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celcích:",[1237,1238,1239,1250,1259,1268,1277,1286],"ol",{},[1105,1240,1241,1249],{},[1242,1243,1248],"a",{"className":1244,"dataFsResolvedFilePath":1246,"href":1247},[1245],"wikilink","topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti"," — distribuční funkce, hustota pravděpodobnosti, normální rozdělení a odvozená rozdělení t, χ² a F.",[1105,1251,1252,1258],{},[1242,1253,1257],{"className":1254,"dataFsResolvedFilePath":1255,"href":1256},[1245],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory"," — empirické charakteristiky, kvantily, empirická distribuční funkce, třídění naměřených dat do tříd a histogram.",[1105,1260,1261,1267],{},[1242,1262,1266],{"className":1263,"dataFsResolvedFilePath":1264,"href":1265},[1245],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","Testování statistických hypotéz"," — jednovýběrový a párový t-test, F-test, dvouvýběrový t-test, testy normality a jejich neparametrické alternativy.",[1105,1269,1270,1276],{},[1242,1271,1275],{"className":1272,"dataFsResolvedFilePath":1273,"href":1274},[1245],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza"," — regresní přímka, nelineární a vícenásobná regrese, korelace a diagnostika modelu.",[1105,1278,1279,1285],{},[1242,1280,1284],{"className":1281,"dataFsResolvedFilePath":1282,"href":1283},[1245],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky","Kontingenční tabulky"," — test nezávislosti dvou kvalitativních znaků, Cramérův koeficient kontingence a McNemarův test pro párovaná data.",[1105,1287,1288,1294,1295,1323,1324,1323,1347,1370,1371,1395],{},[1242,1289,1293],{"className":1290,"dataFsResolvedFilePath":1291,"href":1292},[1245],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti"," — regulační diagramy pro regulaci měřením a srovnáváním, indexy způsobilosti ",[1296,1297,1300],"span",{"className":1298},[1299],"katex",[1301,1302,1304],"math",{"xmlns":1303},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1305,1306,1307,1318],"semantics",{},[1308,1309,1310],"mrow",{},[1311,1312,1313,1316],"msub",{},[1314,1315,1201],"mi",{},[1314,1317,1148],{},[1319,1320,1322],"annotation",{"encoding":1321},"application\u002Fx-tex","C_p",", ",[1296,1325,1327],{"className":1326},[1299],[1301,1328,1329],{"xmlns":1303},[1305,1330,1331,1344],{},[1308,1332,1333],{},[1311,1334,1335,1337],{},[1314,1336,1201],{},[1308,1338,1339,1341],{},[1314,1340,1148],{},[1314,1342,1343],{},"k",[1319,1345,1346],{"encoding":1321},"C_{pk}",[1296,1348,1350],{"className":1349},[1299],[1301,1351,1352],{"xmlns":1303},[1305,1353,1354,1367],{},[1308,1355,1356],{},[1311,1357,1358,1360],{},[1314,1359,1201],{},[1308,1361,1362,1364],{},[1314,1363,1148],{},[1314,1365,1366],{},"m",[1319,1368,1369],{"encoding":1321},"C_{pm}"," a ",[1296,1372,1374],{"className":1373},[1299],[1301,1375,1376],{"xmlns":1303},[1305,1377,1378,1392],{},[1308,1379,1380],{},[1311,1381,1382,1384],{},[1314,1383,1201],{},[1308,1385,1386,1388,1390],{},[1314,1387,1148],{},[1314,1389,1366],{},[1314,1391,1343],{},[1319,1393,1394],{"encoding":1321},"C_{pmk}",".",[1143,1397,1399],{"id":1398},"přednášky","Přednášky",[1148,1401,1402],{},"Látka kurzu je shrnuta do tří přehledů podle tematických celků a doplněna sylabem předmětu:",[1102,1404,1405,1413,1421,1428],{},[1105,1406,1407],{},[1242,1408,1412],{"className":1409,"dataFsResolvedFilePath":1410,"href":1411},[1245],"summaries\u002Fmask-prednasky-veliciny-data-testy.md","\u002Fwiki\u002Fmask-prednasky-veliciny-data-testy","Náhodné veličiny, datové soubory a testy hypotéz",[1105,1414,1415],{},[1242,1416,1420],{"className":1417,"dataFsResolvedFilePath":1418,"href":1419},[1245],"summaries\u002Fmask-prednasky-regrese-kontingence.md","\u002Fwiki\u002Fmask-prednasky-regrese-kontingence","Regresní