26795,26796,26859],{},[1161,26797,26798],{},[1164,26799,26800,26820,26839],{},[1167,26801,26802,26803],{},"Úsudek o ",[1115,26804,26806],{"className":26805},[1668],[1670,26807,26808],{"xmlns":1672},[1674,26809,26810,26818],{},[1677,26811,26812],{},[1680,26813,26814,26816],{},[1683,26815,1685],{},[1687,26817,1689],{},[1691,26819,1694],{"encoding":1693},[1167,26821,26822,8465],{},[1115,26823,26825],{"className":26824},[1668],[1670,26826,26827],{"xmlns":1672},[1674,26828,26829,26837],{},[1677,26830,26831],{},[1680,26832,26833,26835],{},[1683,26834,1685],{},[1687,26836,1689],{},[1691,26838,1694],{"encoding":1693},[1167,26840,26841,26858],{},[1115,26842,26844],{"className":26843},[1668],[1670,26845,26846],{"xmlns":1672},[1674,26847,26848,26856],{},[1677,26849,26850],{},[1680,26851,26852,26854],{},[1683,26853,1685],{},[1687,26855,1689],{},[1691,26857,1694],{"encoding":1693}," neplatí",[1174,26860,26861,26903],{},[1164,26862,26863,26866,26887],{},[1179,26864,26865],{},"Nezamítá se",[1179,26867,26868,26869],{},"správné rozhodnutí, ",[1115,26870,26872],{"className":26871},[1668],[1670,26873,26874],{"xmlns":1672},[1674,26875,26876,26884],{},[1677,26877,26878,26880,26882],{},[1687,26879,1914],{},[1811,26881,3184],{},[1683,26883,3485],{},[1691,26885,26886],{"encoding":1693},"1-\\alpha",[1179,26888,26889,26890],{},"chyba II. druhu, ",[1115,26891,26893],{"className":26892},[1668],[1670,26894,26895],{"xmlns":1672},[1674,26896,26897,26901],{},[1677,26898,26899],{},[1683,26900,16451],{},[1691,26902,26294],{"encoding":1693},[1164,26904,26905,26908,26924],{},[1179,26906,26907],{},"Zamítá se",[1179,26909,26910,26911],{},"chyba I. druhu, ",[1115,26912,26914],{"className":26913},[1668],[1670,26915,26916],{"xmlns":1672},[1674,26917,26918,26922],{},[1677,26919,26920],{},[1683,26921,3485],{},[1691,26923,3548],{"encoding":1693},[1179,26925,26868,26926],{},[1115,26927,26929],{"className":26928},[1668],[1670,26930,26931],{"xmlns":1672},[1674,26932,26933,26941],{},[1677,26934,26935,26937,26939],{},[1687,26936,1914],{},[1811,26938,3184],{},[1683,26940,16451],{},[1691,26942,26943],{"encoding":1693},"1-\\beta",[1110,26945,26946,1418,26949,26962],{},[1136,26947,26948],{},"Hladina významnosti",[1115,26950,26952],{"className":26951},[1668],[1670,26953,26954],{"xmlns":1672},[1674,26955,26956,26960],{},[1677,26957,26958],{},[1683,26959,3485],{},[1691,26961,3548],{"encoding":1693}," 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.",[1110,26964,26965],{},[4504,26966],{"alt":26967,"className":26968,"src":26969},"mask-th-chyba-i-ii",[1131,4508],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,26971,26972,26973,26986,26987,27000,27001,27014,27015,2009,27028,27041,27042,1497],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,26974,26976],{"className":26975},[1668],[1670,26977,26978],{"xmlns":1672},[1674,26979,26980,26984],{},[1677,26981,26982],{},[1683,26983,3840],{},[1691,26985,3840],{"encoding":1693}," doleva zmenší ",[1115,26988,26990],{"className":26989},[1668],[1670,26991,26992],{"xmlns":1672},[1674,26993,26994,26998],{},[1677,26995,26996],{},[1683,26997,16451],{},[1691,26999,26294],{"encoding":1693},", ale zvětší ",[1115,27002,27004],{"className":27003},[1668],[1670,27005,27006],{"xmlns":1672},[1674,27007,27008,27012],{},[1677,27009,27010],{},[1683,27011,3485],{},[1691,27013,3548],{"encoding":1693},", a naopak. Pro danou hladinu ",[1115,27016,27018],{"className":27017},[1668],[1670,27019,27020],{"xmlns":1672},[1674,27021,27022,27026],{},[1677,27023,27024],{},[1683,27025,3485],{},[1691,27027,3548],{"encoding":1693},[1115,27029,27031],{"className":27030},[1668],[1670,27032,27033],{"xmlns":1672},[1674,27034,27035,27039],{},[1677,27036,27037],{},[1683,27038,3840],{},[1691,27040,3840],{"encoding":1693}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,27043,27045],{"className":27044},[1668],[1670,27046,27047],{"xmlns":1672},[1674,27048,27049,27057],{},[1677,27050,27051],{},[1680,27052,27053,27055],{},[1683,27054,1685],{},[1687,27056,1689],{},[1691,27058,1694],{"encoding":1693},[16860,27060,27062],{"id":27061},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,27064,27065,1418,27067,27080,27081,1497],{},[1136,27066,3120],{},[1115,27068,27070],{"className":27069},[1668],[1670,27071,27072],{"xmlns":1672},[1674,27073,27074,27078],{},[1677,27075,27076],{},[1683,27077,7216],{},[1691,27079,7216],{"encoding":1693}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,27082,27084],{"className":27083},[1668],[1670,27085,27086],{"xmlns":1672},[1674,27087,27088,27096],{},[1677,27089,27090],{},[1680,27091,27092,27094],{},[1683,27093,1685],{},[1687,27095,1689],{},[1691,27097,1694],{"encoding":1693},[1110,27099,27100,1418,27103,27116,27117,27134],{},[1136,27101,27102],{},"Kritický obor",[1115,27104,27106],{"className":27105},[1668],[1670,27107,27108],{"xmlns":1672},[1674,27109,27110,27114],{},[1677,27111,27112],{},[1683,27113,1729],{},[1691,27115,1729],{"encoding":1693}," je množina hodnot svědčících pro ",[1115,27118,27120],{"className":27119},[1668],[1670,27121,27122],{"xmlns":1672},[1674,27123,27124,27132],{},[1677,27125,27126],{},[1680,27127,27128,27130],{},[1683,27129,1685],{},[1687,27131,1914],{},[1691,27133,3116],{"encoding":1693},". Je zkonstruován tak, aby",[1115,27136,27138],{"className":27137},[1668],[1670,27139,27140],{"xmlns":1672,"display":2083},[1674,27141,27142,27170],{},[1677,27143,27144,27146,27148,27150,27152,27154,27156,27162,27164,27166,27168],{},[1683,27145,6841],{},[1811,27147,1994],{"stretchy":1993},[1683,27149,7216],{},[1811,27151,7133],{},[1683,27153,1729],{},[1811,27155,23136],{},[1680,27157,27158,27160],{},[1683,27159,1685],{},[1687,27161,1689],{},[1811,27163,2005],{"stretchy":1993},[1811,27165,2101],{},[1683,27167,3485],{},[1811,27169,1917],{"separator":1121},[1691,27171,27172],{"encoding":1693},"P(T \\in W \\mid H_0) = \\alpha,",[1110,27174,27175,27176,27189,27190,27207],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,27177,27179],{"className":27178},[1668],[1670,27180,27181],{"xmlns":1672},[1674,27182,27183,27187],{},[1677,27184,27185],{},[1683,27186,1729],{},[1691,27188,1729],{"encoding":1693}," i při platné ",[1115,27191,27193],{"className":27192},[1668],[1670,27194,27195],{"xmlns":1672},[1674,27196,27197,27205],{},[1677,27198,27199],{},[1680,27200,27201,27203],{},[1683,27202,1685],{},[1687,27204,1689],{},[1691,27206,1694],{"encoding":1693},", byla rovna zvolené hladině významnosti.",[16860,27209,27211],{"id":27210},"postup-testování-hypotézy","Postup testování hypotézy",[1110,27213,27214],{},[4504,27215],{"alt":27216,"className":27217,"src":27218},"mask-ilu-postup-testovani",[1131,4508],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[1262,27220,27221,27258,27261,27277],{},[1265,27222,27223,27224,5862,27241,1497],{},"Formulace hypotéz ",[1115,27225,27227],{"className":27226},[1668],[1670,27228,27229],{"xmlns":1672},[1674,27230,27231,27239],{},[1677,27232,27233],{},[1680,27234,27235,27237],{},[1683,27236,1685],{},[1687,27238,1689],{},[1691,27240,1694],{"encoding":1693},[1115,27242,27244],{"className":27243},[1668],[1670,27245,27246],{"xmlns":1672},[1674,27247,27248,27256],{},[1677,27249,27250],{},[1680,27251,27252,27254],{},[1683,27253,1685],{},[1687,27255,1914],{},[1691,27257,3116],{"encoding":1693},[1265,27259,27260],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1265,27262,27263,27264,1497],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,27265,27267],{"className":27266},[1668],[1670,27268,27269],{"xmlns":1672},[1674,27270,27271,27275],{},[1677,27272,27273],{},[1683,27274,1729],{},[1691,27276,1729],{"encoding":1693},[1265,27278,27279,27280],{},"Formulace závěru:\n",[1503,27281,27282,27360],{},[1265,27283,27284,27285,4109,27303,27320,27321,27341,27342,27359],{},"pokud ",[1115,27286,27288],{"className":27287},[1668],[1670,27289,27290],{"xmlns":1672},[1674,27291,27292,27300],{},[1677,27293,27294,27296,27298],{},[1683,27295,7216],{},[1811,27297,7133],{},[1683,27299,1729],{},[1691,27301,27302],{"encoding":1693},"T \\in W",[1115,27304,27306],{"className":27305},[1668],[1670,27307,27308],{"xmlns":1672},[1674,27309,27310,27318],{},[1677,27311,27312],{},[1680,27313,27314,27316],{},[1683,27315,1685],{},[1687,27317,1914],{},[1691,27319,3116],{"encoding":1693}," je testem prokázána na hladině významnosti ",[1115,27322,27324],{"className":27323},[1668],[1670,27325,27326],{"xmlns":1672},[1674,27327,27328,27338],{},[1677,27329,27330,27332,27334,27336],{},[1687,27331,11932],{},[1683,27333,3485],{},[3028,27335,3030],{},[1683,27337,11939],{"mathvariant":2240},[1691,27339,27340],{"encoding":1693},"100\\alpha\\,\\%"," (zamítáme ",[1115,27343,27345],{"className":27344},[1668],[1670,27346,27347],{"xmlns":1672},[1674,27348,27349,27357],{},[1677,27350,27351],{},[1680,27352,27353,27355],{},[1683,27354,1685],{},[1687,27356,1689],{},[1691,27358,1694],{"encoding":1693},");",[1265,27361,27284,27362,4109,27381,27398,27399,27418,27419,27436],{},[1115,27363,27365],{"className":27364},[1668],[1670,27366,27367],{"xmlns":1672},[1674,27368,27369,27378],{},[1677,27370,27371,27373,27376],{},[1683,27372,7216],{},[1811,27374,27375],{"mathvariant":2240},"∉",[1683,27377,1729],{},[1691,27379,27380],{"encoding":1693},"T \\notin W",[1115,27382,27384],{"className":27383},[1668],[1670,27385,27386],{"xmlns":1672},[1674,27387,27388,27396],{},[1677,27389,27390],{},[1680,27391,27392,27394],{},[1683,27393,1685],{},[1687,27395,1914],{},[1691,27397,3116],{"encoding":1693}," není testem prokázána na hladině významnosti ",[1115,27400,27402],{"className":27401},[1668],[1670,27403,27404],{"xmlns":1672},[1674,27405,27406,27416],{},[1677,27407,27408,27410,27412,27414],{},[1687,27409,11932],{},[1683,27411,3485],{},[3028,27413,3030],{},[1683,27415,11939],{"mathvariant":2240},[1691,27417,27340],{"encoding":1693}," ; ",[1115,27420,27422],{"className":27421},[1668],[1670,27423,27424],{"xmlns":1672},[1674,27425,27426,27434],{},[1677,27427,27428],{},[1680,27429,27430,27432],{},[1683,27431,1685],{},[1687,27433,1689],{},[1691,27435,1694],{"encoding":1693}," nezamítáme.",[1110,27438,27439,27440,27443,27444,27461,27462,27479,27480,27500,27501,25296,27518,1418,27538,27555],{},"Rovnocennou alternativou je ",[1136,27441,27442],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,27445,27447],{"className":27446},[1668],[1670,27448,27449],{"xmlns":1672},[1674,27450,27451,27459],{},[1677,27452,27453],{},[1680,27454,27455,27457],{},[1683,27456,1685],{},[1687,27458,1689],{},[1691,27460,1694],{"encoding":1693},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,27463,27465],{"className":27464},[1668],[1670,27466,27467],{"xmlns":1672},[1674,27468,27469,27477],{},[1677,27470,27471],{},[1680,27472,27473,27475],{},[1683,27474,1685],{},[1687,27476,1689],{},[1691,27478,1694],{"encoding":1693},". Rozhodovací pravidlo: ",[1115,27481,27483],{"className":27482},[1668],[1670,27484,27485],{"xmlns":1672},[1674,27486,27487,27497],{},[1677,27488,27489,27491,27493,27495],{},[1683,27490,1110],{},[1811,27492,6849],{},[1683,27494,3485],{},[1811,27496,7664],{},[1691,27498,27499],{"encoding":1693},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,27502,27504],{"className":27503},[1668],[1670,27505,27506],{"xmlns":1672},[1674,27507,27508,27516],{},[1677,27509,27510],{},[1680,27511,27512,27514],{},[1683,27513,1685],{},[1687,27515,1689],{},[1691,27517,1694],{"encoding":1693},[1115,27519,27521],{"className":27520},[1668],[1670,27522,27523],{"xmlns":1672},[1674,27524,27525,27535],{},[1677,27526,27527,27529,27531,27533],{},[1683,27528,1110],{},[1811,27530,1813],{},[1683,27532,3485],{},[1811,27534,7664],{},[1691,27536,27537],{"encoding":1693},"p > \\alpha \\Rightarrow",[1115,27539,27541],{"className":27540},[1668],[1670,27542,27543],{"xmlns":1672},[1674,27544,27545,27553],{},[1677,27546,27547],{},[1680,27548,27549,27551],{},[1683,27550,1685],{},[1687,27552,1689],{},[1691,27554,1694],{"encoding":1693}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1153,27557,27559],{"id":27558},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,27561,27562,27563,27576,27577,27609,27610,27623,27624,5862,27641,27658,27659,27677,27678,27691],{},"Test o střední hodnotě ",[1115,27564,27566],{"className":27565},[1668],[1670,27567,27568],{"xmlns":1672},[1674,27569,27570,27574],{},[1677,27571,27572],{},[1683,27573,7005],{},[1691,27575,8910],{"encoding":1693}," rozdělení ",[1115,27578,27580],{"className":27579},[1668],[1670,27581,27582],{"xmlns":1672},[1674,27583,27584,27606],{},[1677,27585,27586,27588,27590,27592,27594,27596,27598,27604],{},[1683,27587,6846],{},[1811,27589,9297],{},[1683,27591,7000],{},[1811,27593,1994],{"stretchy":1993},[1683,27595,7005],{},[1811,27597,1917],{"separator":1121},[1706,27599,27600,27602],{},[1683,27601,7013],{},[1687,27603,1713],{},[1811,27605,2005],{"stretchy":1993},[1691,27607,27608],{"encoding":1693},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,27611,27613],{"className":27612},[1668],[1670,27614,27615],{"xmlns":1672},[1674,27616,27617,27621],{},[1677,27618,27619],{},[1683,27620,1809],{},[1691,27622,1809],{"encoding":1693}," se určí charakteristiky ",[1115,27625,27627],{"className":27626},[1668],[1670,27628,27629],{"xmlns":1672},[1674,27630,27631,27639],{},[1677,27632,27633],{},[2843,27634,27635,27637],{"accent":1121},[1683,27636,6834],{},[1811,27638,11573],{},[1691,27640,21677],{"encoding":1693},[1115,27642,27644],{"className":27643},[1668],[1670,27645,27646],{"xmlns":1672},[1674,27647,27648,27656],{},[1677,27649,27650],{},[1706,27651,27652,27654],{},[1683,27653,1974],{},[1687,27655,1713],{},[1691,27657,15891],{"encoding":1693},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,27660,27662],{"className":27661},[1668],[1670,27663,27664],{"xmlns":1672},[1674,27665,27666,27674],{},[1677,27667,27668],{},[1680,27669,27670,27672],{},[1683,27671,7005],{},[1687,27673,1689],{},[1691,27675,27676],{"encoding":1693},"\\mu_0"," a neznámou hodnotou ",[1115,27679,27681],{"className":27680},[1668],[1670,27682,27683],{"xmlns":1672},[1674,27684,27685,27689],{},[1677,27686,27687],{},[1683,27688,7005],{},[1691,27690,8910],{"encoding":1693},". Testové kritérium",[1115,27693,27695],{"className":27694},[1668],[1670,27696,27697],{"xmlns":1672,"display":2083},[1674,27698,27699,27743],{},[1677,27700,27701,27703,27705,27725,27729,27731],{},[1683,27702,7216],{},[1811,27704,2101],{},[2859,27706,27707,27723],{},[1677,27708,27709,27715,27717],{},[2843,27710,27711,27713],{"accent":1121},[1683,27712,6834],{},[1811,27714,11573],{},[1811,27716,3184],{},[1680,27718,27719,27721],{},[1683,27720,7005],{},[1687,27722,1689],{},[1683,27724,1974],{},[4574,27726,27727],{},[1683,27728,1809],{},[1811,27730,9297],{},[1680,27732,27733,27735],{},[1683,27734,7258],{},[1677,27736,27737,27739,27741],{},[1683,27738,1809],{},[1811,27740,3184],{},[1687,27742,1914],{},[1691,27744,27745],{"encoding":1693},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,27747,27748,27749,27767],{},"má Studentovo rozdělení o ",[1115,27750,27752],{"className":27751},[1668],[1670,27753,27754],{"xmlns":1672},[1674,27755,27756,27764],{},[1677,27757,27758,27760,27762],{},[1683,27759,1809],{},[1811,27761,3184],{},[1687,27763,1914],{},[1691,27765,27766],{"encoding":1693},"n-1"," stupních volnosti.",[1158,27769,27770,27828],{},[1161,27771,27772],{},[1164,27773,27774,27793,27812],{},[1167,27775,27776],{},[1115,27777,27779],{"className":27778},[1668],[1670,27780,27781],{"xmlns":1672},[1674,27782,27783,27791],{},[1677,27784,27785],{},[1680,27786,27787,27789],{},[1683,27788,1685],{},[1687,27790,1689],{},[1691,27792,1694],{"encoding":1693},[1167,27794,27795],{},[1115,27796,27798],{"className":27797},[1668],[1670,27799,27800],{"xmlns":1672},[1674,27801,27802,27810],{},[1677,27803,27804],{},[1680,27805,27806,27808],{},[1683,27807,1685],{},[1687,27809,1914],{},[1691,27811,3116],{"encoding":1693},[1167,27813,27814,27815],{},"Kritický obor ",[1115,27816,27818],{"className":27817},[1668],[1670,27819,27820],{"xmlns":1672},[1674,27821,27822,27826],{},[1677,27823,27824],{},[1683,27825,1729],{},[1691,27827,1729],{"encoding":1693},[1174,27829,27830,27920,28018],{},[1164,27831,27832,27856,27880],{},[1179,27833,27834],{},[1115,27835,27837],{"className":27836},[1668],[1670,27838,27839],{"xmlns":1672},[1674,27840,27841,27853],{},[1677,27842,27843,27845,27847],{},[1683,27844,7005],{},[1811,27846,6849],{},[1680,27848,27849,27851],{},[1683,27850,7005],{},[1687,27852,1689],{},[1691,27854,27855],{"encoding":1693},"\\mu \\le \\mu_0",[1179,27857,27858],{},[1115,27859,27861],{"className":27860},[1668],[1670,27862,27863],{"xmlns":1672},[1674,27864,27865,27877],{},[1677,27866,27867,27869,27871],{},[1683,27868,7005],{},[1811,27870,1813],{},[1680,27872,27873,27875],{},[1683,27874,7005],{},[1687,27876,1689],{},[1691,27878,27879],{"encoding":1693},"\\mu > \\mu_0",[1179,27881,27882],{},[1115,27883,27885],{"className":27884},[1668],[1670,27886,27887],{"xmlns":1672},[1674,27888,27889,27917],{},[1677,27890,27891,27893,27895,27907,27909,27911,27913,27915],{},[1683,27892,7258],{},[1811,27894,3471],{},[1680,27896,27897,27899],{},[1683,27898,7258],{},[1677,27900,27901,27903,27905],{},[1687,27902,1914],{},[1811,27904,3184],{},[1683,27906,3485],{},[1811,27908,1994],{"stretchy":1993},[1683,27910,1809],{},[1811,27912,3184],{},[1687,27914,1914],{},[1811,27916,2005],{"stretchy":1993},[1691,27918,27919],{"encoding":1693},"t \\ge t_{1-\\alpha}(n-1)",[1164,27921,27922,27946,27970],{},[1179,27923,27924],{},[1115,27925,27927],{"className":27926},[1668],[1670,27928,27929],{"xmlns":1672},[1674,27930,27931,27943],{},[1677,27932,27933,27935,27937],{},[1683,27934,7005],{},[1811,27936,2101],{},[1680,27938,27939,27941],{},[1683,27940,7005],{},[1687,27942,1689],{},[1691,27944,27945],{"encoding":1693},"\\mu = \\mu_0",[1179,27947,27948],{},[1115,27949,27951],{"className":27950},[1668],[1670,27952,27953],{"xmlns":1672},[1674,27954,27955,27967],{},[1677,27956,27957,27959,27961],{},[1683,27958,7005],{},[1811,27960,11070],{"mathvariant":2240},[1680,27962,27963,27965],{},[1683,27964,7005],{},[1687,27966,1689],{},[1691,27968,27969],{"encoding":1693},"\\mu \\neq \\mu_0",[1179,27971,27972],{},[1115,27973,27975],{"className":27974},[1668],[1670,27976,27977],{"xmlns":1672},[1674,27978,27979,28015],{},[1677,27980,27981,27983,27985,27987,27989,28005,28007,28009,28011,28013],{},[1811,27982,23136],{"stretchy":1993},[1683,27984,7258],{},[1811,27986,23136],{"stretchy":1993},[1811,27988,3471],{},[1680,27990,27991,27993],{},[1683,27992,7258],{},[1677,27994,27995,27997,27999,28001,28003],{},[1687,27996,1914],{},[1811,27998,3184],{},[1683,28000,3485],{},[1683,28002,4725],{"mathvariant":2240},[1687,28004,1713],{},[1811,28006,1994],{"stretchy":1993},[1683,28008,1809],{},[1811,28010,3184],{},[1687,28012,1914],{},[1811,28014,2005],{"stretchy":1993},[1691,28016,28017],{"encoding":1693},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1164,28019,28020,28044,28068],{},[1179,28021,28022],{},[1115,28023,28025],{"className":28024},[1668],[1670,28026,28027],{"xmlns":1672},[1674,28028,28029,28041],{},[1677,28030,28031,28033,28035],{},[1683,28032,7005],{},[1811,28034,3471],{},[1680,28036,28037,28039],{},[1683,28038,7005],{},[1687,28040,1689],{},[1691,28042,28043],{"encoding":1693},"\\mu \\ge \\mu_0",[1179,28045,28046],{},[1115,28047,28049],{"className":28048},[1668],[1670,28050,28051],{"xmlns":1672},[1674,28052,28053,28065],{},[1677,28054,28055,28057,28059],{},[1683,28056,7005],{},[1811,28058,4453],{},[1680,28060,28061,28063],{},[1683,28062,7005],{},[1687,28064,1689],{},[1691,28066,28067],{"encoding":1693},"\\mu \u003C \\mu_0",[1179,28069,28070],{},[1115,28071,28073],{"className":28072},[1668],[1670,28074,28075],{"xmlns":1672},[1674,28076,28077,28107],{},[1677,28078,28079,28081,28083,28085,28097,28099,28101,28103,28105],{},[1683,28080,7258],{},[1811,28082,6849],{},[1811,28084,3184],{},[1680,28086,28087,28089],{},[1683,28088,7258],{},[1677,28090,28091,28093,28095],{},[1687,28092,1914],{},[1811,28094,3184],{},[1683,28096,3485],{},[1811,28098,1994],{"stretchy":1993},[1683,28100,1809],{},[1811,28102,3184],{},[1687,28104,1914],{},[1811,28106,2005],{"stretchy":1993},[1691,28108,28109],{"encoding":1693},"t \\le -t_{1-\\alpha}(n-1)",[1110,28111,28112,28113,28116],{},"V R test provádí ",[3590,28114,28115],{},"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?",[3814,28118,28120],{"className":3816,"code":28119,"language":71,"meta":1603,"style":1603},"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",[3590,28121,28122,28176],{"__ignoreMap":1603},[1115,28123,28124,28126,28128,28130,28132,28135,28137,28140,28142,28145,28147,28150,28152,28155,28157,28160,28162,28164,28166,28169,28171,28174],{"class":3822,"line":10},[1115,28125,6834],{"class":3825},[1115,28127,3830],{"class":3829},[1115,28129,3956],{"class":3833},[1115,28131,1994],{"class":3837},[1115,28133,28134],{"class":3845},"12.5",[1115,28136,1917],{"class":3829},[1115,28138,28139],{"class":3845}," 13.5",[1115,28141,1917],{"class":3829},[1115,28143,28144],{"class":3845}," 11.9",[1115,28146,1917],{"class":3829},[1115,28148,28149],{"class":3845}," 12.2",[1115,28151,1917],{"class":3829},[1115,28153,28154],{"class":3845}," 13.0",[1115,28156,1917],{"class":3829},[1115,28158,28159],{"class":3845}," 14.3",[1115,28161,1917],{"class":3829},[1115,28163,28149],{"class":3845},[1115,28165,1917],{"class":3829},[1115,28167,28168],{"class":3845}," 11.8",[1115,28170,1917],{"class":3829},[1115,28172,28173],{"class":3845}," 14.0",[1115,28175,4022],{"class":3837},[1115,28177,28178,28181,28183,28185,28187,28189,28191,28193,28195,28198,28200,28203],{"class":3822,"line":27},[1115,28179,28180],{"class":3833},"t.test",[1115,28182,1994],{"class":3837},[1115,28184,6834],{"class":3825},[1115,28186,1917],{"class":3829},[1115,28188,25693],{"class":3825},[1115,28190,3918],{"class":3829},[1115,28192,3855],{"class":3845},[1115,28194,1917],{"class":3829},[1115,28196,28197],{"class":3825}," alternative",[1115,28199,3918],{"class":3829},[1115,28201,28202],{"class":3961}," \"two.sided\"",[1115,28204,4022],{"class":3837},[3814,28206,28209],{"className":28207,"code":28208,"language":4044,"meta":1603},[4042],"    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",[3590,28210,28208],{"__ignoreMap":1603},[1110,28212,28213,28215,28216,28219,28220,28223,28224,28227,28228,28251],{},[3590,28214,7258],{}," je testové kritérium, ",[3590,28217,28218],{},"df"," stupně volnosti, ",[3590,28221,28222],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3590,28225,28226],{},"mean of x"," výběrový průměr. Zde ",[1115,28229,28231],{"className":28230},[1668],[1670,28232,28233],{"xmlns":1672},[1674,28234,28235,28248],{},[1677,28236,28237,28239,28241,28244,28246],{},[1683,28238,1110],{},[1811,28240,2101],{},[1687,28242,28243],{},"0,02843",[1811,28245,4453],{},[1687,28247,4105],{},[1691,28249,28250],{"encoding":1693},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,28253,28255,28262,28350,28406,28498],{"className":28254,"dataCallout":3597},[1106,3596],[1110,28256,28258,28261],{"className":28257},[1113],[1115,28259],{"className":28260,"ariaHidden":1121},[1118,3604,1120],"Příklad: Kontrola objemu lahví",[1110,28263,28264,28265,28287,28288,28306,28307,28330,28331,28349],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,28266,28268],{"className":28267},[1668],[1670,28269,28270],{"xmlns":1672},[1674,28271,28272,28284],{},[1677,28273,28274,28280,28282],{},[1680,28275,28276,28278],{},[1683,28277,7005],{},[1687,28279,1689],{},[1811,28281,2101],{},[1687,28283,8571],{},[1691,28285,28286],{"encoding":1693},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,28289,28291],{"className":28290},[1668],[1670,28292,28293],{"xmlns":1672},[1674,28294,28295,28303],{},[1677,28296,28297,28299,28301],{},[1683,28298,1809],{},[1811,28300,2101],{},[1687,28302,4166],{},[1691,28304,28305],{"encoding":1693},"n = 20"," lahví dal ",[1115,28308,28310],{"className":28309},[1668],[1670,28311,28312],{"xmlns":1672},[1674,28313,28314,28327],{},[1677,28315,28316,28322,28324],{},[2843,28317,28318,28320],{"accent":1121},[1683,28319,6834],{},[1811,28321,11573],{},[1811,28323,2101],{},[1687,28325,28326],{},"0,492",[1691,28328,28329],{"encoding":1693},"\\bar{x} = 0{,}492"," l, ",[1115,28332,28334],{"className":28333},[1668],[1670,28335,28336],{"xmlns":1672},[1674,28337,28338,28346],{},[1677,28339,28340,28342,28344],{},[1683,28341,1974],{},[1811,28343,2101],{},[1687,28345,14909],{},[1691,28347,28348],{"encoding":1693},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,28351,28352,28378,28379,28405],{},[1115,28353,28355],{"className":28354},[1668],[1670,28356,28357],{"xmlns":1672},[1674,28358,28359,28375],{},[1677,28360,28361,28367,28369,28371,28373],{},[1680,28362,28363,28365],{},[1683,28364,1685],{},[1687,28366,1689],{},[1811,28368,2077],{},[1683,28370,7005],{},[1811,28372,3471],{},[1687,28374,8571],{},[1691,28376,28377],{"encoding":1693},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,28380,28382],{"className":28381},[1668],[1670,28383,28384],{"xmlns":1672},[1674,28385,28386,28402],{},[1677,28387,28388,28394,28396,28398,28400],{},[1680,28389,28390,28392],{},[1683,28391,1685],{},[1687,28393,1914],{},[1811,28395,2077],{},[1683,28397,7005],{},[1811,28399,4453],{},[1687,28401,8571],{},[1691,28403,28404],{"encoding":1693},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,28407,28408],{},[1115,28409,28411],{"className":28410},[1668],[1670,28412,28413],{"xmlns":1672},[1674,28414,28415,28495],{},[1677,28416,28417,28419,28421,28433,28437,28439,28441,28444,28446,28448,28450,28452,28454,28456,28458,28460,28472,28474,28476,28478,28480,28482,28484,28486,28488,28490,28493],{},[1683,28418,7258],{},[1811,28420,2101],{},[2859,28422,28423,28431],{},[1677,28424,28425,28427,28429],{},[1687,28426,28326],{},[1811,28428,3184],{},[1687,28430,8571],{},[1687,28432,14909],{},[4574,28434,28435],{},[1687,28436,4166],{},[1811,28438,2101],{},[1811,28440,3184],{},[1687,28442,28443],{},"2,385",[1811,28445,1917],{"separator":1121},[2131,28447],{"width":2133},[1683,28449,1729],{},[1811,28451,2101],{},[1811,28453,3454],{"stretchy":1993},[1683,28455,7258],{},[1811,28457,6849],{},[1811,28459,3184],{},[1680,28461,28462,28464],{},[1683,28463,7258],{},[1677,28465,28466,28468,28470],{},[1687,28467,1689],{},[1811,28469,1917],{"separator":1121},[1687,28471,21910],{},[1811,28473,1994],{"stretchy":1993},[1687,28475,14833],{},[1811,28477,2005],{"stretchy":1993},[1811,28479,3514],{"stretchy":1993},[1811,28481,2101],{},[1811,28483,3454],{"stretchy":1993},[1683,28485,7258],{},[1811,28487,6849],{},[1811,28489,3184],{},[1687,28491,28492],{},"1,729",[1811,28494,3514],{"stretchy":1993},[1691,28496,28497],{"encoding":1693},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,28499,28500,28501,6128,28519,28536],{},"Protože ",[1115,28502,28504],{"className":28503},[1668],[1670,28505,28506],{"xmlns":1672},[1674,28507,28508,28516],{},[1677,28509,28510,28512,28514],{},[1683,28511,7258],{},[1811,28513,7133],{},[1683,28515,1729],{},[1691,28517,28518],{"encoding":1693},"t \\in W",[1115,28520,28522],{"className":28521},[1668],[1670,28523,28524],{"xmlns":1672},[1674,28525,28526,28534],{},[1677,28527,28528],{},[1680,28529,28530,28532],{},[1683,28531,1685],{},[1687,28533,1689],{},[1691,28535,1694],{"encoding":1693},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,28538,28539,28540,28542,28543,2077],{},"Ze souhrnných charakteristik bez surových dat ",[3590,28541,28115],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3590,28544,28545],{},"qt()",[3814,28547,28549],{"className":3816,"code":28548,"language":71,"meta":1603,"style":1603},"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",[3590,28550,28551,28589,28621,28651,28656],{"__ignoreMap":1603},[1115,28552,28553,28556,28558,28561,28563,28565,28567,28570,28572,28574,28576,28579,28581,28584,28586],{"class":3822,"line":10},[1115,28554,28555],{"class":3825},"xbar",[1115,28557,3830],{"class":3829},[1115,28559,28560],{"class":3845}," 0.492",[1115,28562,25296],{"class":3837},[1115,28564,1974],{"class":3825},[1115,28566,3830],{"class":3829},[1115,28568,28569],{"class":3845}," 0.015",[1115,28571,25296],{"class":3837},[1115,28573,1809],{"class":3825},[1115,28575,3830],{"class":3829},[1115,28577,28578],{"class":3845}," 20",[1115,28580,25296],{"class":3837},[1115,28582,28583],{"class":3825},"mu0",[1115,28585,3830],{"class":3829},[1115,28587,28588],{"class":3845}," 0.5\n",[1115,28590,28591,28593,28595,28597,28599,28601,28604,28606,28608,28611,28613,28615,28617,28619],{"class":3822,"line":27},[1115,28592,7258],{"class":3825},[1115,28594,3830],{"class":3829},[1115,28596,4728],{"class":3837},[1115,28598,28555],{"class":3825},[1115,28600,25633],{"class":3829},[1115,28602,28603],{"class":3825}," mu0",[1115,28605,4722],{"class":3837},[1115,28607,4725],{"class":3829},[1115,28609,28610],{"class":3825}," s",[1115,28612,18753],{"class":3829},[1115,28614,4699],{"class":3833},[1115,28616,1994],{"class":3837},[1115,28618,1809],{"class":3825},[1115,28620,4022],{"class":3837},[1115,28622,28623,28626,28628,28631,28633,28636,28638,28640,28642,28645,28647,28649],{"class":3822,"line":148},[1115,28624,28625],{"class":3825},"t_krit",[1115,28627,3830],{"class":3829},[1115,28629,28630],{"class":3833}," qt",[1115,28632,1994],{"class":3837},[1115,28634,28635],{"class":3845},"0.05",[1115,28637,1917],{"class":3829},[1115,28639,10923],{"class":3825},[1115,28641,3918],{"class":3829},[1115,28643,28644],{"class":3825}," n",[1115,28646,25633],{"class":3829},[1115,28648,4762],{"class":3845},[1115,28650,4022],{"class":3837},[1115,28652,28653],{"class":3822,"line":111},[1115,28654,28655],{"class":3825},"t\n",[1115,28657,28658],{"class":3822,"line":96},[1115,28659,28660],{"class":3825},"t_krit\n",[3814,28662,28665],{"className":28663,"code":28664,"language":4044,"meta":1603},[4042],"[1] -2.385139\n[1] -1.729133\n",[3590,28666,28664],{"__ignoreMap":1603},[1110,28668,28669],{},[4504,28670],{"alt":28671,"className":28672,"src":28673},"mask-th-t-jednostranny",[1131,4508],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,28675,28676,28677,2077],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3590,28678,28115],{},[1110,28680,28681,28684],{},[1136,28682,28683],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3814,28686,28688],{"className":3816,"code":28687,"language":71,"meta":1603,"style":1603},"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",[3590,28689,28690,28753],{"__ignoreMap":1603},[1115,28691,28692,28695,28697,28699,28701,28704,28706,28709,28711,28714,28716,28719,28721,28724,28726,28729,28731,28733,28735,28738,28740,28742,28744,28747,28749,28751],{"class":3822,"line":10},[1115,28693,28694],{"class":3825},"x2",[1115,28696,3830],{"class":3829},[1115,28698,3956],{"class":3833},[1115,28700,1994],{"class":3837},[1115,28702,28703],{"class":3845},"9.5",[1115,28705,1917],{"class":3829},[1115,28707,28708],{"class":3845}," 10.5",[1115,28710,1917],{"class":3829},[1115,28712,28713],{"class":3845}," 8.9",[1115,28715,1917],{"class":3829},[1115,28717,28718],{"class":3845}," 9.2",[1115,28720,1917],{"class":3829},[1115,28722,28723],{"class":3845}," 10.0",[1115,28725,1917],{"class":3829},[1115,28727,28728],{"class":3845}," 8.5",[1115,28730,1917],{"class":3829},[1115,28732,28718],{"class":3845},[1115,28734,1917],{"class":3829},[1115,28736,28737],{"class":3845}," 8.8",[1115,28739,1917],{"class":3829},[1115,28741,28723],{"class":3845},[1115,28743,1917],{"class":3829},[1115,28745,28746],{"class":3845}," 9.5",[1115,28748,1917],{"class":3829},[1115,28750,28718],{"class":3845},[1115,28752,4022],{"class":3837},[1115,28754,28755,28757,28759,28761,28763,28765,28767,28769,28771,28773,28775,28777],{"class":3822,"line":27},[1115,28756,28180],{"class":3833},[1115,28758,1994],{"class":3837},[1115,28760,28694],{"class":3825},[1115,28762,1917],{"class":3829},[1115,28764,25693],{"class":3825},[1115,28766,3918],{"class":3829},[1115,28768,9591],{"class":3845},[1115,28770,1917],{"class":3829},[1115,28772,28197],{"class":3825},[1115,28774,3918],{"class":3829},[1115,28776,28202],{"class":3961},[1115,28778,4022],{"class":3837},[3814,28780,28783],{"className":28781,"code":28782,"language":4044,"meta":1603},[4042],"    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",[3590,28784,28782],{"__ignoreMap":1603},[1110,28786,28787,28810],{},[1115,28788,28790],{"className":28789},[1668],[1670,28791,28792],{"xmlns":1672},[1674,28793,28794,28807],{},[1677,28795,28796,28798,28800,28803,28805],{},[1683,28797,1110],{},[1811,28799,2101],{},[1687,28801,28802],{},"0,006548",[1811,28804,4453],{},[1687,28806,4105],{},[1691,28808,28809],{"encoding":1693},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,28812,28813,28816],{},[1136,28814,28815],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3814,28818,28820],{"className":3816,"code":28819,"language":71,"meta":1603,"style":1603},"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",[3590,28821,28822,28873,28899],{"__ignoreMap":1603},[1115,28823,28824,28827,28829,28831,28833,28835,28837,28839,28841,28843,28845,28847,28849,28851,28853,28855,28857,28859,28861,28863,28865,28867,28869,28871],{"class":3822,"line":10},[1115,28825,28826],{"class":3825},"x3",[1115,28828,3830],{"class":3829},[1115,28830,3956],{"class":3833},[1115,28832,1994],{"class":3837},[1115,28834,12100],{"class":3845},[1115,28836,1917],{"class":3829},[1115,28838,12105],{"class":3845},[1115,28840,1917],{"class":3829},[1115,28842,12110],{"class":3845},[1115,28844,1917],{"class":3829},[1115,28846,12115],{"class":3845},[1115,28848,1917],{"class":3829},[1115,28850,12110],{"class":3845},[1115,28852,1917],{"class":3829},[1115,28854,12110],{"class":3845},[1115,28856,1917],{"class":3829},[1115,28858,12128],{"class":3845},[1115,28860,1917],{"class":3829},[1115,28862,12133],{"class":3845},[1115,28864,1917],{"class":3829},[1115,28866,12105],{"class":3845},[1115,28868,1917],{"class":3829},[1115,28870,12105],{"class":3845},[1115,28872,4022],{"class":3837},[1115,28874,28875,28877,28879,28881,28883,28885,28887,28889,28891,28893,28895,28897],{"class":3822,"line":27},[1115,28876,28180],{"class":3833},[1115,28878,1994],{"class":3837},[1115,28880,28826],{"class":3825},[1115,28882,1917],{"class":3829},[1115,28884,25693],{"class":3825},[1115,28886,3918],{"class":3829},[1115,28888,3921],{"class":3845},[1115,28890,1917],{"class":3829},[1115,28892,28197],{"class":3825},[1115,28894,3918],{"class":3829},[1115,28896,28202],{"class":3961},[1115,28898,4022],{"class":3837},[1115,28900,28901,28903,28905,28907],{"class":3822,"line":148},[1115,28902,17689],{"class":3833},[1115,28904,1994],{"class":3837},[1115,28906,28826],{"class":3825},[1115,28908,4022],{"class":3837},[3814,28910,28913],{"className":28911,"code":28912,"language":4044,"meta":1603},[4042],"    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",[3590,28914,28912],{"__ignoreMap":1603},[1110,28916,28917,28940,28941,28964],{},[1115,28918,28920],{"className":28919},[1668],[1670,28921,28922],{"xmlns":1672},[1674,28923,28924,28937],{},[1677,28925,28926,28928,28930,28933,28935],{},[1683,28927,1110],{},[1811,28929,2101],{},[1687,28931,28932],{},"0,0343",[1811,28934,4453],{},[1687,28936,4105],{},[1691,28938,28939],{"encoding":1693},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,28942,28944],{"className":28943},[1668],[1670,28945,28946],{"xmlns":1672},[1674,28947,28948,28961],{},[1677,28949,28950,28952,28954,28957,28959],{},[1683,28951,1110],{},[1811,28953,2101],{},[1687,28955,28956],{},"0,4634",[1811,28958,1813],{},[1687,28960,4105],{},[1691,28962,28963],{"encoding":1693},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1153,28966,28968],{"id":28967},"párový-t-test","Párový t-test",[1110,28970,28971,28972,29002,29003,6895,29037,29075,29076,29089,29090,5862,29108,29128,29129,29146,29147,27691],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,28973,28975],{"className":28974},[1668],[1670,28976,28977],{"xmlns":1672},[1674,28978,28979,28999],{},[1677,28980,28981,28983,28989,28991,28997],{},[1811,28982,1994],{"stretchy":1993},[1680,28984,28985,28987],{},[1683,28986,6846],{},[1683,28988,1997],{},[1811,28990,1917],{"separator":1121},[1680,28992,28993,28995],{},[1683,28994,7202],{},[1683,28996,1997],{},[1811,28998,2005],{"stretchy":1993},[1691,29000,29001],{"encoding":1693},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,29004,29006],{"className":29005},[1668],[1670,29007,29008],{"xmlns":1672},[1674,29009,29010,29034],{},[1677,29011,29012,29018,29020,29026,29028],{},[1680,29013,29014,29016],{},[1683,29015,1387],{},[1683,29017,1997],{},[1811,29019,2101],{},[1680,29021,29022,29024],{},[1683,29023,6846],{},[1683,29025,1997],{},[1811,29027,3184],{},[1680,29029,29030,29032],{},[1683,29031,7202],{},[1683,29033,1997],{},[1691,29035,29036],{"encoding":1693},"D_i = X_i - Y_i",[1115,29038,29040],{"className":29039},[1668],[1670,29041,29042],{"xmlns":1672},[1674,29043,29044,29072],{},[1677,29045,29046,29048,29050,29052,29054,29060,29062,29070],{},[1683,29047,1387],{},[1811,29049,9297],{},[1683,29051,7000],{},[1811,29053,1994],{"stretchy":1993},[1680,29055,29056,29058],{},[1683,29057,7005],{},[1683,29059,1387],{},[1811,29061,1917],{"separator":1121},[3473,29063,29064,29066,29068],{},[1683,29065,7013],{},[1683,29067,1387],{},[1687,29069,1713],{},[1811,29071,2005],{"stretchy":1993},[1691,29073,29074],{"encoding":1693},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,29077,29079],{"className":29078},[1668],[1670,29080,29081],{"xmlns":1672},[1674,29082,29083,29087],{},[1677,29084,29085],{},[1683,29086,1809],{},[1691,29088,1809],{"encoding":1693}," dvojic se určí ",[1115,29091,29093],{"className":29092},[1668],[1670,29094,29095],{"xmlns":1672},[1674,29096,29097,29105],{},[1677,29098,29099],{},[2843,29100,29101,29103],{"accent":1121},[1683,29102,7911],{},[1811,29104,11573],{},[1691,29106,29107],{"encoding":1693},"\\bar{d}",[1115,29109,29111],{"className":29110},[1668],[1670,29112,29113],{"xmlns":1672},[1674,29114,29115,29125],{},[1677,29116,29117],{},[3473,29118,29119,29121,29123],{},[1683,29120,1974],{},[1683,29122,7911],{},[1687,29124,1713],{},[1691,29126,29127],{"encoding":1693},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,29130,29132],{"className":29131},[1668],[1670,29133,29134],{"xmlns":1672},[1674,29135,29136,29144],{},[1677,29137,29138],{},[1680,29139,29140,29142],{},[1683,29141,7005],{},[1687,29143,1689],{},[1691,29145,27676],{"encoding":1693}," (obvykle 0) a ",[1115,29148,29150],{"className":29149},[1668],[1670,29151,29152],{"xmlns":1672},[1674,29153,29154,29162],{},[1677,29155,29156],{},[1680,29157,29158,29160],{},[1683,29159,7005],{},[1683,29161,1387],{},[1691,29163,29164],{"encoding":1693},"\\mu_D",[1115,29166,29168],{"className":29167},[1668],[1670,29169,29170],{"xmlns":1672,"display":2083},[1674,29171,29172,29222],{},[1677,29173,29174,29176,29178,29202,29206,29208,29220],{},[1683,29175,7216],{},[1811,29177,2101],{},[2859,29179,29180,29196],{},[1677,29181,29182,29188,29190],{},[2843,29183,29184,29186],{"accent":1121},[1683,29185,7911],{},[1811,29187,11573],{},[1811,29189,3184],{},[1680,29191,29192,29194],{},[1683,29193,7005],{},[1687,29195,1689],{},[1680,29197,29198,29200],{},[1683,29199,1974],{},[1683,29201,7911],{},[4574,29203,29204],{},[1683,29205,1809],{},[1811,29207,9297],{},[1680,29209,29210,29212],{},[1683,29211,7258],{},[1677,29213,29214,29216,29218],{},[1683,29215,1809],{},[1811,29217,3184],{},[1687,29219,1914],{},[1683,29221,1497],{"mathvariant":2240},[1691,29223,29224],{"encoding":1693},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1158,29226,29227,29284],{},[1161,29228,29229],{},[1164,29230,29231,29250,29269],{},[1167,29232,29233],{},[1115,29234,29236],{"className":29235},[1668],[1670,29237,29238],{"xmlns":1672},[1674,29239,29240,29248],{},[1677,29241,29242],{},[1680,29243,29244,29246],{},[1683,29245,1685],{},[1687,29247,1689],{},[1691,29249,1694],{"encoding":1693},[1167,29251,29252],{},[1115,29253,29255],{"className":29254},[1668],[1670,29256,29257],{"xmlns":1672},[1674,29258,29259,29267],{},[1677,29260,29261],{},[1680,29262,29263,29265],{},[1683,29264,1685],{},[1687,29266,1914],{},[1691,29268,3116],{"encoding":1693},[1167,29270,27814,29271],{},[1115,29272,29274],{"className":29273},[1668],[1670,29275,29276],{"xmlns":1672},[1674,29277,29278,29282],{},[1677,29279,29280],{},[1683,29281,1729],{},[1691,29283,1729],{"encoding":1693},[1174,29285,29286,29383,29488],{},[1164,29287,29288,29316,29344],{},[1179,29289,29290],{},[1115,29291,29293],{"className":29292},[1668],[1670,29294,29295],{"xmlns":1672},[1674,29296,29297,29313],{},[1677,29298,29299,29305,29307],{},[1680,29300,29301,29303],{},[1683,29302,7005],{},[1683,29304,1387],{},[1811,29306,6849],{},[1680,29308,29309,29311],{},[1683,29310,7005],{},[1687,29312,1689],{},[1691,29314,29315],{"encoding":1693},"\\mu_D \\le \\mu_0",[1179,29317,29318],{},[1115,29319,29321],{"className":29320},[1668],[1670,29322,29323],{"xmlns":1672},[1674,29324,29325,29341],{},[1677,29326,29327,29333,29335],{},[1680,29328,29329,29331],{},[1683,29330,7005],{},[1683,29332,1387],{},[1811,29334,1813],{},[1680,29336,29337,29339],{},[1683,29338,7005],{},[1687,29340,1689],{},[1691,29342,29343],{"encoding":1693},"\\mu_D > \\mu_0",[1179,29345,29346],{},[1115,29347,29349],{"className":29348},[1668],[1670,29350,29351],{"xmlns":1672},[1674,29352,29353,29381],{},[1677,29354,29355,29357,29359,29371,29373,29375,29377,29379],{},[1683,29356,7258],{},[1811,29358,3471],{},[1680,29360,29361,29363],{},[1683,29362,7258],{},[1677,29364,29365,29367,29369],{},[1687,29366,1914],{},[1811,29368,3184],{},[1683,29370,3485],{},[1811,29372,1994],{"stretchy":1993},[1683,29374,1809],{},[1811,29376,3184],{},[1687,29378,1914],{},[1811,29380,2005],{"stretchy":1993},[1691,29382,27919],{"encoding":1693},[1164,29384,29385,29413,29441],{},[1179,29386,29387],{},[1115,29388,29390],{"className":29389},[1668],[1670,29391,29392],{"xmlns":1672},[1674,29393,29394,29410],{},[1677,29395,29396,29402,29404],{},[1680,29397,29398,29400],{},[1683,29399,7005],{},[1683,29401,1387],{},[1811,29403,2101],{},[1680,29405,29406,29408],{},[1683,29407,7005],{},[1687,29409,1689],{},[1691,29411,29412],{"encoding":1693},"\\mu_D = \\mu_0",[1179,29414,29415],{},[1115,29416,29418],{"className":29417},[1668],[1670,29419,29420],{"xmlns":1672},[1674,29421,29422,29438],{},[1677,29423,29424,29430,29432],{},[1680,29425,29426,29428],{},[1683,29427,7005],{},[1683,29429,1387],{},[1811,29431,11070],{"mathvariant":2240},[1680,29433,29434,29436],{},[1683,29435,7005],{},[1687,29437,1689],{},[1691,29439,29440],{"encoding":1693},"\\mu_D \\neq \\mu_0",[1179,29442,29443],{},[1115,29444,29446],{"className":29445},[1668],[1670,29447,29448],{"xmlns":1672},[1674,29449,29450,29486],{},[1677,29451,29452,29454,29456,29458,29460,29476,29478,29480,29482,29484],{},[1811,29453,23136],{"stretchy":1993},[1683,29455,7258],{},[1811,29457,23136],{"stretchy":1993},[1811,29459,3471],{},[1680,29461,29462,29464],{},[1683,29463,7258],{},[1677,29465,29466,29468,29470,29472,29474],{},[1687,29467,1914],{},[1811,29469,3184],{},[1683,29471,3485],{},[1683,29473,4725],{"mathvariant":2240},[1687,29475,1713],{},[1811,29477,1994],{"stretchy":1993},[1683,29479,1809],{},[1811,29481,3184],{},[1687,29483,1914],{},[1811,29485,2005],{"stretchy":1993},[1691,29487,28017],{"encoding":1693},[1164,29489,29490,29518,29546],{},[1179,29491,29492],{},[1115,29493,29495],{"className":29494},[1668],[1670,29496,29497],{"xmlns":1672},[1674,29498,29499,29515],{},[1677,29500,29501,29507,29509],{},[1680,29502,29503,29505],{},[1683,29504,7005],{},[1683,29506,1387],{},[1811,29508,3471],{},[1680,29510,29511,29513],{},[1683,29512,7005],{},[1687,29514,1689],{},[1691,29516,29517],{"encoding":1693},"\\mu_D \\ge \\mu_0",[1179,29519,29520],{},[1115,29521,29523],{"className":29522},[1668],[1670,29524,29525],{"xmlns":1672},[1674,29526,29527,29543],{},[1677,29528,29529,29535,29537],{},[1680,29530,29531,29533],{},[1683,29532,7005],{},[1683,29534,1387],{},[1811,29536,4453],{},[1680,29538,29539,29541],{},[1683,29540,7005],{},[1687,29542,1689],{},[1691,29544,29545],{"encoding":1693},"\\mu_D \u003C \\mu_0",[1179,29547,29548],{},[1115,29549,29551],{"className":29550},[1668],[1670,29552,29553],{"xmlns":1672},[1674,29554,29555,29585],{},[1677,29556,29557,29559,29561,29563,29575,29577,29579,29581,29583],{},[1683,29558,7258],{},[1811,29560,6849],{},[1811,29562,3184],{},[1680,29564,29565,29567],{},[1683,29566,7258],{},[1677,29568,29569,29571,29573],{},[1687,29570,1914],{},[1811,29572,3184],{},[1683,29574,3485],{},[1811,29576,1994],{"stretchy":1993},[1683,29578,1809],{},[1811,29580,3184],{},[1687,29582,1914],{},[1811,29584,2005],{"stretchy":1993},[1691,29586,28109],{"encoding":1693},[1103,29588,29590,29597,29739,29803,29889],{"className":29589,"dataCallout":3597},[1106,3596],[1110,29591,29593,29596],{"className":29592},[1113],[1115,29594],{"className":29595,"ariaHidden":1121},[1118,3604,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,29598,29599,29600,29618,29619,29637,29638,29656,29657,29690,29691,29714,29715,29738],{},"U ",[1115,29601,29603],{"className":29602},[1668],[1670,29604,29605],{"xmlns":1672},[1674,29606,29607,29615],{},[1677,29608,29609,29611,29613],{},[1683,29610,1809],{},[1811,29612,2101],{},[1687,29614,9147],{},[1691,29616,29617],{"encoding":1693},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,29620,29622],{"className":29621},[1668],[1670,29623,29624],{"xmlns":1672},[1674,29625,29626,29634],{},[1677,29627,29628],{},[1680,29629,29630,29632],{},[1683,29631,6846],{},[1683,29633,1997],{},[1691,29635,29636],{"encoding":1693},"X_i",") a po něm (",[1115,29639,29641],{"className":29640},[1668],[1670,29642,29643],{"xmlns":1672},[1674,29644,29645,29653],{},[1677,29646,29647],{},[1680,29648,29649,29651],{},[1683,29650,7202],{},[1683,29652,1997],{},[1691,29654,29655],{"encoding":1693},"Y_i","), diference ",[1115,29658,29660],{"className":29659},[1668],[1670,29661,29662],{"xmlns":1672},[1674,29663,29664,29688],{},[1677,29665,29666,29672,29674,29680,29682],{},[1680,29667,29668,29670],{},[1683,29669,1387],{},[1683,29671,1997],{},[1811,29673,2101],{},[1680,29675,29676,29678],{},[1683,29677,6846],{},[1683,29679,1997],{},[1811,29681,3184],{},[1680,29683,29684,29686],{},[1683,29685,7202],{},[1683,29687,1997],{},[1691,29689,29036],{"encoding":1693}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,29692,29694],{"className":29693},[1668],[1670,29695,29696],{"xmlns":1672},[1674,29697,29698,29711],{},[1677,29699,29700,29706,29708],{},[2843,29701,29702,29704],{"accent":1121},[1683,29703,7911],{},[1811,29705,11573],{},[1811,29707,2101],{},[1687,29709,29710],{},"0,4",[1691,29712,29713],{"encoding":1693},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,29716,29718],{"className":29717},[1668],[1670,29719,29720],{"xmlns":1672},[1674,29721,29722,29735],{},[1677,29723,29724,29730,29732],{},[1680,29725,29726,29728],{},[1683,29727,1974],{},[1683,29729,7911],{},[1811,29731,2101],{},[1687,29733,29734],{},"0,35",[1691,29736,29737],{"encoding":1693},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,29740,29741,29771,29772,29802],{},[1115,29742,29744],{"className":29743},[1668],[1670,29745,29746],{"xmlns":1672},[1674,29747,29748,29768],{},[1677,29749,29750,29756,29758,29764,29766],{},[1680,29751,29752,29754],{},[1683,29753,1685],{},[1687,29755,1689],{},[1811,29757,2077],{},[1680,29759,29760,29762],{},[1683,29761,7005],{},[1683,29763,1387],{},[1811,29765,6849],{},[1687,29767,1689],{},[1691,29769,29770],{"encoding":1693},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,29773,29775],{"className":29774},[1668],[1670,29776,29777],{"xmlns":1672},[1674,29778,29779,29799],{},[1677,29780,29781,29787,29789,29795,29797],{},[1680,29782,29783,29785],{},[1683,29784,1685],{},[1687,29786,1914],{},[1811,29788,2077],{},[1680,29790,29791,29793],{},[1683,29792,7005],{},[1683,29794,1387],{},[1811,29796,1813],{},[1687,29798,1689],{},[1691,29800,29801],{"encoding":1693},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,29804,29805],{},[1115,29806,29808],{"className":29807},[1668],[1670,29809,29810],{"xmlns":1672},[1674,29811,29812,29886],{},[1677,29813,29814,29816,29818,29830,29834,29836,29839,29841,29843,29845,29847,29849,29851,29853,29865,29867,29869,29871,29873,29875,29877,29879,29881,29884],{},[1683,29815,7258],{},[1811,29817,2101],{},[2859,29819,29820,29828],{},[1677,29821,29822,29824,29826],{},[1687,29823,29710],{},[1811,29825,3184],{},[1687,29827,1689],{},[1687,29829,29734],{},[4574,29831,29832],{},[1687,29833,9147],{},[1811,29835,2101],{},[1687,29837,29838],{},"3,614",[1811,29840,1917],{"separator":1121},[2131,29842],{"width":2133},[1683,29844,1729],{},[1811,29846,2101],{},[1811,29848,3454],{"stretchy":1993},[1683,29850,7258],{},[1811,29852,3471],{},[1680,29854,29855,29857],{},[1683,29856,7258],{},[1677,29858,29859,29861,29863],{},[1687,29860,1689],{},[1811,29862,1917],{"separator":1121},[1687,29864,21910],{},[1811,29866,1994],{"stretchy":1993},[1687,29868,3715],{},[1811,29870,2005],{"stretchy":1993},[1811,29872,3514],{"stretchy":1993},[1811,29874,2101],{},[1811,29876,3454],{"stretchy":1993},[1683,29878,7258],{},[1811,29880,3471],{},[1687,29882,29883],{},"1,833",[1811,29885,3514],{"stretchy":1993},[1691,29887,29888],{"encoding":1693},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,29890,28500,29891,6128,29908,29925],{},[1115,29892,29894],{"className":29893},[1668],[1670,29895,29896],{"xmlns":1672},[1674,29897,29898,29906],{},[1677,29899,29900,29902,29904],{},[1683,29901,7258],{},[1811,29903,7133],{},[1683,29905,1729],{},[1691,29907,28518],{"encoding":1693},[1115,29909,29911],{"className":29910},[1668],[1670,29912,29913],{"xmlns":1672},[1674,29914,29915,29923],{},[1677,29916,29917],{},[1680,29918,29919,29921],{},[1683,29920,1685],{},[1687,29922,1689],{},[1691,29924,1694],{"encoding":1693},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3814,29927,29929],{"className":3816,"code":29928,"language":71,"meta":1603,"style":1603},"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",[3590,29930,29931,29960,29991,30017,30021],{"__ignoreMap":1603},[1115,29932,29933,29936,29938,29941,29943,29946,29948,29951,29953,29955,29957],{"class":3822,"line":10},[1115,29934,29935],{"class":3825},"dbar",[1115,29937,3830],{"class":3829},[1115,29939,29940],{"class":3845}," 0.4",[1115,29942,25296],{"class":3837},[1115,29944,29945],{"class":3825},"sd_d",[1115,29947,3830],{"class":3829},[1115,29949,29950],{"class":3845}," 0.35",[1115,29952,25296],{"class":3837},[1115,29954,1809],{"class":3825},[1115,29956,3830],{"class":3829},[1115,29958,29959],{"class":3845}," 10\n",[1115,29961,29962,29964,29966,29968,29970,29972,29974,29976,29978,29981,29983,29985,29987,29989],{"class":3822,"line":27},[1115,29963,7258],{"class":3825},[1115,29965,3830],{"class":3829},[1115,29967,4728],{"class":3837},[1115,29969,29935],{"class":3825},[1115,29971,25633],{"class":3829},[1115,29973,10084],{"class":3845},[1115,29975,4722],{"class":3837},[1115,29977,4725],{"class":3829},[1115,29979,29980],{"class":3825}," sd_d",[1115,29982,18753],{"class":3829},[1115,29984,4699],{"class":3833},[1115,29986,1994],{"class":3837},[1115,29988,1809],{"class":3825},[1115,29990,4022],{"class":3837},[1115,29992,29993,29995,29997,29999,30001,30003,30005,30007,30009,30011,30013,30015],{"class":3822,"line":148},[1115,29994,28625],{"class":3825},[1115,29996,3830],{"class":3829},[1115,29998,28630],{"class":3833},[1115,30000,1994],{"class":3837},[1115,30002,10940],{"class":3845},[1115,30004,1917],{"class":3829},[1115,30006,10923],{"class":3825},[1115,30008,3918],{"class":3829},[1115,30010,28644],{"class":3825},[1115,30012,25633],{"class":3829},[1115,30014,4762],{"class":3845},[1115,30016,4022],{"class":3837},[1115,30018,30019],{"class":3822,"line":111},[1115,30020,28655],{"class":3825},[1115,30022,30023],{"class":3822,"line":96},[1115,30024,28660],{"class":3825},[3814,30026,30029],{"className":30027,"code":30028,"language":4044,"meta":1603},[4042],"[1] 3.614032\n[1] 1.833113\n",[3590,30030,30028],{"__ignoreMap":1603},[1103,30032,30034,30041,30044,30189,30195],{"className":30033,"dataCallout":6534},[1106,6533],[1110,30035,30037,30040],{"className":30036},[1113],[1115,30038],{"className":30039,"ariaHidden":1121},[1118,6541,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,30042,30043],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3814,30045,30047],{"className":3816,"code":30046,"language":71,"meta":1603,"style":1603},"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",[3590,30048,30049,30100,30151,30175],{"__ignoreMap":1603},[1115,30050,30051,30054,30056,30058,30060,30063,30065,30068,30070,30073,30075,30078,30080,30083,30085,30088,30090,30093,30095,30098],{"class":3822,"line":10},[1115,30052,30053],{"class":3825},"estA",[1115,30055,3830],{"class":3829},[1115,30057,3956],{"class":3833},[1115,30059,1994],{"class":3837},[1115,30061,30062],{"class":3845},"3282",[1115,30064,1917],{"class":3829},[1115,30066,30067],{"class":3845}," 2506",[1115,30069,1917],{"class":3829},[1115,30071,30072],{"class":3845}," 2812",[1115,30074,1917],{"class":3829},[1115,30076,30077],{"class":3845}," 5453",[1115,30079,1917],{"class":3829},[1115,30081,30082],{"class":3845}," 3263",[1115,30084,1917],{"class":3829},[1115,30086,30087],{"class":3845}," 4571",[1115,30089,1917],{"class":3829},[1115,30091,30092],{"class":3845}," 3121",[1115,30094,1917],{"class":3829},[1115,30096,30097],{"class":3845}," 2963",[1115,30099,4022],{"class":3837},[1115,30101,30102,30105,30107,30109,30111,30114,30116,30119,30121,30124,30126,30129,30131,30134,30136,30139,30141,30144,30146,30149],{"class":3822,"line":27},[1115,30103,30104],{"class":3825},"estB",[1115,30106,3830],{"class":3829},[1115,30108,3956],{"class":3833},[1115,30110,1994],{"class":3837},[1115,30112,30113],{"class":3845},"3271",[1115,30115,1917],{"class":3829},[1115,30117,30118],{"class":3845}," 2531",[1115,30120,1917],{"class":3829},[1115,30122,30123],{"class":3845}," 2799",[1115,30125,1917],{"class":3829},[1115,30127,30128],{"class":3845}," 5471",[1115,30130,1917],{"class":3829},[1115,30132,30133],{"class":3845}," 3285",[1115,30135,1917],{"class":3829},[1115,30137,30138],{"class":3845}," 4557",[1115,30140,1917],{"class":3829},[1115,30142,30143],{"class":3845}," 3139",[1115,30145,1917],{"class":3829},[1115,30147,30148],{"class":3845}," 2976",[1115,30150,4022],{"class":3837},[1115,30152,30153,30155,30157,30159,30161,30164,30166,30169,30171,30173],{"class":3822,"line":148},[1115,30154,28180],{"class":3833},[1115,30156,1994],{"class":3837},[1115,30158,30053],{"class":3825},[1115,30160,1917],{"class":3829},[1115,30162,30163],{"class":3825}," estB",[1115,30165,1917],{"class":3829},[1115,30167,30168],{"class":3825}," paired",[1115,30170,3918],{"class":3829},[1115,30172,3931],{"class":3845},[1115,30174,4022],{"class":3837},[1115,30176,30177,30179,30181,30183,30185,30187],{"class":3822,"line":111},[1115,30178,17689],{"class":3833},[1115,30180,1994],{"class":3837},[1115,30182,30053],{"class":3825},[1115,30184,25633],{"class":3829},[1115,30186,30163],{"class":3825},[1115,30188,4022],{"class":3837},[3814,30190,30193],{"className":30191,"code":30192,"language":4044,"meta":1603},[4042],"    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",[3590,30194,30192],{"__ignoreMap":1603},[1110,30196,30197,30198,4728,30215,30234,30235,30258],{},"Párový t-test sám nezamítá ",[1115,30199,30201],{"className":30200},[1668],[1670,30202,30203],{"xmlns":1672},[1674,30204,30205,30213],{},[1677,30206,30207],{},[1680,30208,30209,30211],{},[1683,30210,1685],{},[1687,30212,1689],{},[1691,30214,1694],{"encoding":1693},[1115,30216,30218],{"className":30217},[1668],[1670,30219,30220],{"xmlns":1672},[1674,30221,30222,30231],{},[1677,30223,30224,30226,30228],{},[1683,30225,1110],{},[1811,30227,2101],{},[1687,30229,30230],{},"0,2635",[1691,30232,30233],{"encoding":1693},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,30236,30238],{"className":30237},[1668],[1670,30239,30240],{"xmlns":1672},[1674,30241,30242,30255],{},[1677,30243,30244,30246,30248,30251,30253],{},[1683,30245,1110],{},[1811,30247,2101],{},[1687,30249,30250],{},"0,03203",[1811,30252,4453],{},[1687,30254,4105],{},[1691,30256,30257],{"encoding":1693},"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).",[1153,30260,30262],{"id":30261},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,30264,30265,30266,30292,30293,30331,30332,5862,30350,30331,30388,30406,30407,5862,30439,30471,30472,30498,30499,1497],{},"Uvažují se dva nezávislé základní soubory ",[1115,30267,30269],{"className":30268},[1668],[1670,30270,30271],{"xmlns":1672},[1674,30272,30273,30289],{},[1677,30274,30275,30281,30283],{},[1680,30276,30277,30279],{},[1683,30278,9039],{},[1687,30280,1914],{},[1811,30282,1917],{"separator":1121},[1680,30284,30285,30287],{},[1683,30286,9039],{},[1687,30288,1713],{},[1691,30290,30291],{"encoding":1693},"Z_1, Z_2"," se znakem ",[1115,30294,30296],{"className":30295},[1668],[1670,30297,30298],{"xmlns":1672},[1674,30299,30300,30328],{},[1677,30301,30302,30304,30306,30308,30310,30316,30318,30326],{},[1683,30303,6846],{},[1811,30305,9297],{},[1683,30307,7000],{},[1811,30309,1994],{"stretchy":1993},[1680,30311,30312,30314],{},[1683,30313,7005],{},[1687,30315,1914],{},[1811,30317,1917],{"separator":1121},[3473,30319,30320,30322,30324],{},[1683,30321,7013],{},[1687,30323,1914],{},[1687,30325,1713],{},[1811,30327,2005],{"stretchy":1993},[1691,30329,30330],{"encoding":1693},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,30333,30335],{"className":30334},[1668],[1670,30336,30337],{"xmlns":1672},[1674,30338,30339,30347],{},[1677,30340,30341],{},[1680,30342,30343,30345],{},[1683,30344,9039],{},[1687,30346,1914],{},[1691,30348,30349],{"encoding":1693},"Z_1",[1115,30351,30353],{"className":30352},[1668],[1670,30354,30355],{"xmlns":1672},[1674,30356,30357,30385],{},[1677,30358,30359,30361,30363,30365,30367,30373,30375,30383],{},[1683,30360,6846],{},[1811,30362,9297],{},[1683,30364,7000],{},[1811,30366,1994],{"stretchy":1993},[1680,30368,30369,30371],{},[1683,30370,7005],{},[1687,30372,1713],{},[1811,30374,1917],{"separator":1121},[3473,30376,30377,30379,30381],{},[1683,30378,7013],{},[1687,30380,1713],{},[1687,30382,1713],{},[1811,30384,2005],{"stretchy":1993},[1691,30386,30387],{"encoding":1693},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,30389,30391],{"className":30390},[1668],[1670,30392,30393],{"xmlns":1672},[1674,30394,30395,30403],{},[1677,30396,30397],{},[1680,30398,30399,30401],{},[1683,30400,9039],{},[1687,30402,1713],{},[1691,30404,30405],{"encoding":1693},"Z_2",". Z výběrů se určí ",[1115,30408,30410],{"className":30409},[1668],[1670,30411,30412],{"xmlns":1672},[1674,30413,30414,30436],{},[1677,30415,30416,30426,30428],{},[1680,30417,30418,30424],{},[2843,30419,30420,30422],{"accent":1121},[1683,30421,6834],{},[1811,30423,11573],{},[1687,30425,1914],{},[1811,30427,1917],{"separator":1121},[3473,30429,30430,30432,30434],{},[1683,30431,1974],{},[1687,30433,1914],{},[1687,30435,1713],{},[1691,30437,30438],{"encoding":1693},"\\bar{x}_1, s_1^2",[1115,30440,30442],{"className":30441},[1668],[1670,30443,30444],{"xmlns":1672},[1674,30445,30446,30468],{},[1677,30447,30448,30458,30460],{},[1680,30449,30450,30456],{},[2843,30451,30452,30454],{"accent":1121},[1683,30453,6834],{},[1811,30455,11573],{},[1687,30457,1713],{},[1811,30459,1917],{"separator":1121},[3473,30461,30462,30464,30466],{},[1683,30463,1974],{},[1687,30465,1713],{},[1687,30467,1713],{},[1691,30469,30470],{"encoding":1693},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,30473,30475],{"className":30474},[1668],[1670,30476,30477],{"xmlns":1672},[1674,30478,30479,30495],{},[1677,30480,30481,30487,30489],{},[1680,30482,30483,30485],{},[1683,30484,7005],{},[1687,30486,1914],{},[1811,30488,1917],{"separator":1121},[1680,30490,30491,30493],{},[1683,30492,7005],{},[1687,30494,1713],{},[1691,30496,30497],{"encoding":1693},"\\mu_1, \\mu_2",", resp. mezi ",[1115,30500,30502],{"className":30501},[1668],[1670,30503,30504],{"xmlns":1672},[1674,30505,30506,30526],{},[1677,30507,30508,30516,30518],{},[3473,30509,30510,30512,30514],{},[1683,30511,7013],{},[1687,30513,1914],{},[1687,30515,1713],{},[1811,30517,1917],{"separator":1121},[3473,30519,30520,30522,30524],{},[1683,30521,7013],{},[1687,30523,1713],{},[1687,30525,1713],{},[1691,30527,30528],{"encoding":1693},"\\sigma_1^2, \\sigma_2^2",[16860,30530,30532],{"id":30531},"f-test-o-rozptylech","F-test o rozptylech",[1110,30534,30535],{},"Statistika",[1115,30537,30539],{"className":30538},[1668],[1670,30540,30541],{"xmlns":1672,"display":2083},[1674,30542,30543,30599],{},[1677,30544,30545,30547,30549,30567,30569],{},[1683,30546,1403],{},[1811,30548,2101],{},[2859,30550,30551,30559],{},[3473,30552,30553,30555,30557],{},[1683,30554,1974],{},[1687,30556,1914],{},[1687,30558,1713],{},[3473,30560,30561,30563,30565],{},[1683,30562,1974],{},[1687,30564,1713],{},[1687,30566,1713],{},[1811,30568,9297],{},[1680,30570,30571,30573],{},[1683,30572,1403],{},[1677,30574,30575,30581,30583,30585,30587,30589,30595,30597],{},[1680,30576,30577,30579],{},[1683,30578,1809],{},[1687,30580,1914],{},[1811,30582,3184],{},[1687,30584,1914],{},[1811,30586,1917],{"separator":1121},[3028,30588,3030],{},[1680,30590,30591,30593],{},[1683,30592,1809],{},[1687,30594,1713],{},[1811,30596,3184],{},[1687,30598,1914],{},[1691,30600,30601],{"encoding":1693},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,30603,30604,30605,5862,30627,27767],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,30606,30608],{"className":30607},[1668],[1670,30609,30610],{"xmlns":1672},[1674,30611,30612,30624],{},[1677,30613,30614,30620,30622],{},[1680,30615,30616,30618],{},[1683,30617,1809],{},[1687,30619,1914],{},[1811,30621,3184],{},[1687,30623,1914],{},[1691,30625,30626],{"encoding":1693},"n_1-1",[1115,30628,30630],{"className":30629},[1668],[1670,30631,30632],{"xmlns":1672},[1674,30633,30634,30646],{},[1677,30635,30636,30642,30644],{},[1680,30637,30638,30640],{},[1683,30639,1809],{},[1687,30641,1713],{},[1811,30643,3184],{},[1687,30645,1914],{},[1691,30647,30648],{"encoding":1693},"n_2-1",[1158,30650,30651,30708],{},[1161,30652,30653],{},[1164,30654,30655,30674,30693],{},[1167,30656,30657],{},[1115,30658,30660],{"className":30659},[1668],[1670,30661,30662],{"xmlns":1672},[1674,30663,30664,30672],{},[1677,30665,30666],{},[1680,30667,30668,30670],{},[1683,30669,1685],{},[1687,30671,1689],{},[1691,30673,1694],{"encoding":1693},[1167,30675,30676],{},[1115,30677,30679],{"className":30678},[1668],[1670,30680,30681],{"xmlns":1672},[1674,30682,30683,30691],{},[1677,30684,30685],{},[1680,30686,30687,30689],{},[1683,30688,1685],{},[1687,30690,1914],{},[1691,30692,3116],{"encoding":1693},[1167,30694,27814,30695],{},[1115,30696,30698],{"className":30697},[1668],[1670,30699,30700],{"xmlns":1672},[1674,30701,30702,30706],{},[1677,30703,30704],{},[1683,30705,1729],{},[1691,30707,1729],{"encoding":1693},[1174,30709,30710,30824,30997],{},[1164,30711,30712,30740,30768],{},[1179,30713,30714],{},[1115,30715,30717],{"className":30716},[1668],[1670,30718,30719],{"xmlns":1672},[1674,30720,30721,30737],{},[1677,30722,30723,30729,30731],{},[1680,30724,30725,30727],{},[1683,30726,7013],{},[1687,30728,1914],{},[1811,30730,6849],{},[1680,30732,30733,30735],{},[1683,30734,7013],{},[1687,30736,1713],{},[1691,30738,30739],{"encoding":1693},"\\sigma_1 \\le \\sigma_2",[1179,30741,30742],{},[1115,30743,30745],{"className":30744},[1668],[1670,30746,30747],{"xmlns":1672},[1674,30748,30749,30765],{},[1677,30750,30751,30757,30759],{},[1680,30752,30753,30755],{},[1683,30754,7013],{},[1687,30756,1914],{},[1811,30758,1813],{},[1680,30760,30761,30763],{},[1683,30762,7013],{},[1687,30764,1713],{},[1691,30766,30767],{"encoding":1693},"\\sigma_1 > \\sigma_2",[1179,30769,30770],{},[1115,30771,30773],{"className":30772},[1668],[1670,30774,30775],{"xmlns":1672},[1674,30776,30777,30821],{},[1677,30778,30779,30781,30783,30795,30797,30803,30805,30807,30809,30815,30817,30819],{},[1683,30780,1403],{},[1811,30782,3471],{},[1680,30784,30785,30787],{},[1683,30786,1403],{},[1677,30788,30789,30791,30793],{},[1687,30790,1914],{},[1811,30792,3184],{},[1683,30794,3485],{},[1811,30796,1994],{"stretchy":1993},[1680,30798,30799,30801],{},[1683,30800,1809],{},[1687,30802,1914],{},[1811,30804,3184],{},[1687,30806,1914],{},[1811,30808,1917],{"separator":1121},[1680,30810,30811,30813],{},[1683,30812,1809],{},[1687,30814,1713],{},[1811,30816,3184],{},[1687,30818,1914],{},[1811,30820,2005],{"stretchy":1993},[1691,30822,30823],{"encoding":1693},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1164,30825,30826,30854,30882],{},[1179,30827,30828],{},[1115,30829,30831],{"className":30830},[1668],[1670,30832,30833],{"xmlns":1672},[1674,30834,30835,30851],{},[1677,30836,30837,30843,30845],{},[1680,30838,30839,30841],{},[1683,30840,7013],{},[1687,30842,1914],{},[1811,30844,2101],{},[1680,30846,30847,30849],{},[1683,30848,7013],{},[1687,30850,1713],{},[1691,30852,30853],{"encoding":1693},"\\sigma_1 = \\sigma_2",[1179,30855,30856],{},[1115,30857,30859],{"className":30858},[1668],[1670,30860,30861],{"xmlns":1672},[1674,30862,30863,30879],{},[1677,30864,30865,30871,30873],{},[1680,30866,30867,30869],{},[1683,30868,7013],{},[1687,30870,1914],{},[1811,30872,11070],{"mathvariant":2240},[1680,30874,30875,30877],{},[1683,30876,7013],{},[1687,30878,1713],{},[1691,30880,30881],{"encoding":1693},"\\sigma_1 \\neq \\sigma_2",[1179,30883,30884,30938,30939],{},[1115,30885,30887],{"className":30886},[1668],[1670,30888,30889],{"xmlns":1672},[1674,30890,30891,30935],{},[1677,30892,30893,30895,30897,30909,30911,30917,30919,30921,30923,30929,30931,30933],{},[1683,30894,1403],{},[1811,30896,6849],{},[1680,30898,30899,30901],{},[1683,30900,1403],{},[1677,30902,30903,30905,30907],{},[1683,30904,3485],{},[1683,30906,4725],{"mathvariant":2240},[1687,30908,1713],{},[1811,30910,1994],{"stretchy":1993},[1680,30912,30913,30915],{},[1683,30914,1809],{},[1687,30916,1914],{},[1811,30918,3184],{},[1687,30920,1914],{},[1811,30922,1917],{"separator":1121},[1680,30924,30925,30927],{},[1683,30926,1809],{},[1687,30928,1713],{},[1811,30930,3184],{},[1687,30932,1914],{},[1811,30934,2005],{"stretchy":1993},[1691,30936,30937],{"encoding":1693},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,30940,30942],{"className":30941},[1668],[1670,30943,30944],{"xmlns":1672},[1674,30945,30946,30994],{},[1677,30947,30948,30950,30952,30968,30970,30976,30978,30980,30982,30988,30990,30992],{},[1683,30949,1403],{},[1811,30951,3471],{},[1680,30953,30954,30956],{},[1683,30955,1403],{},[1677,30957,30958,30960,30962,30964,30966],{},[1687,30959,1914],{},[1811,30961,3184],{},[1683,30963,3485],{},[1683,30965,4725],{"mathvariant":2240},[1687,30967,1713],{},[1811,30969,1994],{"stretchy":1993},[1680,30971,30972,30974],{},[1683,30973,1809],{},[1687,30975,1914],{},[1811,30977,3184],{},[1687,30979,1914],{},[1811,30981,1917],{"separator":1121},[1680,30983,30984,30986],{},[1683,30985,1809],{},[1687,30987,1713],{},[1811,30989,3184],{},[1687,30991,1914],{},[1811,30993,2005],{"stretchy":1993},[1691,30995,30996],{"encoding":1693},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1164,30998,30999,31027,31055],{},[1179,31000,31001],{},[1115,31002,31004],{"className":31003},[1668],[1670,31005,31006],{"xmlns":1672},[1674,31007,31008,31024],{},[1677,31009,31010,31016,31018],{},[1680,31011,31012,31014],{},[1683,31013,7013],{},[1687,31015,1914],{},[1811,31017,3471],{},[1680,31019,31020,31022],{},[1683,31021,7013],{},[1687,31023,1713],{},[1691,31025,31026],{"encoding":1693},"\\sigma_1 \\ge \\sigma_2",[1179,31028,31029],{},[1115,31030,31032],{"className":31031},[1668],[1670,31033,31034],{"xmlns":1672},[1674,31035,31036,31052],{},[1677,31037,31038,31044,31046],{},[1680,31039,31040,31042],{},[1683,31041,7013],{},[1687,31043,1914],{},[1811,31045,4453],{},[1680,31047,31048,31050],{},[1683,31049,7013],{},[1687,31051,1713],{},[1691,31053,31054],{"encoding":1693},"\\sigma_1 \u003C \\sigma_2",[1179,31056,31057],{},[1115,31058,31060],{"className":31059},[1668],[1670,31061,31062],{"xmlns":1672},[1674,31063,31064,31102],{},[1677,31065,31066,31068,31070,31076,31078,31084,31086,31088,31090,31096,31098,31100],{},[1683,31067,1403],{},[1811,31069,6849],{},[1680,31071,31072,31074],{},[1683,31073,1403],{},[1683,31075,3485],{},[1811,31077,1994],{"stretchy":1993},[1680,31079,31080,31082],{},[1683,31081,1809],{},[1687,31083,1914],{},[1811,31085,3184],{},[1687,31087,1914],{},[1811,31089,1917],{"separator":1121},[1680,31091,31092,31094],{},[1683,31093,1809],{},[1687,31095,1713],{},[1811,31097,3184],{},[1687,31099,1914],{},[1811,31101,2005],{"stretchy":1993},[1691,31103,31104],{"encoding":1693},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[16860,31106,31108],{"id":31107},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,31110,31111],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,31113,31115],{"className":31114},[1668],[1670,31116,31117],{"xmlns":1672,"display":2083},[1674,31118,31119,31296],{},[1677,31120,31121,31127,31129,31205,31253,31255,31257,31266,31268,31274,31276,31282,31284,31290,31292,31294],{},[1680,31122,31123,31125],{},[1683,31124,7216],{},[1687,31126,1914],{},[1811,31128,2101],{},[2859,31130,31131,31155],{},[1677,31132,31133,31143,31145],{},[1680,31134,31135,31141],{},[2843,31136,31137,31139],{"accent":1121},[1683,31138,6834],{},[1811,31140,11573],{},[1687,31142,1914],{},[1811,31144,3184],{},[1680,31146,31147,31153],{},[2843,31148,31149,31151],{"accent":1121},[1683,31150,6834],{},[1811,31152,11573],{},[1687,31154,1713],{},[4574,31156,31157],{},[1677,31158,31159,31161,31167,31169,31171,31173,31181,31183,31185,31191,31193,31195,31197],{},[1811,31160,1994],{"stretchy":1993},[1680,31162,31163,31165],{},[1683,31164,1809],{},[1687,31166,1914],{},[1811,31168,3184],{},[1687,31170,1914],{},[1811,31172,2005],{"stretchy":1993},[3473,31174,31175,31177,31179],{},[1683,31176,1974],{},[1687,31178,1914],{},[1687,31180,1713],{},[1811,31182,5598],{},[1811,31184,1994],{"stretchy":1993},[1680,31186,31187,31189],{},[1683,31188,1809],{},[1687,31190,1713],{},[1811,31192,3184],{},[1687,31194,1914],{},[1811,31196,2005],{"stretchy":1993},[3473,31198,31199,31201,31203],{},[1683,31200,1974],{},[1687,31202,1713],{},[1687,31204,1713],{},[4574,31206,31207],{},[2859,31208,31209,31229],{},[1677,31210,31211,31217,31219,31225,31227],{},[1680,31212,31213,31215],{},[1683,31214,1809],{},[1687,31216,1914],{},[1811,31218,5598],{},[1680,31220,31221,31223],{},[1683,31222,1809],{},[1687,31224,1713],{},[1811,31226,3184],{},[1687,31228,1713],{},[1677,31230,31231,31241,31243],{},[2859,31232,31233,31235],{},[1687,31234,1914],{},[1680,31236,31237,31239],{},[1683,31238,1809],{},[1687,31240,1914],{},[1811,31242,5598],{},[2859,31244,31245,31247],{},[1687,31246,1914],{},[1680,31248,31249,31251],{},[1683,31250,1809],{},[1687,31252,1713],{},[1811,31254,1917],{"separator":1121},[2131,31256],{"width":2133},[3473,31258,31259,31261,31263],{},[1683,31260,7258],{},[1683,31262,1110],{},[1811,31264,31265],{},"∗",[1811,31267,2101],{},[1680,31269,31270,31272],{},[1683,31271,7258],{},[1683,31273,1110],{},[1811,31275,1994],{"stretchy":1993},[1680,31277,31278,31280],{},[1683,31279,1809],{},[1687,31281,1914],{},[1811,31283,5598],{},[1680,31285,31286,31288],{},[1683,31287,1809],{},[1687,31289,1713],{},[1811,31291,3184],{},[1687,31293,1713],{},[1811,31295,2005],{"stretchy":1993},[1691,31297,31298],{"encoding":1693},"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)",[1110,31300,31301,31302,31331],{},"se použije, pokud jsou rozptyly ",[1115,31303,31305],{"className":31304},[1668],[1670,31306,31307],{"xmlns":1672},[1674,31308,31309,31329],{},[1677,31310,31311,31319,31321],{},[3473,31312,31313,31315,31317],{},[1683,31314,7013],{},[1687,31316,1914],{},[1687,31318,1713],{},[1811,31320,1917],{"separator":1121},[3473,31322,31323,31325,31327],{},[1683,31324,7013],{},[1687,31326,1713],{},[1687,31328,1713],{},[1691,31330,30528],{"encoding":1693}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,31333,31335],{"className":31334},[1668],[1670,31336,31337],{"xmlns":1672,"display":2083},[1674,31338,31339,31551],{},[1677,31340,31341,31347,31349,31413,31415,31417,31425,31427,31549],{},[1680,31342,31343,31345],{},[1683,31344,7216],{},[1687,31346,1713],{},[1811,31348,2101],{},[2859,31350,31351,31375],{},[1677,31352,31353,31363,31365],{},[1680,31354,31355,31361],{},[2843,31356,31357,31359],{"accent":1121},[1683,31358,6834],{},[1811,31360,11573],{},[1687,31362,1914],{},[1811,31364,3184],{},[1680,31366,31367,31373],{},[2843,31368,31369,31371],{"accent":1121},[1683,31370,6834],{},[1811,31372,11573],{},[1687,31374,1713],{},[4574,31376,31377],{},[1677,31378,31379,31387,31389,31395,31397,31405,31407],{},[3473,31380,31381,31383,31385],{},[1683,31382,1974],{},[1687,31384,1914],{},[1687,31386,1713],{},[1683,31388,4725],{"mathvariant":2240},[1680,31390,31391,31393],{},[1683,31392,1809],{},[1687,31394,1914],{},[1811,31396,5598],{},[3473,31398,31399,31401,31403],{},[1683,31400,1974],{},[1687,31402,1713],{},[1687,31404,1713],{},[1683,31406,4725],{"mathvariant":2240},[1680,31408,31409,31411],{},[1683,31410,1809],{},[1687,31412,1713],{},[1811,31414,1917],{"separator":1121},[2131,31416],{"width":2133},[3473,31418,31419,31421,31423],{},[1683,31420,7258],{},[1683,31422,1110],{},[1811,31424,31265],{},[1811,31426,2101],{},[2859,31428,31429,31509],{},[1677,31430,31431,31449,31455,31457,31463,31465,31467,31469,31471,31489,31495,31497,31503,31505,31507],{},[3361,31432,31433],{"scriptlevel":1689,"displaystyle":1121},[2859,31434,31435,31443],{},[3473,31436,31437,31439,31441],{},[1683,31438,1974],{},[1687,31440,1914],{},[1687,31442,1713],{},[1680,31444,31445,31447],{},[1683,31446,1809],{},[1687,31448,1914],{},[1680,31450,31451,31453],{},[1683,31452,7258],{},[1683,31454,1110],{},[1811,31456,1994],{"stretchy":1993},[1680,31458,31459,31461],{},[1683,31460,1809],{},[1687,31462,1914],{},[1811,31464,3184],{},[1687,31466,1914],{},[1811,31468,2005],{"stretchy":1993},[1811,31470,5598],{},[3361,31472,31473],{"scriptlevel":1689,"displaystyle":1121},[2859,31474,31475,31483],{},[3473,31476,31477,31479,31481],{},[1683,31478,1974],{},[1687,31480,1713],{},[1687,31482,1713],{},[1680,31484,31485,31487],{},[1683,31486,1809],{},[1687,31488,1713],{},[1680,31490,31491,31493],{},[1683,31492,7258],{},[1683,31494,1110],{},[1811,31496,1994],{"stretchy":1993},[1680,31498,31499,31501],{},[1683,31500,1809],{},[1687,31502,1713],{},[1811,31504,3184],{},[1687,31506,1914],{},[1811,31508,2005],{"stretchy":1993},[1677,31510,31511,31529,31531],{},[3361,31512,31513],{"scriptlevel":1689,"displaystyle":1121},[2859,31514,31515,31523],{},[3473,31516,31517,31519,31521],{},[1683,31518,1974],{},[1687,31520,1914],{},[1687,31522,1713],{},[1680,31524,31525,31527],{},[1683,31526,1809],{},[1687,31528,1914],{},[1811,31530,5598],{},[3361,31532,31533],{"scriptlevel":1689,"displaystyle":1121},[2859,31534,31535,31543],{},[3473,31536,31537,31539,31541],{},[1683,31538,1974],{},[1687,31540,1713],{},[1687,31542,1713],{},[1680,31544,31545,31547],{},[1683,31546,1809],{},[1687,31548,1713],{},[1683,31550,1497],{"mathvariant":2240},[1691,31552,31553],{"encoding":1693},"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}}.",[1158,31555,31556,31613],{},[1161,31557,31558],{},[1164,31559,31560,31579,31598],{},[1167,31561,31562],{},[1115,31563,31565],{"className":31564},[1668],[1670,31566,31567],{"xmlns":1672},[1674,31568,31569,31577],{},[1677,31570,31571],{},[1680,31572,31573,31575],{},[1683,31574,1685],{},[1687,31576,1689],{},[1691,31578,1694],{"encoding":1693},[1167,31580,31581],{},[1115,31582,31584],{"className":31583},[1668],[1670,31585,31586],{"xmlns":1672},[1674,31587,31588,31596],{},[1677,31589,31590],{},[1680,31591,31592,31594],{},[1683,31593,1685],{},[1687,31595,1914],{},[1691,31597,3116],{"encoding":1693},[1167,31599,27814,31600],{},[1115,31601,31603],{"className":31602},[1668],[1670,31604,31605],{"xmlns":1672},[1674,31606,31607,31611],{},[1677,31608,31609],{},[1683,31610,1729],{},[1691,31612,1729],{"encoding":1693},[1174,31614,31615,31699,31787],{},[1164,31616,31617,31645,31673],{},[1179,31618,31619],{},[1115,31620,31622],{"className":31621},[1668],[1670,31623,31624],{"xmlns":1672},[1674,31625,31626,31642],{},[1677,31627,31628,31634,31636],{},[1680,31629,31630,31632],{},[1683,31631,7005],{},[1687,31633,1914],{},[1811,31635,6849],{},[1680,31637,31638,31640],{},[1683,31639,7005],{},[1687,31641,1713],{},[1691,31643,31644],{"encoding":1693},"\\mu_1 \\le \\mu_2",[1179,31646,31647],{},[1115,31648,31650],{"className":31649},[1668],[1670,31651,31652],{"xmlns":1672},[1674,31653,31654,31670],{},[1677,31655,31656,31662,31664],{},[1680,31657,31658,31660],{},[1683,31659,7005],{},[1687,31661,1914],{},[1811,31663,1813],{},[1680,31665,31666,31668],{},[1683,31667,7005],{},[1687,31669,1713],{},[1691,31671,31672],{"encoding":1693},"\\mu_1 > \\mu_2",[1179,31674,31675],{},[1115,31676,31678],{"className":31677},[1668],[1670,31679,31680],{"xmlns":1672},[1674,31681,31682,31696],{},[1677,31683,31684,31686,31688],{},[1683,31685,7258],{},[1811,31687,3471],{},[3473,31689,31690,31692,31694],{},[1683,31691,7258],{},[1683,31693,1110],{},[1811,31695,31265],{},[1691,31697,31698],{"encoding":1693},"t \\ge t_p^*",[1164,31700,31701,31729,31757],{},[1179,31702,31703],{},[1115,31704,31706],{"className":31705},[1668],[1670,31707,31708],{"xmlns":1672},[1674,31709,31710,31726],{},[1677,31711,31712,31718,31720],{},[1680,31713,31714,31716],{},[1683,31715,7005],{},[1687,31717,1914],{},[1811,31719,2101],{},[1680,31721,31722,31724],{},[1683,31723,7005],{},[1687,31725,1713],{},[1691,31727,31728],{"encoding":1693},"\\mu_1 = \\mu_2",[1179,31730,31731],{},[1115,31732,31734],{"className":31733},[1668],[1670,31735,31736],{"xmlns":1672},[1674,31737,31738,31754],{},[1677,31739,31740,31746,31748],{},[1680,31741,31742,31744],{},[1683,31743,7005],{},[1687,31745,1914],{},[1811,31747,11070],{"mathvariant":2240},[1680,31749,31750,31752],{},[1683,31751,7005],{},[1687,31753,1713],{},[1691,31755,31756],{"encoding":1693},"\\mu_1 \\neq \\mu_2",[1179,31758,31759],{},[1115,31760,31762],{"className":31761},[1668],[1670,31763,31764],{"xmlns":1672},[1674,31765,31766,31784],{},[1677,31767,31768,31770,31772,31774,31776],{},[1811,31769,23136],{"stretchy":1993},[1683,31771,7258],{},[1811,31773,23136],{"stretchy":1993},[1811,31775,3471],{},[3473,31777,31778,31780,31782],{},[1683,31779,7258],{},[1683,31781,1110],{},[1811,31783,31265],{},[1691,31785,31786],{"encoding":1693},"\\lvert t \\rvert \\ge t_p^*",[1164,31788,31789,31817,31845],{},[1179,31790,31791],{},[1115,31792,31794],{"className":31793},[1668],[1670,31795,31796],{"xmlns":1672},[1674,31797,31798,31814],{},[1677,31799,31800,31806,31808],{},[1680,31801,31802,31804],{},[1683,31803,7005],{},[1687,31805,1914],{},[1811,31807,3471],{},[1680,31809,31810,31812],{},[1683,31811,7005],{},[1687,31813,1713],{},[1691,31815,31816],{"encoding":1693},"\\mu_1 \\ge \\mu_2",[1179,31818,31819],{},[1115,31820,31822],{"className":31821},[1668],[1670,31823,31824],{"xmlns":1672},[1674,31825,31826,31842],{},[1677,31827,31828,31834,31836],{},[1680,31829,31830,31832],{},[1683,31831,7005],{},[1687,31833,1914],{},[1811,31835,4453],{},[1680,31837,31838,31840],{},[1683,31839,7005],{},[1687,31841,1713],{},[1691,31843,31844],{"encoding":1693},"\\mu_1 \u003C \\mu_2",[1179,31846,31847],{},[1115,31848,31850],{"className":31849},[1668],[1670,31851,31852],{"xmlns":1672},[1674,31853,31854,31870],{},[1677,31855,31856,31858,31860,31862],{},[1683,31857,7258],{},[1811,31859,6849],{},[1811,31861,3184],{},[3473,31863,31864,31866,31868],{},[1683,31865,7258],{},[1683,31867,1110],{},[1811,31869,31265],{},[1691,31871,31872],{"encoding":1693},"t \\le -t_p^*",[1110,31874,31875,31876,30938,31894,1497],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,31877,31879],{"className":31878},[1668],[1670,31880,31881],{"xmlns":1672},[1674,31882,31883,31891],{},[1677,31884,31885],{},[1680,31886,31887,31889],{},[1683,31888,7216],{},[1687,31890,1914],{},[1691,31892,31893],{"encoding":1693},"T_1",[1115,31895,31897],{"className":31896},[1668],[1670,31898,31899],{"xmlns":1672},[1674,31900,31901,31909],{},[1677,31902,31903],{},[1680,31904,31905,31907],{},[1683,31906,7216],{},[1687,31908,1713],{},[1691,31910,31911],{"encoding":1693},"T_2",[1110,31913,31914],{},[4504,31915],{"alt":31916,"className":31917,"src":31918},"mask-th-f-kriticky-obor",[1131,4508],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,31920,31922,31929,32079,32160,32289,32327,32400,32539],{"className":31921,"dataCallout":3597},[1106,3596],[1110,31923,31925,31928],{"className":31924},[1113],[1115,31926],{"className":31927,"ariaHidden":1121},[1118,3604,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,31930,31931,31932,3071,31954,31980,31981,32005,32006,3071,32028,31980,32054,32078],{},"Pevnost plastových dílů: dodavatel A (",[1115,31933,31935],{"className":31934},[1668],[1670,31936,31937],{"xmlns":1672},[1674,31938,31939,31951],{},[1677,31940,31941,31947,31949],{},[1680,31942,31943,31945],{},[1683,31944,1809],{},[1687,31946,1914],{},[1811,31948,2101],{},[1687,31950,9147],{},[1691,31952,31953],{"encoding":1693},"n_1 = 10",[1115,31955,31957],{"className":31956},[1668],[1670,31958,31959],{"xmlns":1672},[1674,31960,31961,31977],{},[1677,31962,31963,31973,31975],{},[1680,31964,31965,31971],{},[2843,31966,31967,31969],{"accent":1121},[1683,31968,6834],{},[1811,31970,11573],{},[1687,31972,1914],{},[1811,31974,2101],{},[1687,31976,3748],{},[1691,31978,31979],{"encoding":1693},"\\bar{x}_1 = 82"," MPa, ",[1115,31982,31984],{"className":31983},[1668],[1670,31985,31986],{"xmlns":1672},[1674,31987,31988,32002],{},[1677,31989,31990,31998,32000],{},[3473,31991,31992,31994,31996],{},[1683,31993,1974],{},[1687,31995,1914],{},[1687,31997,1713],{},[1811,31999,2101],{},[1687,32001,4179],{},[1691,32003,32004],{"encoding":1693},"s_1^2 = 25","), dodavatel B (",[1115,32007,32009],{"className":32008},[1668],[1670,32010,32011],{"xmlns":1672},[1674,32012,32013,32025],{},[1677,32014,32015,32021,32023],{},[1680,32016,32017,32019],{},[1683,32018,1809],{},[1687,32020,1713],{},[1811,32022,2101],{},[1687,32024,2395],{},[1691,32026,32027],{"encoding":1693},"n_2 = 12",[1115,32029,32031],{"className":32030},[1668],[1670,32032,32033],{"xmlns":1672},[1674,32034,32035,32051],{},[1677,32036,32037,32047,32049],{},[1680,32038,32039,32045],{},[2843,32040,32041,32043],{"accent":1121},[1683,32042,6834],{},[1811,32044,11573],{},[1687,32046,1713],{},[1811,32048,2101],{},[1687,32050,14846],{},[1691,32052,32053],{"encoding":1693},"\\bar{x}_2 = 75",[1115,32055,32057],{"className":32056},[1668],[1670,32058,32059],{"xmlns":1672},[1674,32060,32061,32075],{},[1677,32062,32063,32071,32073],{},[3473,32064,32065,32067,32069],{},[1683,32066,1974],{},[1687,32068,1713],{},[1687,32070,1713],{},[1811,32072,2101],{},[1687,32074,22138],{},[1691,32076,32077],{"encoding":1693},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,32080,32081,1418,32084,3071,32122,1497],{},[1136,32082,32083],{},"Krok 1 — F-test rozptylů.",[1115,32085,32087],{"className":32086},[1668],[1670,32088,32089],{"xmlns":1672},[1674,32090,32091,32119],{},[1677,32092,32093,32099,32101,32109,32111],{},[1680,32094,32095,32097],{},[1683,32096,1685],{},[1687,32098,1689],{},[1811,32100,2077],{},[3473,32102,32103,32105,32107],{},[1683,32104,7013],{},[1687,32106,1914],{},[1687,32108,1713],{},[1811,32110,2101],{},[3473,32112,32113,32115,32117],{},[1683,32114,7013],{},[1687,32116,1713],{},[1687,32118,1713],{},[1691,32120,32121],{"encoding":1693},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,32123,32125],{"className":32124},[1668],[1670,32126,32127],{"xmlns":1672},[1674,32128,32129,32157],{},[1677,32130,32131,32137,32139,32147,32149],{},[1680,32132,32133,32135],{},[1683,32134,1685],{},[1687,32136,1914],{},[1811,32138,2077],{},[3473,32140,32141,32143,32145],{},[1683,32142,7013],{},[1687,32144,1914],{},[1687,32146,1713],{},[1811,32148,11070],{"mathvariant":2240},[3473,32150,32151,32153,32155],{},[1683,32152,7013],{},[1687,32154,1713],{},[1687,32156,1713],{},[1691,32158,32159],{"encoding":1693},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,32161,32162],{},[1115,32163,32165],{"className":32164},[1668],[1670,32166,32167],{"xmlns":1672},[1674,32168,32169,32286],{},[1677,32170,32171,32173,32175,32181,32183,32186,32188,32190,32192,32194,32196,32198,32200,32213,32215,32217,32219,32221,32223,32226,32229,32231,32233,32235,32248,32250,32252,32254,32256,32258,32260,32262,32264,32266,32268,32271,32273,32275,32277,32279,32281,32284],{},[1683,32172,1403],{},[1811,32174,2101],{},[2859,32176,32177,32179],{},[1687,32178,4179],{},[1687,32180,22138],{},[1811,32182,2101],{},[1687,32184,32185],{},"1,5625",[1811,32187,1917],{"separator":1121},[2131,32189],{"width":2133},[1683,32191,1729],{},[1811,32193,2101],{},[1811,32195,3454],{"stretchy":1993},[1683,32197,1403],{},[1811,32199,6849],{},[1680,32201,32202,32204],{},[1683,32203,1403],{},[1677,32205,32206,32208,32210],{},[1687,32207,1689],{},[1811,32209,1917],{"separator":1121},[1687,32211,32212],{},"025",[1811,32214,1994],{"stretchy":1993},[1687,32216,3715],{},[1811,32218,1917],{"separator":1121},[1687,32220,2374],{},[1811,32222,2005],{"stretchy":1993},[3028,32224,32225],{},"  ",[3028,32227,32228],{},"nebo",[3028,32230,32225],{},[1683,32232,1403],{},[1811,32234,3471],{},[1680,32236,32237,32239],{},[1683,32238,1403],{},[1677,32240,32241,32243,32245],{},[1687,32242,1689],{},[1811,32244,1917],{"separator":1121},[1687,32246,32247],{},"975",[1811,32249,1994],{"stretchy":1993},[1687,32251,3715],{},[1811,32253,1917],{"separator":1121},[1687,32255,2374],{},[1811,32257,2005],{"stretchy":1993},[1811,32259,3514],{"stretchy":1993},[1811,32261,2101],{},[1811,32263,3454],{"stretchy":1993},[1683,32265,1403],{},[1811,32267,6849],{},[1687,32269,32270],{},"0,256",[3028,32272,32225],{},[3028,32274,32228],{},[3028,32276,32225],{},[1683,32278,1403],{},[1811,32280,3471],{},[1687,32282,32283],{},"3,588",[1811,32285,3514],{"stretchy":1993},[1691,32287,32288],{"encoding":1693},"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\\}",[1110,32290,32291,32309,32310,1497],{},[1115,32292,32294],{"className":32293},[1668],[1670,32295,32296],{"xmlns":1672},[1674,32297,32298,32306],{},[1677,32299,32300,32302,32304],{},[1683,32301,1403],{},[1811,32303,27375],{"mathvariant":2240},[1683,32305,1729],{},[1691,32307,32308],{"encoding":1693},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,32311,32313],{"className":32312},[1668],[1670,32314,32315],{"xmlns":1672},[1674,32316,32317,32325],{},[1677,32318,32319],{},[1680,32320,32321,32323],{},[1683,32322,7216],{},[1687,32324,1914],{},[1691,32326,31893],{"encoding":1693},[1110,32328,32329,1418,32332,3071,32366,1497],{},[1136,32330,32331],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,32333,32335],{"className":32334},[1668],[1670,32336,32337],{"xmlns":1672},[1674,32338,32339,32363],{},[1677,32340,32341,32347,32349,32355,32357],{},[1680,32342,32343,32345],{},[1683,32344,1685],{},[1687,32346,1689],{},[1811,32348,2077],{},[1680,32350,32351,32353],{},[1683,32352,7005],{},[1687,32354,1914],{},[1811,32356,2101],{},[1680,32358,32359,32361],{},[1683,32360,7005],{},[1687,32362,1713],{},[1691,32364,32365],{"encoding":1693},"H_0: \\mu_1 = \\mu_2",[1115,32367,32369],{"className":32368},[1668],[1670,32370,32371],{"xmlns":1672},[1674,32372,32373,32397],{},[1677,32374,32375,32381,32383,32389,32391],{},[1680,32376,32377,32379],{},[1683,32378,1685],{},[1687,32380,1914],{},[1811,32382,2077],{},[1680,32384,32385,32387],{},[1683,32386,7005],{},[1687,32388,1914],{},[1811,32390,11070],{"mathvariant":2240},[1680,32392,32393,32395],{},[1683,32394,7005],{},[1687,32396,1713],{},[1691,32398,32399],{"encoding":1693},"H_1: \\mu_1 \\neq \\mu_2",[1110,32401,32402],{},[1115,32403,32405],{"className":32404},[1668],[1670,32406,32407],{"xmlns":1672},[1674,32408,32409,32536],{},[1677,32410,32411,32419,32421,32441,32443,32446,32448,32450,32452,32454,32468,32476,32478,32481,32483,32485,32487,32489,32491,32493,32495,32497,32499,32511,32513,32515,32517,32519,32521,32523,32525,32527,32529,32531,32534],{},[3473,32412,32413,32415,32417],{},[1683,32414,1974],{},[1683,32416,1110],{},[1687,32418,1713],{},[1811,32420,2101],{},[2859,32422,32423,32439],{},[1677,32424,32425,32427,32429,32431,32433,32435,32437],{},[1687,32426,3715],{},[1811,32428,8225],{},[1687,32430,4179],{},[1811,32432,5598],{},[1687,32434,2374],{},[1811,32436,8225],{},[1687,32438,22138],{},[1687,32440,4166],{},[1811,32442,2101],{},[1687,32444,32445],{},"20,05",[1811,32447,1917],{"separator":1121},[2131,32449],{"width":2133},[1683,32451,7258],{},[1811,32453,2101],{},[2859,32455,32456,32464],{},[1677,32457,32458,32460,32462],{},[1687,32459,3748],{},[1811,32461,3184],{},[1687,32463,14846],{},[4574,32465,32466],{},[1687,32467,32445],{},[4574,32469,32470],{},[2859,32471,32472,32474],{},[1687,32473,21998],{},[1687,32475,2509],{},[1811,32477,9554],{},[1687,32479,32480],{},"3,651",[1811,32482,1917],{"separator":1121},[2131,32484],{"width":2133},[1683,32486,1729],{},[1811,32488,2101],{},[1811,32490,3454],{"stretchy":1993},[1811,32492,23136],{"stretchy":1993},[1683,32494,7258],{},[1811,32496,23136],{"stretchy":1993},[1811,32498,3471],{},[1680,32500,32501,32503],{},[1683,32502,7258],{},[1677,32504,32505,32507,32509],{},[1687,32506,1689],{},[1811,32508,1917],{"separator":1121},[1687,32510,32247],{},[1811,32512,1994],{"stretchy":1993},[1687,32514,4166],{},[1811,32516,2005],{"stretchy":1993},[1811,32518,3514],{"stretchy":1993},[1811,32520,2101],{},[1811,32522,3454],{"stretchy":1993},[1811,32524,23136],{"stretchy":1993},[1683,32526,7258],{},[1811,32528,23136],{"stretchy":1993},[1811,32530,3471],{},[1687,32532,32533],{},"2,086",[1811,32535,3514],{"stretchy":1993},[1691,32537,32538],{"encoding":1693},"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\\}",[1110,32540,32541,6128,32558,32575],{},[1115,32542,32544],{"className":32543},[1668],[1670,32545,32546],{"xmlns":1672},[1674,32547,32548,32556],{},[1677,32549,32550,32552,32554],{},[1683,32551,7258],{},[1811,32553,7133],{},[1683,32555,1729],{},[1691,32557,28518],{"encoding":1693},[1115,32559,32561],{"className":32560},[1668],[1670,32562,32563],{"xmlns":1672},[1674,32564,32565,32573],{},[1677,32566,32567],{},[1680,32568,32569,32571],{},[1683,32570,1685],{},[1687,32572,1689],{},[1691,32574,1694],{"encoding":1693},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3814,32577,32579],{"className":3816,"code":32578,"language":71,"meta":1603,"style":1603},"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",[3590,32580,32581,32599,32619,32634,32669,32700,32705,32710],{"__ignoreMap":1603},[1115,32582,32583,32586,32588,32590,32592,32595,32597],{"class":3822,"line":10},[1115,32584,32585],{"class":3825},"s1",[1115,32587,3830],{"class":3829},[1115,32589,14516],{"class":3845},[1115,32591,25296],{"class":3837},[1115,32593,32594],{"class":3825},"n1",[1115,32596,3830],{"class":3829},[1115,32598,29959],{"class":3845},[1115,32600,32601,32604,32606,32609,32611,32614,32616],{"class":3822,"line":27},[1115,32602,32603],{"class":3825},"s2",[1115,32605,3830],{"class":3829},[1115,32607,32608],{"class":3845}," 16",[1115,32610,25296],{"class":3837},[1115,32612,32613],{"class":3825},"n2",[1115,32615,3830],{"class":3829},[1115,32617,32618],{"class":3845}," 12\n",[1115,32620,32621,32624,32626,32629,32631],{"class":3822,"line":148},[1115,32622,32623],{"class":3825},"Fstat",[1115,32625,3830],{"class":3829},[1115,32627,32628],{"class":3825}," s1",[1115,32630,10189],{"class":3829},[1115,32632,32633],{"class":3825}," s2\n",[1115,32635,32636,32639,32641,32644,32646,32649,32651,32654,32656,32658,32660,32663,32665,32667],{"class":3822,"line":111},[1115,32637,32638],{"class":3825},"F_dolni",[1115,32640,3830],{"class":3829},[1115,32642,32643],{"class":3833}," qf",[1115,32645,1994],{"class":3837},[1115,32647,32648],{"class":3845},"0.025",[1115,32650,1917],{"class":3829},[1115,32652,32653],{"class":3825}," n1",[1115,32655,25633],{"class":3829},[1115,32657,4762],{"class":3845},[1115,32659,1917],{"class":3829},[1115,32661,32662],{"class":3825}," n2",[1115,32664,25633],{"class":3829},[1115,32666,4762],{"class":3845},[1115,32668,4022],{"class":3837},[1115,32670,32671,32674,32676,32678,32680,32682,32684,32686,32688,32690,32692,32694,32696,32698],{"class":3822,"line":96},[1115,32672,32673],{"class":3825},"F_horni",[1115,32675,3830],{"class":3829},[1115,32677,32643],{"class":3833},[1115,32679,1994],{"class":3837},[1115,32681,9203],{"class":3845},[1115,32683,1917],{"class":3829},[1115,32685,32653],{"class":3825},[1115,32687,25633],{"class":3829},[1115,32689,4762],{"class":3845},[1115,32691,1917],{"class":3829},[1115,32693,32662],{"class":3825},[1115,32695,25633],{"class":3829},[1115,32697,4762],{"class":3845},[1115,32699,4022],{"class":3837},[1115,32701,32702],{"class":3822,"line":89},[1115,32703,32704],{"class":3825},"Fstat\n",[1115,32706,32707],{"class":3822,"line":82},[1115,32708,32709],{"class":3825},"F_dolni\n",[1115,32711,32712],{"class":3822,"line":75},[1115,32713,32714],{"class":3825},"F_horni\n",[3814,32716,32719],{"className":32717,"code":32718,"language":4044,"meta":1603},[4042],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3590,32720,32718],{"__ignoreMap":1603},[3814,32722,32724],{"className":3816,"code":32723,"language":71,"meta":1603,"style":1603},"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",[3590,32725,32726,32783,32834,32864,32869,32873],{"__ignoreMap":1603},[1115,32727,32728,32731,32733,32736,32738,32740,32742,32744,32746,32748,32750,32752,32754,32756,32758,32760,32762,32765,32767,32769,32771,32773,32775,32777,32779,32781],{"class":3822,"line":10},[1115,32729,32730],{"class":3825},"sp2",[1115,32732,3830],{"class":3829},[1115,32734,32735],{"class":3837}," ((",[1115,32737,32594],{"class":3825},[1115,32739,25633],{"class":3829},[1115,32741,4762],{"class":3845},[1115,32743,4722],{"class":3837},[1115,32745,4740],{"class":3829},[1115,32747,32628],{"class":3825},[1115,32749,18628],{"class":3829},[1115,32751,4728],{"class":3837},[1115,32753,32613],{"class":3825},[1115,32755,25633],{"class":3829},[1115,32757,4762],{"class":3845},[1115,32759,4722],{"class":3837},[1115,32761,4740],{"class":3829},[1115,32763,32764],{"class":3825}," s2",[1115,32766,4722],{"class":3837},[1115,32768,4725],{"class":3829},[1115,32770,4728],{"class":3837},[1115,32772,32594],{"class":3825},[1115,32774,18628],{"class":3829},[1115,32776,32662],{"class":3825},[1115,32778,25633],{"class":3829},[1115,32780,4301],{"class":3845},[1115,32782,4022],{"class":3837},[1115,32784,32785,32787,32789,32791,32793,32795,32798,32800,32802,32804,32806,32808,32810,32812,32814,32816,32818,32820,32822,32824,32826,32828,32830,32832],{"class":3822,"line":27},[1115,32786,7258],{"class":3825},[1115,32788,3830],{"class":3829},[1115,32790,4728],{"class":3837},[1115,32792,3748],{"class":3845},[1115,32794,25633],{"class":3829},[1115,32796,32797],{"class":3845}," 75",[1115,32799,4722],{"class":3837},[1115,32801,4725],{"class":3829},[1115,32803,4699],{"class":3833},[1115,32805,1994],{"class":3837},[1115,32807,32730],{"class":3825},[1115,32809,4722],{"class":3837},[1115,32811,4740],{"class":3829},[1115,32813,4699],{"class":3833},[1115,32815,1994],{"class":3837},[1115,32817,32594],{"class":3825},[1115,32819,18753],{"class":3829},[1115,32821,32662],{"class":3825},[1115,32823,10189],{"class":3829},[1115,32825,4728],{"class":3837},[1115,32827,32594],{"class":3825},[1115,32829,18628],{"class":3829},[1115,32831,32662],{"class":3825},[1115,32833,9607],{"class":3837},[1115,32835,32836,32838,32840,32842,32844,32846,32848,32850,32852,32854,32856,32858,32860,32862],{"class":3822,"line":148},[1115,32837,28625],{"class":3825},[1115,32839,3830],{"class":3829},[1115,32841,28630],{"class":3833},[1115,32843,1994],{"class":3837},[1115,32845,9203],{"class":3845},[1115,32847,1917],{"class":3829},[1115,32849,10923],{"class":3825},[1115,32851,3918],{"class":3829},[1115,32853,32653],{"class":3825},[1115,32855,18628],{"class":3829},[1115,32857,32662],{"class":3825},[1115,32859,25633],{"class":3829},[1115,32861,4301],{"class":3845},[1115,32863,4022],{"class":3837},[1115,32865,32866],{"class":3822,"line":111},[1115,32867,32868],{"class":3825},"sp2\n",[1115,32870,32871],{"class":3822,"line":96},[1115,32872,28655],{"class":3825},[1115,32874,32875],{"class":3822,"line":89},[1115,32876,28660],{"class":3825},[3814,32878,32881],{"className":32879,"code":32880,"language":4044,"meta":1603},[4042],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3590,32882,32880],{"__ignoreMap":1603},[1110,32884,32885],{},[4504,32886],{"alt":32887,"className":32888,"src":32889},"mask-th-t-dvoustranny",[1131,4508],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,32891,32892,32893,5862,32896,32898,32899,32902,32903,5862,32920,4109,32937,32939,32940,32942],{},"V R provede obě kroky ",[3590,32894,32895],{},"var.test()",[3590,32897,28115],{},". Parametr ",[3590,32900,32901],{},"var.equal"," nastavuje volbu mezi ",[1115,32904,32906],{"className":32905},[1668],[1670,32907,32908],{"xmlns":1672},[1674,32909,32910,32918],{},[1677,32911,32912],{},[1680,32913,32914,32916],{},[1683,32915,7216],{},[1687,32917,1914],{},[1691,32919,31893],{"encoding":1693},[1115,32921,32923],{"className":32922},[1668],[1670,32924,32925],{"xmlns":1672},[1674,32926,32927,32935],{},[1677,32928,32929],{},[1680,32930,32931,32933],{},[1683,32932,7216],{},[1687,32934,1713],{},[1691,32936,31911],{"encoding":1693},[3590,32938,9638],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3590,32941,9641],{}," předpoklad rozdílných rozptylů.",[1110,32944,32945,32948],{},[1136,32946,32947],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3814,32950,32952],{"className":3816,"code":32951,"language":71,"meta":1603,"style":1603},"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",[3590,32953,32954,33020,33083,33099],{"__ignoreMap":1603},[1115,32955,32956,32958,32960,32962,32964,32967,32969,32972,32974,32977,32979,32982,32984,32986,32988,32991,32993,32996,32998,33000,33002,33005,33007,33009,33011,33014,33016,33018],{"class":3822,"line":10},[1115,32957,1363],{"class":3825},[1115,32959,3830],{"class":3829},[1115,32961,3956],{"class":3833},[1115,32963,1994],{"class":3837},[1115,32965,32966],{"class":3845},"313",[1115,32968,1917],{"class":3829},[1115,32970,32971],{"class":3845}," 299",[1115,32973,1917],{"class":3829},[1115,32975,32976],{"class":3845}," 315",[1115,32978,1917],{"class":3829},[1115,32980,32981],{"class":3845}," 312",[1115,32983,1917],{"class":3829},[1115,32985,15484],{"class":3845},[1115,32987,1917],{"class":3829},[1115,32989,32990],{"class":3845}," 308",[1115,32992,1917],{"class":3829},[1115,32994,32995],{"class":3845}," 314",[1115,32997,1917],{"class":3829},[1115,32999,14276],{"class":3845},[1115,33001,1917],{"class":3829},[1115,33003,33004],{"class":3845}," 305",[1115,33006,1917],{"class":3829},[1115,33008,15484],{"class":3845},[1115,33010,1917],{"class":3829},[1115,33012,33013],{"class":3845}," 309",[1115,33015,1917],{"class":3829},[1115,33017,32995],{"class":3845},[1115,33019,4022],{"class":3837},[1115,33021,33022,33024,33026,33028,33030,33033,33035,33038,33040,33042,33044,33046,33048,33051,33053,33056,33058,33060,33062,33064,33066,33068,33070,33073,33075,33077,33079,33081],{"class":3822,"line":27},[1115,33023,1371],{"class":3825},[1115,33025,3830],{"class":3829},[1115,33027,3956],{"class":3833},[1115,33029,1994],{"class":3837},[1115,33031,33032],{"class":3845},"307",[1115,33034,1917],{"class":3829},[1115,33036,33037],{"class":3845}," 322",[1115,33039,1917],{"class":3829},[1115,33041,14276],{"class":3845},[1115,33043,1917],{"class":3829},[1115,33045,14276],{"class":3845},[1115,33047,1917],{"class":3829},[1115,33049,33050],{"class":3845}," 311",[1115,33052,1917],{"class":3829},[1115,33054,33055],{"class":3845}," 316",[1115,33057,1917],{"class":3829},[1115,33059,32976],{"class":3845},[1115,33061,1917],{"class":3829},[1115,33063,32995],{"class":3845},[1115,33065,1917],{"class":3829},[1115,33067,32990],{"class":3845},[1115,33069,1917],{"class":3829},[1115,33071,33072],{"class":3845}," 319",[1115,33074,1917],{"class":3829},[1115,33076,14276],{"class":3845},[1115,33078,1917],{"class":3829},[1115,33080,32981],{"class":3845},[1115,33082,4022],{"class":3837},[1115,33084,33085,33088,33090,33092,33094,33097],{"class":3822,"line":148},[1115,33086,33087],{"class":3833},"var.test",[1115,33089,1994],{"class":3837},[1115,33091,1363],{"class":3825},[1115,33093,1917],{"class":3829},[1115,33095,33096],{"class":3825}," B",[1115,33098,4022],{"class":3837},[1115,33100,33101,33103,33105,33107,33109,33111,33113,33116,33118,33120],{"class":3822,"line":111},[1115,33102,28180],{"class":3833},[1115,33104,1994],{"class":3837},[1115,33106,1363],{"class":3825},[1115,33108,1917],{"class":3829},[1115,33110,33096],{"class":3825},[1115,33112,1917],{"class":3829},[1115,33114,33115],{"class":3825}," var.equal",[1115,33117,3918],{"class":3829},[1115,33119,3931],{"class":3845},[1115,33121,4022],{"class":3837},[3814,33123,33126],{"className":33124,"code":33125,"language":4044,"meta":1603},[4042],"    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",[3590,33127,33125],{"__ignoreMap":1603},[1110,33129,33130,33131,12168,33150,33153,33154,33173,33174,33191],{},"F-test shodu rozptylů nezamítá (",[1115,33132,33134],{"className":33133},[1668],[1670,33135,33136],{"xmlns":1672},[1674,33137,33138,33147],{},[1677,33139,33140,33142,33144],{},[1683,33141,1110],{},[1811,33143,2101],{},[1687,33145,33146],{},"0,7776",[1691,33148,33149],{"encoding":1693},"p = 0{,}7776",[3590,33151,33152],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,33155,33157],{"className":33156},[1668],[1670,33158,33159],{"xmlns":1672},[1674,33160,33161,33170],{},[1677,33162,33163,33165,33167],{},[1683,33164,1110],{},[1811,33166,2101],{},[1687,33168,33169],{},"0,06932",[1691,33171,33172],{"encoding":1693},"p = 0{,}06932"," — na hladině 5 % se ",[1115,33175,33177],{"className":33176},[1668],[1670,33178,33179],{"xmlns":1672},[1674,33180,33181,33189],{},[1677,33182,33183],{},[1680,33184,33185,33187],{},[1683,33186,1685],{},[1687,33188,1689],{},[1691,33190,1694],{"encoding":1693}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,33193,33194],{},[1136,33195,33196],{},"Výšky chlapců a dívek v páté třídě:",[3814,33198,33200],{"className":3816,"code":33199,"language":71,"meta":1603,"style":1603},"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",[3590,33201,33202,33282,33345,33360],{"__ignoreMap":1603},[1115,33203,33204,33207,33209,33211,33213,33216,33218,33220,33222,33225,33227,33230,33232,33235,33237,33240,33242,33244,33246,33248,33250,33252,33254,33256,33258,33261,33263,33266,33268,33271,33273,33275,33277,33280],{"class":3822,"line":10},[1115,33205,33206],{"class":3825},"boys",[1115,33208,3830],{"class":3829},[1115,33210,3956],{"class":3833},[1115,33212,1994],{"class":3837},[1115,33214,33215],{"class":3845},"130",[1115,33217,1917],{"class":3829},[1115,33219,15433],{"class":3845},[1115,33221,1917],{"class":3829},[1115,33223,33224],{"class":3845}," 136",[1115,33226,1917],{"class":3829},[1115,33228,33229],{"class":3845}," 141",[1115,33231,1917],{"class":3829},[1115,33233,33234],{"class":3845}," 139",[1115,33236,1917],{"class":3829},[1115,33238,33239],{"class":3845}," 133",[1115,33241,1917],{"class":3829},[1115,33243,18585],{"class":3845},[1115,33245,1917],{"class":3829},[1115,33247,14291],{"class":3845},[1115,33249,1917],{"class":3829},[1115,33251,33234],{"class":3845},[1115,33253,1917],{"class":3829},[1115,33255,33224],{"class":3845},[1115,33257,1917],{"class":3829},[1115,33259,33260],{"class":3845}," 138",[1115,33262,1917],{"class":3829},[1115,33264,33265],{"class":3845}," 142",[1115,33267,1917],{"class":3829},[1115,33269,33270],{"class":3845}," 127",[1115,33272,1917],{"class":3829},[1115,33274,33234],{"class":3845},[1115,33276,1917],{"class":3829},[1115,33278,33279],{"class":3845}," 147",[1115,33281,4022],{"class":3837},[1115,33283,33284,33287,33289,33291,33293,33295,33297,33299,33301,33304,33306,33309,33311,33314,33316,33318,33320,33322,33324,33326,33328,33330,33332,33335,33337,33339,33341,33343],{"class":3822,"line":27},[1115,33285,33286],{"class":3825},"girls",[1115,33288,3830],{"class":3829},[1115,33290,3956],{"class":3833},[1115,33292,1994],{"class":3837},[1115,33294,21949],{"class":3845},[1115,33296,1917],{"class":3829},[1115,33298,33229],{"class":3845},[1115,33300,1917],{"class":3829},[1115,33302,33303],{"class":3845}," 143",[1115,33305,1917],{"class":3829},[1115,33307,33308],{"class":3845}," 132",[1115,33310,1917],{"class":3829},[1115,33312,33313],{"class":3845}," 146",[1115,33315,1917],{"class":3829},[1115,33317,33313],{"class":3845},[1115,33319,1917],{"class":3829},[1115,33321,14291],{"class":3845},[1115,33323,1917],{"class":3829},[1115,33325,33229],{"class":3845},[1115,33327,1917],{"class":3829},[1115,33329,33229],{"class":3845},[1115,33331,1917],{"class":3829},[1115,33333,33334],{"class":3845}," 131",[1115,33336,1917],{"class":3829},[1115,33338,33265],{"class":3845},[1115,33340,1917],{"class":3829},[1115,33342,33229],{"class":3845},[1115,33344,4022],{"class":3837},[1115,33346,33347,33349,33351,33353,33355,33358],{"class":3822,"line":148},[1115,33348,33087],{"class":3833},[1115,33350,1994],{"class":3837},[1115,33352,33206],{"class":3825},[1115,33354,1917],{"class":3829},[1115,33356,33357],{"class":3825}," girls",[1115,33359,4022],{"class":3837},[1115,33361,33362,33364,33366,33368,33370,33372,33374,33376,33378,33380],{"class":3822,"line":111},[1115,33363,28180],{"class":3833},[1115,33365,1994],{"class":3837},[1115,33367,33206],{"class":3825},[1115,33369,1917],{"class":3829},[1115,33371,33357],{"class":3825},[1115,33373,1917],{"class":3829},[1115,33375,33115],{"class":3825},[1115,33377,3918],{"class":3829},[1115,33379,3931],{"class":3845},[1115,33381,4022],{"class":3837},[3814,33383,33386],{"className":33384,"code":33385,"language":4044,"meta":1603},[4042],"    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",[3590,33387,33385],{"__ignoreMap":1603},[1110,33389,33130,33390,33409,33410,33412,33413,33432],{},[1115,33391,33393],{"className":33392},[1668],[1670,33394,33395],{"xmlns":1672},[1674,33396,33397,33406],{},[1677,33398,33399,33401,33403],{},[1683,33400,1110],{},[1811,33402,2101],{},[1687,33404,33405],{},"0,6977",[1691,33407,33408],{"encoding":1693},"p = 0{,}6977","), t-test s ",[3590,33411,33152],{}," dává ",[1115,33414,33416],{"className":33415},[1668],[1670,33417,33418],{"xmlns":1672},[1674,33419,33420,33429],{},[1677,33421,33422,33424,33426],{},[1683,33423,1110],{},[1811,33425,2101],{},[1687,33427,33428],{},"0,4883",[1691,33430,33431],{"encoding":1693},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1153,33434,33436],{"id":33435},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,33438,33439],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[16860,33441,33443],{"id":33442},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,33445,33446,33447,33470,33471,33490],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,33448,33450],{"className":33449},[1668],[1670,33451,33452],{"xmlns":1672},[1674,33453,33454,33468],{},[1677,33455,33456,33462,33464,33466],{},[1680,33457,33458,33460],{},[1683,33459,1403],{},[1683,33461,1809],{},[1811,33463,1994],{"stretchy":1993},[1683,33465,6834],{},[1811,33467,2005],{"stretchy":1993},[1691,33469,11297],{"encoding":1693}," s teoretickou distribuční funkcí ",[1115,33472,33474],{"className":33473},[1668],[1670,33475,33476],{"xmlns":1672},[1674,33477,33478,33488],{},[1677,33479,33480,33482,33484,33486],{},[1683,33481,1403],{},[1811,33483,1994],{"stretchy":1993},[1683,33485,6834],{},[1811,33487,2005],{"stretchy":1993},[1691,33489,7450],{"encoding":1693}," testovaného rozdělení.",[1503,33492,33493,33556,33576,33632],{},[1265,33494,33495,33512,33513,5862,33536,33555],{},[1115,33496,33498],{"className":33497},[1668],[1670,33499,33500],{"xmlns":1672},[1674,33501,33502,33510],{},[1677,33503,33504],{},[1680,33505,33506,33508],{},[1683,33507,1685],{},[1687,33509,1689],{},[1691,33511,1694],{"encoding":1693},": odchylky mezi ",[1115,33514,33516],{"className":33515},[1668],[1670,33517,33518],{"xmlns":1672},[1674,33519,33520,33534],{},[1677,33521,33522,33528,33530,33532],{},[1680,33523,33524,33526],{},[1683,33525,1403],{},[1683,33527,1809],{},[1811,33529,1994],{"stretchy":1993},[1683,33531,6834],{},[1811,33533,2005],{"stretchy":1993},[1691,33535,11297],{"encoding":1693},[1115,33537,33539],{"className":33538},[1668],[1670,33540,33541],{"xmlns":1672},[1674,33542,33543,33553],{},[1677,33544,33545,33547,33549,33551],{},[1683,33546,1403],{},[1811,33548,1994],{"stretchy":1993},[1683,33550,6834],{},[1811,33552,2005],{"stretchy":1993},[1691,33554,7450],{"encoding":1693}," jsou náhodné (data mají dané rozdělení).",[1265,33557,33558,33575],{},[1115,33559,33561],{"className":33560},[1668],[1670,33562,33563],{"xmlns":1672},[1674,33564,33565,33573],{},[1677,33566,33567],{},[1680,33568,33569,33571],{},[1683,33570,1685],{},[1687,33572,1914],{},[1691,33574,3116],{"encoding":1693},": data nemají dané rozdělení.",[1265,33577,33578,33579,1497],{},"Testové kritérium: ",[1115,33580,33582],{"className":33581},[1668],[1670,33583,33584],{"xmlns":1672},[1674,33585,33586,33629],{},[1677,33587,33588,33590,33592,33603,33605,33611,33613,33615,33617,33619,33621,33623,33625,33627],{},[1683,33589,1387],{},[1811,33591,2101],{},[1680,33593,33594,33601],{},[1677,33595,33596,33599],{},[1683,33597,33598],{},"sup",[1811,33600,4612],{},[1683,33602,6834],{},[1811,33604,23136],{"stretchy":1993},[1680,33606,33607,33609],{},[1683,33608,1403],{},[1683,33610,1809],{},[1811,33612,1994],{"stretchy":1993},[1683,33614,6834],{},[1811,33616,2005],{"stretchy":1993},[1811,33618,3184],{},[1683,33620,1403],{},[1811,33622,1994],{"stretchy":1993},[1683,33624,6834],{},[1811,33626,2005],{"stretchy":1993},[1811,33628,23136],{"stretchy":1993},[1691,33630,33631],{"encoding":1693},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1265,33633,3438,33634,33678,33679,33697,33698,1497],{},[1115,33635,33637],{"className":33636},[1668],[1670,33638,33639],{"xmlns":1672},[1674,33640,33641,33675],{},[1677,33642,33643,33649,33651,33653,33655,33657,33659,33661,33667,33669,33671,33673],{},[1680,33644,33645,33647],{},[1683,33646,1729],{},[1683,33648,3485],{},[1811,33650,2101],{},[1811,33652,3454],{"stretchy":1993},[1683,33654,7911],{},[1811,33656,2077],{},[1683,33658,7911],{},[1811,33660,1813],{},[1680,33662,33663,33665],{},[1683,33664,1387],{},[1683,33666,3485],{},[1811,33668,1994],{"stretchy":1993},[1683,33670,1809],{},[1811,33672,2005],{"stretchy":1993},[1811,33674,3514],{"stretchy":1993},[1691,33676,33677],{"encoding":1693},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,33680,33682],{"className":33681},[1668],[1670,33683,33684],{"xmlns":1672},[1674,33685,33686,33694],{},[1677,33687,33688,33690,33692],{},[1683,33689,1809],{},[1811,33691,1813],{},[1687,33693,22148],{},[1691,33695,33696],{"encoding":1693},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,33699,33701],{"className":33700},[1668],[1670,33702,33703],{"xmlns":1672},[1674,33704,33705,33716],{},[1677,33706,33707,33710,33712],{},[1687,33708,33709],{},"1,36",[1683,33711,4725],{"mathvariant":2240},[4574,33713,33714],{},[1683,33715,1809],{},[1691,33717,33718],{"encoding":1693},"1{,}36\u002F\\sqrt{n}",[1110,33720,28112,33721,33724,33725,33727,33728,3071,33731,33734],{},[3590,33722,33723],{},"ks.test()",", kde se za ",[3590,33726,7450],{}," dosadí příslušná distribuční funkce (",[3590,33729,33730],{},"\"pnorm\"",[3590,33732,33733],{},"\"pexp\"",", …) s jejími parametry:",[3814,33736,33738],{"className":3816,"code":33737,"language":71,"meta":1603,"style":1603},"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",[3590,33739,33740,33790],{"__ignoreMap":1603},[1115,33741,33742,33744,33746,33748,33750,33752,33754,33756,33758,33760,33762,33764,33766,33768,33770,33772,33774,33776,33778,33780,33782,33784,33786,33788],{"class":3822,"line":10},[1115,33743,28826],{"class":3825},[1115,33745,3830],{"class":3829},[1115,33747,3956],{"class":3833},[1115,33749,1994],{"class":3837},[1115,33751,12100],{"class":3845},[1115,33753,1917],{"class":3829},[1115,33755,12105],{"class":3845},[1115,33757,1917],{"class":3829},[1115,33759,12110],{"class":3845},[1115,33761,1917],{"class":3829},[1115,33763,12115],{"class":3845},[1115,33765,1917],{"class":3829},[1115,33767,12110],{"class":3845},[1115,33769,1917],{"class":3829},[1115,33771,12110],{"class":3845},[1115,33773,1917],{"class":3829},[1115,33775,12128],{"class":3845},[1115,33777,1917],{"class":3829},[1115,33779,12133],{"class":3845},[1115,33781,1917],{"class":3829},[1115,33783,12105],{"class":3845},[1115,33785,1917],{"class":3829},[1115,33787,12105],{"class":3845},[1115,33789,4022],{"class":3837},[1115,33791,33792,33795,33797,33799,33801,33804,33806,33808,33810,33812,33814,33816,33818,33820,33822],{"class":3822,"line":27},[1115,33793,33794],{"class":3833},"ks.test",[1115,33796,1994],{"class":3837},[1115,33798,28826],{"class":3825},[1115,33800,1917],{"class":3829},[1115,33802,33803],{"class":3961}," \"pnorm\"",[1115,33805,1917],{"class":3829},[1115,33807,9345],{"class":3833},[1115,33809,1994],{"class":3837},[1115,33811,28826],{"class":3825},[1115,33813,2005],{"class":3837},[1115,33815,1917],{"class":3829},[1115,33817,9355],{"class":3833},[1115,33819,1994],{"class":3837},[1115,33821,28826],{"class":3825},[1115,33823,9607],{"class":3837},[3814,33825,33828],{"className":33826,"code":33827,"language":4044,"meta":1603},[4042],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3590,33829,33827],{"__ignoreMap":1603},[1110,33831,33832,33855],{},[1115,33833,33835],{"className":33834},[1668],[1670,33836,33837],{"xmlns":1672},[1674,33838,33839,33852],{},[1677,33840,33841,33843,33845,33848,33850],{},[1683,33842,1110],{},[1811,33844,2101],{},[1687,33846,33847],{},"0,8847",[1811,33849,1813],{},[1687,33851,4105],{},[1691,33853,33854],{"encoding":1693},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[16860,33857,33859],{"id":33858},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,33861,33862],{},"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.",[1503,33864,33865,33885,33905],{},[1265,33866,33867,33884],{},[1115,33868,33870],{"className":33869},[1668],[1670,33871,33872],{"xmlns":1672},[1674,33873,33874,33882],{},[1677,33875,33876],{},[1680,33877,33878,33880],{},[1683,33879,1685],{},[1687,33881,1689],{},[1691,33883,1694],{"encoding":1693},": data mají normální rozdělení.",[1265,33886,33887,33904],{},[1115,33888,33890],{"className":33889},[1668],[1670,33891,33892],{"xmlns":1672},[1674,33893,33894,33902],{},[1677,33895,33896],{},[1680,33897,33898,33900],{},[1683,33899,1685],{},[1687,33901,1914],{},[1691,33903,3116],{"encoding":1693},": data nemají normální rozdělení.",[1265,33906,33907,33908,33934],{},"Testová statistika ",[1115,33909,33911],{"className":33910},[1668],[1670,33912,33913],{"xmlns":1672},[1674,33914,33915,33931],{},[1677,33916,33917,33919,33921,33923,33925,33927,33929],{},[1683,33918,1729],{},[1811,33920,7133],{},[1811,33922,8539],{"stretchy":1993},[1687,33924,1689],{},[1811,33926,1917],{"separator":1121},[1687,33928,1914],{},[1811,33930,7558],{"stretchy":1993},[1691,33932,33933],{"encoding":1693},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,33936,33937,33938,33951,33952,1418,33972,33989,33990,1418,34010,34027],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,33939,33941],{"className":33940},[1668],[1670,33942,33943],{"xmlns":1672},[1674,33944,33945,33949],{},[1677,33946,33947],{},[1683,33948,1729],{},[1691,33950,1729],{"encoding":1693}," se běžně neudává): ",[1115,33953,33955],{"className":33954},[1668],[1670,33956,33957],{"xmlns":1672},[1674,33958,33959,33969],{},[1677,33960,33961,33963,33965,33967],{},[1683,33962,1110],{},[1811,33964,3471],{},[1683,33966,3485],{},[1811,33968,7664],{},[1691,33970,33971],{"encoding":1693},"p \\ge \\alpha \\Rightarrow",[1115,33973,33975],{"className":33974},[1668],[1670,33976,33977],{"xmlns":1672},[1674,33978,33979,33987],{},[1677,33980,33981],{},[1680,33982,33983,33985],{},[1683,33984,1685],{},[1687,33986,1689],{},[1691,33988,1694],{"encoding":1693}," nezamítáme (normalitu lze předpokládat); ",[1115,33991,33993],{"className":33992},[1668],[1670,33994,33995],{"xmlns":1672},[1674,33996,33997,34007],{},[1677,33998,33999,34001,34003,34005],{},[1683,34000,1110],{},[1811,34002,4453],{},[1683,34004,3485],{},[1811,34006,7664],{},[1691,34008,34009],{"encoding":1693},"p \u003C \\alpha \\Rightarrow",[1115,34011,34013],{"className":34012},[1668],[1670,34014,34015],{"xmlns":1672},[1674,34016,34017,34025],{},[1677,34018,34019],{},[1680,34020,34021,34023],{},[1683,34022,1685],{},[1687,34024,1689],{},[1691,34026,1694],{"encoding":1693}," zamítáme (předpoklad normality je porušen).",[3814,34029,34031],{"className":3816,"code":34030,"language":71,"meta":1603,"style":1603},"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",[3590,34032,34033,34087],{"__ignoreMap":1603},[1115,34034,34035,34037,34039,34041,34043,34045,34047,34049,34051,34053,34055,34057,34059,34061,34063,34065,34067,34069,34071,34073,34075,34077,34079,34081,34083,34085],{"class":3822,"line":10},[1115,34036,28694],{"class":3825},[1115,34038,3830],{"class":3829},[1115,34040,3956],{"class":3833},[1115,34042,1994],{"class":3837},[1115,34044,28703],{"class":3845},[1115,34046,1917],{"class":3829},[1115,34048,28708],{"class":3845},[1115,34050,1917],{"class":3829},[1115,34052,28713],{"class":3845},[1115,34054,1917],{"class":3829},[1115,34056,28718],{"class":3845},[1115,34058,1917],{"class":3829},[1115,34060,28723],{"class":3845},[1115,34062,1917],{"class":3829},[1115,34064,28728],{"class":3845},[1115,34066,1917],{"class":3829},[1115,34068,28718],{"class":3845},[1115,34070,1917],{"class":3829},[1115,34072,28737],{"class":3845},[1115,34074,1917],{"class":3829},[1115,34076,28723],{"class":3845},[1115,34078,1917],{"class":3829},[1115,34080,28746],{"class":3845},[1115,34082,1917],{"class":3829},[1115,34084,28718],{"class":3845},[1115,34086,4022],{"class":3837},[1115,34088,34089,34091,34093,34095],{"class":3822,"line":27},[1115,34090,17689],{"class":3833},[1115,34092,1994],{"class":3837},[1115,34094,28694],{"class":3825},[1115,34096,4022],{"class":3837},[3814,34098,34101],{"className":34099,"code":34100,"language":4044,"meta":1603},[4042],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3590,34102,34100],{"__ignoreMap":1603},[1110,34104,34105,34106,34125],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,34107,34109],{"className":34108},[1668],[1670,34110,34111],{"xmlns":1672},[1674,34112,34113,34122],{},[1677,34114,34115,34117,34119],{},[1683,34116,1110],{},[1811,34118,2101],{},[1687,34120,34121],{},"0,7744",[1691,34123,34124],{"encoding":1693},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,34127,34129,34136,34139,34506,34512],{"className":34128,"dataCallout":3597},[1106,3596],[1110,34130,34132,34135],{"className":34131},[1113],[1115,34133],{"className":34134,"ariaHidden":1121},[1118,3604,1120],"Příklad: Doba do poruchy výrobku",[1110,34137,34138],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3814,34140,34142],{"className":3816,"code":34141,"language":71,"meta":1603,"style":1603},"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",[3590,34143,34144,34235,34313,34401,34435,34445,34455,34465,34475],{"__ignoreMap":1603},[1115,34145,34146,34148,34150,34152,34154,34156,34158,34160,34162,34164,34166,34168,34170,34172,34174,34176,34178,34180,34182,34184,34186,34188,34190,34192,34194,34197,34199,34201,34203,34205,34207,34209,34211,34213,34215,34217,34219,34221,34223,34225,34227,34229,34231,34233],{"class":3822,"line":10},[1115,34147,14190],{"class":3825},[1115,34149,3830],{"class":3829},[1115,34151,3956],{"class":3833},[1115,34153,1994],{"class":3837},[1115,34155,14199],{"class":3845},[1115,34157,1917],{"class":3829},[1115,34159,14204],{"class":3845},[1115,34161,1917],{"class":3829},[1115,34163,14209],{"class":3845},[1115,34165,1917],{"class":3829},[1115,34167,14214],{"class":3845},[1115,34169,1917],{"class":3829},[1115,34171,9591],{"class":3845},[1115,34173,1917],{"class":3829},[1115,34175,4301],{"class":3845},[1115,34177,1917],{"class":3829},[1115,34179,3855],{"class":3845},[1115,34181,1917],{"class":3829},[1115,34183,14231],{"class":3845},[1115,34185,1917],{"class":3829},[1115,34187,10108],{"class":3845},[1115,34189,1917],{"class":3829},[1115,34191,14240],{"class":3845},[1115,34193,1917],{"class":3829},[1115,34195,34196],{"class":3845}," 367",[1115,34198,1917],{"class":3829},[1115,34200,14252],{"class":3845},[1115,34202,1917],{"class":3829},[1115,34204,14257],{"class":3845},[1115,34206,1917],{"class":3829},[1115,34208,14262],{"class":3845},[1115,34210,1917],{"class":3829},[1115,34212,3873],{"class":3845},[1115,34214,1917],{"class":3829},[1115,34216,14271],{"class":3845},[1115,34218,1917],{"class":3829},[1115,34220,14276],{"class":3845},[1115,34222,1917],{"class":3829},[1115,34224,14281],{"class":3845},[1115,34226,1917],{"class":3829},[1115,34228,14286],{"class":3845},[1115,34230,1917],{"class":3829},[1115,34232,14291],{"class":3845},[1115,34234,3858],{"class":3829},[1115,34236,34237,34239,34241,34243,34245,34247,34249,34251,34253,34255,34257,34259,34261,34263,34265,34267,34269,34271,34273,34275,34277,34279,34281,34283,34285,34287,34289,34291,34293,34295,34297,34299,34301,34303,34305,34307,34309,34311],{"class":3822,"line":27},[1115,34238,14298],{"class":3845},[1115,34240,1917],{"class":3829},[1115,34242,14303],{"class":3845},[1115,34244,1917],{"class":3829},[1115,34246,14308],{"class":3845},[1115,34248,1917],{"class":3829},[1115,34250,14313],{"class":3845},[1115,34252,1917],{"class":3829},[1115,34254,14318],{"class":3845},[1115,34256,1917],{"class":3829},[1115,34258,3873],{"class":3845},[1115,34260,1917],{"class":3829},[1115,34262,14327],{"class":3845},[1115,34264,1917],{"class":3829},[1115,34266,3855],{"class":3845},[1115,34268,1917],{"class":3829},[1115,34270,14336],{"class":3845},[1115,34272,1917],{"class":3829},[1115,34274,14341],{"class":3845},[1115,34276,1917],{"class":3829},[1115,34278,15433],{"class":3845},[1115,34280,1917],{"class":3829},[1115,34282,14353],{"class":3845},[1115,34284,1917],{"class":3829},[1115,34286,14358],{"class":3845},[1115,34288,1917],{"class":3829},[1115,34290,14252],{"class":3845},[1115,34292,1917],{"class":3829},[1115,34294,14367],{"class":3845},[1115,34296,1917],{"class":3829},[1115,34298,14372],{"class":3845},[1115,34300,1917],{"class":3829},[1115,34302,14377],{"class":3845},[1115,34304,1917],{"class":3829},[1115,34306,14382],{"class":3845},[1115,34308,1917],{"class":3829},[1115,34310,14387],{"class":3845},[1115,34312,3858],{"class":3829},[1115,34314,34315,34317,34319,34322,34324,34326,34328,34330,34332,34334,34336,34338,34340,34342,34344,34346,34348,34350,34352,34354,34356,34358,34360,34363,34365,34367,34369,34371,34373,34375,34377,34379,34381,34383,34385,34387,34389,34391,34393,34395,34397,34399],{"class":3822,"line":148},[1115,34316,14497],{"class":3845},[1115,34318,1917],{"class":3829},[1115,34320,34321],{"class":3845}," 74",[1115,34323,1917],{"class":3829},[1115,34325,14404],{"class":3845},[1115,34327,1917],{"class":3829},[1115,34329,14409],{"class":3845},[1115,34331,1917],{"class":3829},[1115,34333,14414],{"class":3845},[1115,34335,1917],{"class":3829},[1115,34337,14419],{"class":3845},[1115,34339,1917],{"class":3829},[1115,34341,14336],{"class":3845},[1115,34343,1917],{"class":3829},[1115,34345,14428],{"class":3845},[1115,34347,1917],{"class":3829},[1115,34349,10969],{"class":3845},[1115,34351,1917],{"class":3829},[1115,34353,14437],{"class":3845},[1115,34355,1917],{"class":3829},[1115,34357,14442],{"class":3845},[1115,34359,1917],{"class":3829},[1115,34361,34362],{"class":3845}," 194",[1115,34364,1917],{"class":3829},[1115,34366,4266],{"class":3845},[1115,34368,1917],{"class":3829},[1115,34370,14458],{"class":3845},[1115,34372,1917],{"class":3829},[1115,34374,14463],{"class":3845},[1115,34376,1917],{"class":3829},[1115,34378,14468],{"class":3845},[1115,34380,1917],{"class":3829},[1115,34382,14419],{"class":3845},[1115,34384,1917],{"class":3829},[1115,34386,10108],{"class":3845},[1115,34388,1917],{"class":3829},[1115,34390,4301],{"class":3845},[1115,34392,1917],{"class":3829},[1115,34394,14485],{"class":3845},[1115,34396,1917],{"class":3829},[1115,34398,14490],{"class":3845},[1115,34400,3858],{"class":3829},[1115,34402,34403,34405,34407,34409,34411,34413,34415,34417,34419,34421,34423,34425,34427,34429,34431,34433],{"class":3822,"line":111},[1115,34404,14497],{"class":3845},[1115,34406,1917],{"class":3829},[1115,34408,3850],{"class":3845},[1115,34410,1917],{"class":3829},[1115,34412,14506],{"class":3845},[1115,34414,1917],{"class":3829},[1115,34416,14511],{"class":3845},[1115,34418,1917],{"class":3829},[1115,34420,14516],{"class":3845},[1115,34422,1917],{"class":3829},[1115,34424,14521],{"class":3845},[1115,34426,1917],{"class":3829},[1115,34428,14252],{"class":3845},[1115,34430,1917],{"class":3829},[1115,34432,14530],{"class":3845},[1115,34434,4022],{"class":3837},[1115,34436,34437,34439,34441,34443],{"class":3822,"line":96},[1115,34438,12252],{"class":3833},[1115,34440,1994],{"class":3837},[1115,34442,14190],{"class":3825},[1115,34444,4022],{"class":3837},[1115,34446,34447,34449,34451,34453],{"class":3822,"line":89},[1115,34448,12274],{"class":3833},[1115,34450,1994],{"class":3837},[1115,34452,14190],{"class":3825},[1115,34454,4022],{"class":3837},[1115,34456,34457,34459,34461,34463],{"class":3822,"line":82},[1115,34458,12974],{"class":3833},[1115,34460,1994],{"class":3837},[1115,34462,14190],{"class":3825},[1115,34464,4022],{"class":3837},[1115,34466,34467,34469,34471,34473],{"class":3822,"line":75},[1115,34468,17689],{"class":3833},[1115,34470,1994],{"class":3837},[1115,34472,14190],{"class":3825},[1115,34474,4022],{"class":3837},[1115,34476,34477,34479,34481,34483,34485,34488,34490,34492,34494,34496,34498,34500,34502,34504],{"class":3822,"line":4012},[1115,34478,33794],{"class":3833},[1115,34480,1994],{"class":3837},[1115,34482,14190],{"class":3825},[1115,34484,1917],{"class":3829},[1115,34486,34487],{"class":3961}," \"pexp\"",[1115,34489,1917],{"class":3829},[1115,34491,10182],{"class":3825},[1115,34493,3918],{"class":3829},[1115,34495,4762],{"class":3845},[1115,34497,10189],{"class":3829},[1115,34499,9345],{"class":3833},[1115,34501,1994],{"class":3837},[1115,34503,14190],{"class":3825},[1115,34505,9607],{"class":3837},[3814,34507,34510],{"className":34508,"code":34509,"language":4044,"meta":1603},[4042],"[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",[3590,34511,34509],{"__ignoreMap":1603},[1110,34513,34514,34515,34534,34535,34552,34553,34572],{},"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 (",[1115,34516,34518],{"className":34517},[1668],[1670,34519,34520],{"xmlns":1672},[1674,34521,34522,34531],{},[1677,34523,34524,34526,34528],{},[1683,34525,1110],{},[1811,34527,4453],{},[1687,34529,34530],{},"0,0001",[1691,34532,34533],{"encoding":1693},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,34536,34538],{"className":34537},[1668],[1670,34539,34540],{"xmlns":1672},[1674,34541,34542,34550],{},[1677,34543,34544],{},[2843,34545,34546,34548],{"accent":1121},[1683,34547,6834],{},[1811,34549,11573],{},[1691,34551,21677],{"encoding":1693}," shodu nezamítá (",[1115,34554,34556],{"className":34555},[1668],[1670,34557,34558],{"xmlns":1672},[1674,34559,34560,34569],{},[1677,34561,34562,34564,34566],{},[1683,34563,1110],{},[1811,34565,2101],{},[1687,34567,34568],{},"0,8421",[1691,34570,34571],{"encoding":1693},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,34574,34575],{},[4504,34576],{"alt":34577,"className":34578,"src":34579},"mask-th-exponencialni-shoda",[1131,4508],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1153,34581,34583],{"id":34582},"neparametrické-testy","Neparametrické testy",[1110,34585,34586,34587,4728,34589,34613],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1136,34588,11665],{},[1115,34590,34592],{"className":34591},[1668],[1670,34593,34594],{"xmlns":1672},[1674,34595,34596,34610],{},[1677,34597,34598],{},[1680,34599,34600,34602],{},[1683,34601,6834],{},[1677,34603,34604,34606,34608],{},[1687,34605,1689],{},[1811,34607,1917],{"separator":1121},[1687,34609,10040],{},[1691,34611,34612],{"encoding":1693},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[16860,34615,34617],{"id":34616},"wilcoxonovy-testy","Wilcoxonovy testy",[1158,34619,34620,34665],{},[1161,34621,34622],{},[1164,34623,34624,34643,34662],{},[1167,34625,34626],{},[1115,34627,34629],{"className":34628},[1668],[1670,34630,34631],{"xmlns":1672},[1674,34632,34633,34641],{},[1677,34634,34635],{},[1680,34636,34637,34639],{},[1683,34638,1685],{},[1687,34640,1689],{},[1691,34642,1694],{"encoding":1693},[1167,34644,34645],{},[1115,34646,34648],{"className":34647},[1668],[1670,34649,34650],{"xmlns":1672},[1674,34651,34652,34660],{},[1677,34653,34654],{},[1680,34655,34656,34658],{},[1683,34657,1685],{},[1687,34659,1914],{},[1691,34661,3116],{"encoding":1693},[1167,34663,34664],{},"Příkaz v R",[1174,34666,34667,34734,34801],{},[1164,34668,34669,34699,34729],{},[1179,34670,34671],{},[1115,34672,34674],{"className":34673},[1668],[1670,34675,34676],{"xmlns":1672},[1674,34677,34678,34696],{},[1677,34679,34680,34692,34694],{},[1680,34681,34682,34684],{},[1683,34683,6834],{},[1677,34685,34686,34688,34690],{},[1687,34687,1689],{},[1811,34689,1917],{"separator":1121},[1687,34691,10040],{},[1811,34693,6849],{},[1683,34695,3840],{},[1691,34697,34698],{"encoding":1693},"x_{0,5} \\le c",[1179,34700,34701],{},[1115,34702,34704],{"className":34703},[1668],[1670,34705,34706],{"xmlns":1672},[1674,34707,34708,34726],{},[1677,34709,34710,34722,34724],{},[1680,34711,34712,34714],{},[1683,34713,6834],{},[1677,34715,34716,34718,34720],{},[1687,34717,1689],{},[1811,34719,1917],{"separator":1121},[1687,34721,10040],{},[1811,34723,1813],{},[1683,34725,3840],{},[1691,34727,34728],{"encoding":1693},"x_{0,5} > c",[1179,34730,34731],{},[3590,34732,34733],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1164,34735,34736,34766,34796],{},[1179,34737,34738],{},[1115,34739,34741],{"className":34740},[1668],[1670,34742,34743],{"xmlns":1672},[1674,34744,34745,34763],{},[1677,34746,34747,34759,34761],{},[1680,34748,34749,34751],{},[1683,34750,6834],{},[1677,34752,34753,34755,34757],{},[1687,34754,1689],{},[1811,34756,1917],{"separator":1121},[1687,34758,10040],{},[1811,34760,2101],{},[1683,34762,3840],{},[1691,34764,34765],{"encoding":1693},"x_{0,5} = c",[1179,34767,34768],{},[1115,34769,34771],{"className":34770},[1668],[1670,34772,34773],{"xmlns":1672},[1674,34774,34775,34793],{},[1677,34776,34777,34789,34791],{},[1680,34778,34779,34781],{},[1683,34780,6834],{},[1677,34782,34783,34785,34787],{},[1687,34784,1689],{},[1811,34786,1917],{"separator":1121},[1687,34788,10040],{},[1811,34790,11070],{"mathvariant":2240},[1683,34792,3840],{},[1691,34794,34795],{"encoding":1693},"x_{0,5} \\neq c",[1179,34797,34798],{},[3590,34799,34800],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1164,34802,34803,34833,34863],{},[1179,34804,34805],{},[1115,34806,34808],{"className":34807},[1668],[1670,34809,34810],{"xmlns":1672},[1674,34811,34812,34830],{},[1677,34813,34814,34826,34828],{},[1680,34815,34816,34818],{},[1683,34817,6834],{},[1677,34819,34820,34822,34824],{},[1687,34821,1689],{},[1811,34823,1917],{"separator":1121},[1687,34825,10040],{},[1811,34827,3471],{},[1683,34829,3840],{},[1691,34831,34832],{"encoding":1693},"x_{0,5} \\ge c",[1179,34834,34835],{},[1115,34836,34838],{"className":34837},[1668],[1670,34839,34840],{"xmlns":1672},[1674,34841,34842,34860],{},[1677,34843,34844,34856,34858],{},[1680,34845,34846,34848],{},[1683,34847,6834],{},[1677,34849,34850,34852,34854],{},[1687,34851,1689],{},[1811,34853,1917],{"separator":1121},[1687,34855,10040],{},[1811,34857,4453],{},[1683,34859,3840],{},[1691,34861,34862],{"encoding":1693},"x_{0,5} \u003C c",[1179,34864,34865],{},[3590,34866,34867],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,34869,34870,34873,34874,1497],{},[1420,34871,34872],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,34875,34877],{"className":34876},[1668],[1670,34878,34879],{"xmlns":1672},[1674,34880,34881,34885],{},[1677,34882,34883],{},[1683,34884,3840],{},[1691,34886,3840],{"encoding":1693},[1110,34888,34889,34892,34893,8948,34931,34944,34945,1497],{},[1420,34890,34891],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,34894,34896],{"className":34895},[1668],[1670,34897,34898],{"xmlns":1672},[1674,34899,34900,34928],{},[1677,34901,34902,34914,34916],{},[1680,34903,34904,34906],{},[1683,34905,6834],{},[1677,34907,34908,34910,34912],{},[1687,34909,1689],{},[1811,34911,1917],{"separator":1121},[1687,34913,10040],{},[1811,34915,3184],{},[1680,34917,34918,34920],{},[1683,34919,7244],{},[1677,34921,34922,34924,34926],{},[1687,34923,1689],{},[1811,34925,1917],{"separator":1121},[1687,34927,10040],{},[1691,34929,34930],{"encoding":1693},"x_{0,5}-y_{0,5}",[1115,34932,34934],{"className":34933},[1668],[1670,34935,34936],{"xmlns":1672},[1674,34937,34938,34942],{},[1677,34939,34940],{},[1683,34941,3840],{},[1691,34943,3840],{"encoding":1693},"; v R se volá se stejnými argumenty jako výše a navíc ",[3590,34946,34947],{},"paired = TRUE",[1110,34949,34950,34953,34954,34956],{},[1420,34951,34952],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3590,34955,25560],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3814,34958,34960],{"className":3816,"code":34959,"language":71,"meta":1603,"style":1603},"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",[3590,34961,34962,35032,35090],{"__ignoreMap":1603},[1115,34963,34964,34966,34968,34970,34972,34974,34976,34978,34980,34982,34984,34986,34988,34990,34992,34994,34996,34998,35000,35002,35004,35006,35008,35010,35012,35014,35016,35018,35020,35022,35024,35026,35028,35030],{"class":3822,"line":10},[1115,34965,33206],{"class":3825},[1115,34967,3830],{"class":3829},[1115,34969,3956],{"class":3833},[1115,34971,1994],{"class":3837},[1115,34973,33215],{"class":3845},[1115,34975,1917],{"class":3829},[1115,34977,15433],{"class":3845},[1115,34979,1917],{"class":3829},[1115,34981,33224],{"class":3845},[1115,34983,1917],{"class":3829},[1115,34985,33229],{"class":3845},[1115,34987,1917],{"class":3829},[1115,34989,33234],{"class":3845},[1115,34991,1917],{"class":3829},[1115,34993,33239],{"class":3845},[1115,34995,1917],{"class":3829},[1115,34997,18585],{"class":3845},[1115,34999,1917],{"class":3829},[1115,35001,14291],{"class":3845},[1115,35003,1917],{"class":3829},[1115,35005,33234],{"class":3845},[1115,35007,1917],{"class":3829},[1115,35009,33224],{"class":3845},[1115,35011,1917],{"class":3829},[1115,35013,33260],{"class":3845},[1115,35015,1917],{"class":3829},[1115,35017,33265],{"class":3845},[1115,35019,1917],{"class":3829},[1115,35021,33270],{"class":3845},[1115,35023,1917],{"class":3829},[1115,35025,33234],{"class":3845},[1115,35027,1917],{"class":3829},[1115,35029,33279],{"class":3845},[1115,35031,4022],{"class":3837},[1115,35033,35034,35036,35038,35040,35042,35044,35046,35048,35050,35052,35054,35056,35058,35060,35062,35064,35066,35068,35070,35072,35074,35076,35078,35080,35082,35084,35086,35088],{"class":3822,"line":27},[1115,35035,33286],{"class":3825},[1115,35037,3830],{"class":3829},[1115,35039,3956],{"class":3833},[1115,35041,1994],{"class":3837},[1115,35043,21949],{"class":3845},[1115,35045,1917],{"class":3829},[1115,35047,33229],{"class":3845},[1115,35049,1917],{"class":3829},[1115,35051,33303],{"class":3845},[1115,35053,1917],{"class":3829},[1115,35055,33308],{"class":3845},[1115,35057,1917],{"class":3829},[1115,35059,33313],{"class":3845},[1115,35061,1917],{"class":3829},[1115,35063,33313],{"class":3845},[1115,35065,1917],{"class":3829},[1115,35067,14291],{"class":3845},[1115,35069,1917],{"class":3829},[1115,35071,33229],{"class":3845},[1115,35073,1917],{"class":3829},[1115,35075,33229],{"class":3845},[1115,35077,1917],{"class":3829},[1115,35079,33334],{"class":3845},[1115,35081,1917],{"class":3829},[1115,35083,33265],{"class":3845},[1115,35085,1917],{"class":3829},[1115,35087,33229],{"class":3845},[1115,35089,4022],{"class":3837},[1115,35091,35092,35095,35097,35099,35101,35103,35105,35107,35109,35111],{"class":3822,"line":148},[1115,35093,35094],{"class":3833},"wilcox.test",[1115,35096,1994],{"class":3837},[1115,35098,33206],{"class":3825},[1115,35100,1917],{"class":3829},[1115,35102,33357],{"class":3825},[1115,35104,1917],{"class":3829},[1115,35106,28197],{"class":3825},[1115,35108,3918],{"class":3829},[1115,35110,28202],{"class":3961},[1115,35112,4022],{"class":3837},[3814,35114,35117],{"className":35115,"code":35116,"language":4044,"meta":1603},[4042],"    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",[3590,35118,35116],{"__ignoreMap":1603},[1110,35120,35121,35144],{},[1115,35122,35124],{"className":35123},[1668],[1670,35125,35126],{"xmlns":1672},[1674,35127,35128,35141],{},[1677,35129,35130,35132,35134,35137,35139],{},[1683,35131,1110],{},[1811,35133,2101],{},[1687,35135,35136],{},"0,315",[1811,35138,1813],{},[1687,35140,4105],{},[1691,35142,35143],{"encoding":1693},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,35146,35148,35155,35177,35288,35294],{"className":35147,"dataCallout":3597},[1106,3596],[1110,35149,35151,35154],{"className":35150},[1113],[1115,35152],{"className":35153,"ariaHidden":1121},[1118,3604,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,35156,35157,35158,35176],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,35159,35161],{"className":35160},[1668],[1670,35162,35163],{"xmlns":1672},[1674,35164,35165,35173],{},[1677,35166,35167,35169,35171],{},[1683,35168,1110],{},[1811,35170,2101],{},[1687,35172,30250],{},[1691,35174,35175],{"encoding":1693},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3814,35178,35180],{"className":3816,"code":35179,"language":71,"meta":1603,"style":1603},"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",[3590,35181,35182,35224,35266],{"__ignoreMap":1603},[1115,35183,35184,35186,35188,35190,35192,35194,35196,35198,35200,35202,35204,35206,35208,35210,35212,35214,35216,35218,35220,35222],{"class":3822,"line":10},[1115,35185,30053],{"class":3825},[1115,35187,3830],{"class":3829},[1115,35189,3956],{"class":3833},[1115,35191,1994],{"class":3837},[1115,35193,30062],{"class":3845},[1115,35195,1917],{"class":3829},[1115,35197,30067],{"class":3845},[1115,35199,1917],{"class":3829},[1115,35201,30072],{"class":3845},[1115,35203,1917],{"class":3829},[1115,35205,30077],{"class":3845},[1115,35207,1917],{"class":3829},[1115,35209,30082],{"class":3845},[1115,35211,1917],{"class":3829},[1115,35213,30087],{"class":3845},[1115,35215,1917],{"class":3829},[1115,35217,30092],{"class":3845},[1115,35219,1917],{"class":3829},[1115,35221,30097],{"class":3845},[1115,35223,4022],{"class":3837},[1115,35225,35226,35228,35230,35232,35234,35236,35238,35240,35242,35244,35246,35248,35250,35252,35254,35256,35258,35260,35262,35264],{"class":3822,"line":27},[1115,35227,30104],{"class":3825},[1115,35229,3830],{"class":3829},[1115,35231,3956],{"class":3833},[1115,35233,1994],{"class":3837},[1115,35235,30113],{"class":3845},[1115,35237,1917],{"class":3829},[1115,35239,30118],{"class":3845},[1115,35241,1917],{"class":3829},[1115,35243,30123],{"class":3845},[1115,35245,1917],{"class":3829},[1115,35247,30128],{"class":3845},[1115,35249,1917],{"class":3829},[1115,35251,30133],{"class":3845},[1115,35253,1917],{"class":3829},[1115,35255,30138],{"class":3845},[1115,35257,1917],{"class":3829},[1115,35259,30143],{"class":3845},[1115,35261,1917],{"class":3829},[1115,35263,30148],{"class":3845},[1115,35265,4022],{"class":3837},[1115,35267,35268,35270,35272,35274,35276,35278,35280,35282,35284,35286],{"class":3822,"line":148},[1115,35269,35094],{"class":3833},[1115,35271,1994],{"class":3837},[1115,35273,30053],{"class":3825},[1115,35275,1917],{"class":3829},[1115,35277,30163],{"class":3825},[1115,35279,1917],{"class":3829},[1115,35281,30168],{"class":3825},[1115,35283,3918],{"class":3829},[1115,35285,3931],{"class":3845},[1115,35287,4022],{"class":3837},[3814,35289,35292],{"className":35290,"code":35291,"language":4044,"meta":1603},[4042],"    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",[3590,35293,35291],{"__ignoreMap":1603},[1110,35295,35296,35319],{},[1115,35297,35299],{"className":35298},[1668],[1670,35300,35301],{"xmlns":1672},[1674,35302,35303,35316],{},[1677,35304,35305,35307,35309,35312,35314],{},[1683,35306,1110],{},[1811,35308,2101],{},[1687,35310,35311],{},"0,1484",[1811,35313,1813],{},[1687,35315,4105],{},[1691,35317,35318],{"encoding":1693},"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.",[16860,35321,35323],{"id":35322},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,35325,35326,35327,35344],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,35328,35330],{"className":35329},[1668],[1670,35331,35332],{"xmlns":1672},[1674,35333,35334,35342],{},[1677,35335,35336],{},[1680,35337,35338,35340],{},[1683,35339,1685],{},[1687,35341,1689],{},[1691,35343,1694],{"encoding":1693},": všechny výběry pocházejí ze stejného rozdělení.",[3814,35346,35348],{"className":3816,"code":35347,"language":71,"meta":1603,"style":1603},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3590,35349,35350],{"__ignoreMap":1603},[1115,35351,35352,35355,35357,35360,35362,35365,35367,35369,35371,35374],{"class":3822,"line":10},[1115,35353,35354],{"class":3833},"kruskal.test",[1115,35356,1994],{"class":3837},[1115,35358,35359],{"class":3825},"kvantitativní_proměnná",[1115,35361,16971],{"class":3829},[1115,35363,35364],{"class":3825}," faktor",[1115,35366,1917],{"class":3829},[1115,35368,20279],{"class":3825},[1115,35370,3918],{"class":3829},[1115,35372,35373],{"class":3825}," soubor",[1115,35375,4022],{"class":3837},[16860,35377,35379],{"id":35378},"mediánový-test","Mediánový test",[1110,35381,35382,35383,35400,35401,2077],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,35384,35386],{"className":35385},[1668],[1670,35387,35388],{"xmlns":1672},[1674,35389,35390,35398],{},[1677,35391,35392],{},[1680,35393,35394,35396],{},[1683,35395,1685],{},[1687,35397,1689],{},[1691,35399,1694],{"encoding":1693},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3590,35402,35403],{},"agricolae",[3814,35405,35407],{"className":3816,"code":35406,"language":71,"meta":1603,"style":1603},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3590,35408,35409,35419],{"__ignoreMap":1603},[1115,35410,35411,35413,35415,35417],{"class":3822,"line":10},[1115,35412,17509],{"class":3829},[1115,35414,1994],{"class":3837},[1115,35416,35403],{"class":3825},[1115,35418,4022],{"class":3837},[1115,35420,35421,35424,35426,35428,35430,35432],{"class":3822,"line":27},[1115,35422,35423],{"class":3833},"Median.test",[1115,35425,1994],{"class":3837},[1115,35427,35359],{"class":3825},[1115,35429,1917],{"class":3829},[1115,35431,35364],{"class":3825},[1115,35433,4022],{"class":3837},[16860,35435,35437],{"id":35436},"friedmanův-test","Friedmanův test",[1110,35439,35440,35441,35458,35459,35497],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,35442,35444],{"className":35443},[1668],[1670,35445,35446],{"xmlns":1672},[1674,35447,35448,35456],{},[1677,35449,35450],{},[1680,35451,35452,35454],{},[1683,35453,1685],{},[1687,35455,1689],{},[1691,35457,1694],{"encoding":1693},": distribuční funkce veličin ",[1115,35460,35462],{"className":35461},[1668],[1670,35463,35464],{"xmlns":1672},[1674,35465,35466,35494],{},[1677,35467,35468,35478,35480,35482,35484],{},[1680,35469,35470,35472],{},[1683,35471,6846],{},[1677,35473,35474,35476],{},[1683,35475,1997],{},[1687,35477,1914],{},[1811,35479,1917],{"separator":1121},[1811,35481,1920],{},[1811,35483,1917],{"separator":1121},[1680,35485,35486,35488],{},[1683,35487,6846],{},[1677,35489,35490,35492],{},[1683,35491,1997],{},[1683,35493,7374],{},[1691,35495,35496],{"encoding":1693},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3814,35499,35501],{"className":3816,"code":35500,"language":71,"meta":1603,"style":1603},"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",[3590,35502,35503,35533,35538],{"__ignoreMap":1603},[1115,35504,35505,35508,35510,35512,35514,35517,35520,35523,35525,35527,35529,35531],{"class":3822,"line":10},[1115,35506,35507],{"class":3833},"friedman.test",[1115,35509,1994],{"class":3837},[1115,35511,35359],{"class":3825},[1115,35513,16971],{"class":3829},[1115,35515,35516],{"class":3825}," faktor_A",[1115,35518,35519],{"class":3829}," |",[1115,35521,35522],{"class":3825}," faktor_B",[1115,35524,1917],{"class":3829},[1115,35526,20279],{"class":3825},[1115,35528,3918],{"class":3829},[1115,35530,35373],{"class":3825},[1115,35532,4022],{"class":3837},[1115,35534,35535],{"class":3822,"line":27},[1115,35536,35537],{"class":12147},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,35539,35540,35542,35544,35546,35548,35550,35552,35554],{"class":3822,"line":148},[1115,35541,35507],{"class":3833},[1115,35543,1994],{"class":3837},[1115,35545,35359],{"class":3825},[1115,35547,1917],{"class":3829},[1115,35549,35516],{"class":3825},[1115,35551,1917],{"class":3829},[1115,35553,35522],{"class":3825},[1115,35555,4022],{"class":3837},[1153,35557,35559],{"id":35558},"přehled-testů","Přehled testů",[1110,35561,35562],{},[4504,35563],{"alt":35564,"className":35565,"src":35566},"mask-ilu-volba-testu",[1131,4508],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1158,35568,35569,35582],{},[1161,35570,35571],{},[1164,35572,35573,35576,35579],{},[1167,35574,35575],{},"Situace",[1167,35577,35578],{},"Test",[1167,35580,35581],{},"R funkce",[1174,35583,35584,35597,35610,35622,35635,35650,35662,35675,35688,35701,35713,35728],{},[1164,35585,35586,35589,35592],{},[1179,35587,35588],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1179,35590,35591],{},"jednovýběrový t-test",[1179,35593,35594],{},[3590,35595,35596],{},"t.test(x, mu = ..., alternative = ...)",[1164,35598,35599,35602,35605],{},[1179,35600,35601],{},"Rozdíl dvou závislých měření, diference normální",[1179,35603,35604],{},"párový t-test",[1179,35606,35607],{},[3590,35608,35609],{},"t.test(x, y, paired = TRUE)",[1164,35611,35612,35615,35617],{},[1179,35613,35614],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1179,35616,20187],{},[1179,35618,35619],{},[3590,35620,35621],{},"var.test(x, y)",[1164,35623,35624,35627,35630],{},[1179,35625,35626],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1179,35628,35629],{},"dvouvýběrový t-test",[1179,35631,35632],{},[3590,35633,35634],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1164,35636,35637,35640,35642],{},[1179,35638,35639],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1179,35641,33443],{},[1179,35643,35644,3071,35647],{},[3590,35645,35646],{},"ks.test(x, \"pnorm\", mu, sigma)",[3590,35648,35649],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1164,35651,35652,35655,35657],{},[1179,35653,35654],{},"Normalita dat",[1179,35656,33859],{},[1179,35658,35659],{},[3590,35660,35661],{},"shapiro.test(x)",[1164,35663,35664,35667,35670],{},[1179,35665,35666],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1179,35668,35669],{},"jednovýběrový Wilcoxonův test",[1179,35671,35672],{},[3590,35673,35674],{},"wilcox.test(x, mu = c, alternative = ...)",[1164,35676,35677,35680,35683],{},[1179,35678,35679],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1179,35681,35682],{},"párový Wilcoxonův test",[1179,35684,35685],{},[3590,35686,35687],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1164,35689,35690,35693,35696],{},[1179,35691,35692],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1179,35694,35695],{},"dvouvýběrový Wilcoxonův test",[1179,35697,35698],{},[3590,35699,35700],{},"wilcox.test(x, y)",[1164,35702,35703,35706,35708],{},[1179,35704,35705],{},"Více než dva nezávislé výběry, data nejsou normální",[1179,35707,35323],{},[1179,35709,35710],{},[3590,35711,35712],{},"kruskal.test(y ~ faktor, data)",[1164,35714,35715,35718,35721],{},[1179,35716,35717],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1179,35719,35720],{},"mediánový test",[1179,35722,35723,22777,35726],{},[3590,35724,35725],{},"Median.test(y, faktor)",[3590,35727,35403],{},[1164,35729,35730,35733,35735],{},[1179,35731,35732],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1179,35734,35437],{},[1179,35736,35737],{},[3590,35738,35739],{},"friedman.test(y ~ A | B, data)",[1153,35741,6529],{"id":6528},[1503,35743,35744,35821,35827,35844,35875],{},[1265,35745,35746,35785,35786,33173,35803,35820],{},[1136,35747,35748,35749,35766,35767,35784],{},"Nezamítnutí ",[1115,35750,35752],{"className":35751},[1668],[1670,35753,35754],{"xmlns":1672},[1674,35755,35756,35764],{},[1677,35757,35758],{},[1680,35759,35760,35762],{},[1683,35761,1685],{},[1687,35763,1689],{},[1691,35765,1694],{"encoding":1693}," není důkaz, že ",[1115,35768,35770],{"className":35769},[1668],[1670,35771,35772],{"xmlns":1672},[1674,35773,35774,35782],{},[1677,35775,35776],{},[1680,35777,35778,35780],{},[1683,35779,1685],{},[1687,35781,1689],{},[1691,35783,1694],{"encoding":1693}," platí."," U kabelů A\u002FB vyšlo ",[1115,35787,35789],{"className":35788},[1668],[1670,35790,35791],{"xmlns":1672},[1674,35792,35793,35801],{},[1677,35794,35795,35797,35799],{},[1683,35796,1110],{},[1811,35798,2101],{},[1687,35800,33169],{},[1691,35802,33172],{"encoding":1693},[1115,35804,35806],{"className":35805},[1668],[1670,35807,35808],{"xmlns":1672},[1674,35809,35810,35818],{},[1677,35811,35812],{},[1680,35813,35814,35816],{},[1683,35815,1685],{},[1687,35817,1689],{},[1691,35819,1694],{"encoding":1693}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1265,35822,35823,35826],{},[1136,35824,35825],{},"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.",[1265,35828,35829,35836,35837,35840,35841,35843],{},[1136,35830,35831,30331,35833,35835],{},[3590,35832,32901],{},[3590,35834,28115],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3590,35838,35839],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3590,35842,33152],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1265,35845,35846,35849,35850,35853,35854,35871,35872,1497],{},[1136,35847,35848],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3590,35851,35852],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,35855,35857],{"className":35856},[1668],[1670,35858,35859],{"xmlns":1672},[1674,35860,35861,35869],{},[1677,35862,35863],{},[1680,35864,35865,35867],{},[1683,35866,1685],{},[1687,35868,1914],{},[1691,35870,3116],{"encoding":1693}," v zadání, ne být ponechána na výchozí hodnotě ",[3590,35873,35874],{},"\"two.sided\"",[1265,35876,35877,35880,35881,35894],{},[1136,35878,35879],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,35882,35884],{"className":35883},[1668],[1670,35885,35886],{"xmlns":1672},[1674,35887,35888,35892],{},[1677,35889,35890],{},[1683,35891,1729],{},[1691,35893,1729],{"encoding":1693}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1153,35896,1501],{"id":1500},[1503,35898,35899,35904,35909,35914,35919,35924,35929],{},[1265,35900,35901],{},[1127,35902,1133],{"className":35903,"dataFsResolvedFilePath":1132,"href":1129},[1131],[1265,35905,35906],{},[1127,35907,1515],{"className":35908,"dataFsResolvedFilePath":1275,"href":1273},[1131],[1265,35910,35911],{},[1127,35912,1521],{"className":35913,"dataFsResolvedFilePath":1288,"href":1286},[1131],[1265,35915,35916],{},[1127,35917,1306],{"className":35918,"dataFsResolvedFilePath":1312,"href":1310},[1131],[1265,35920,35921],{},[1127,35922,1318],{"className":35923,"dataFsResolvedFilePath":1324,"href":1322},[1131],[1265,35925,35926],{},[1127,35927,1543],{"className":35928,"dataFsResolvedFilePath":1336,"href":1334},[1131],[1265,35930,35931],{},[1127,35932,6753],{"className":35933,"dataFsResolvedFilePath":1550,"href":1548},[1131],[1153,35935,1554],{"id":934},[1110,35937,1557,35938,1561],{},[1420,35939,1560],{},[6761,35941,35942],{},"html pre.shiki code .sP4rz, html 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