analýza a kontingenční tabulky",[1105,1422,1423],{},[1242,1424,1293],{"className":1425,"dataFsResolvedFilePath":1426,"href":1427},[1245],"summaries\u002Fmask-prednasky-regulace-zpusobilost.md","\u002Fwiki\u002Fmask-prednasky-regulace-zpusobilost",[1105,1429,1430],{},[1242,1431,1435],{"className":1432,"dataFsResolvedFilePath":1433,"href":1434},[1245],"summaries\u002Fmask-detail-predmetu.md","\u002Fwiki\u002Fmask-detail-predmetu","Detail předmětu",[1143,1437,1439],{"id":1438},"příprava-na-zkoušku","Příprava na zkoušku",[1102,1441,1442],{},[1105,1443,1444,1450],{},[1242,1445,1449],{"className":1446,"dataFsResolvedFilePath":1447,"href":1448},[1245],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","masK — Tahák pro R"," — přehled volby statistického testu podle situace a funkcí v R použitých v kurzu.",{"title":1452,"searchDepth":27,"depth":27,"links":1453},"",[1454,1455,1456,1457,1458],{"id":1145,"depth":27,"text":1146},{"id":1156,"depth":27,"text":1157},{"id":1231,"depth":27,"text":1232},{"id":1398,"depth":27,"text":1399},{"id":1438,"depth":27,"text":1439},null,"2026-10-02","md",false,{},true,"\u002Fcourses\u002Fmask",{"title":24,"description":1452},[1468,1469],"raw\u002Fmask\u002FDetail předmětu.md","raw\u002Fmask\u002Finformace k předmětu.docx","courses\u002Fmask",[23,67,71,141,135,137],"course","e5jlOAYFcW6RMPSLgeYQyEgh_rw3ULQRUfbPc4Ntf9k","courses",[1476,1478,1482,1486,1490,1494,1497,1500],{"slug":716,"path":1283,"title":1284,"snippet":1477},"… žívá **McNemarův test**, ne obyčejný test nezávislosti. ## Kontingenční tabulka V rámci \u003C\u003Cmask>> navazují kontingenční tabulky na testování statistických hypotéz: m …",{"slug":1479,"path":1434,"title":1480,"snippet":1481},"mask-detail-predmetu","Detail předmětu — Metody aplikované statistiky","# Detail předmětu — Metody aplikované statistiky > [!abstract] TL;DR > Předmět \u003C\u003Cmask>> (zkratka **masK**) je inženýrský kurz na Fakultě podnikatelské VUT v Brně v zimním semest …",{"slug":1483,"path":1419,"title":1484,"snippet":1485},"mask-prednasky-regrese-kontingence","MasK — Regresní analýza a kontingenční tabulky","… sK — Regresní analýza a kontingenční tabulky > [!abstract] TL;DR > Prostřední část kurzu \u003C\u003Cmask>>: hledání vztahu mezi kvantitativními veličinami pomocí regresní přímky, nelineárních mode …",{"slug":1487,"path":1427,"title":1488,"snippet":1489},"mask-prednasky-regulace-zpusobilost","MasK — Regulační diagramy a indexy způsobilosti","… sK — Regulační diagramy a indexy způsobilosti > [!abstract] TL;DR > Závěrečná část kurzu \u003C\u003Cmask>>: statistická regulace výrobního procesu pomocí regulačních diagramů pro měřené i počítané …",{"slug":1491,"path":1411,"title":1492,"snippet":1493},"mask-prednasky-veliciny-data-testy","MasK — Náhodné veličiny, datové soubory a testy hypotéz","… Náhodné veličiny, datové soubory a testy hypotéz > [!abstract] TL;DR > Úvodní část kurzu \u003C\u003Cmask>>: popis náhodných veličin a jejich rozdělení, zpracování naměřených dat do empirických cha …",{"slug":1495,"path":1448,"title":1449,"snippet":1496},"mask-r-tahak","… asK — Tahák pro R > [!abstract] TL;DR > Referenční přehled příkazů R používaných v kurzu \u003C\u003Cmask>>: načtení dat, volba statistického testu podle situace, funkce jednotlivých kapitol a vých …",{"slug":1498,"path":1247,"title":1248,"snippet":1499},"nahodne-veliciny-a-rozdeleni","… ro pozdější konstrukci intervalů spolehlivosti a testování hypotéz. ## Náhodná veličina \u003C\u003Cmask>> pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní pros …",{"slug":1501,"path":1502,"title":1503,"snippet":1504},"overview","\u002F","Přehled — Fakulta podnikatelská VUT v Brně","… ny (sylabus + ~700 řádek poznámek z konzultací + strukturální karta knihy Bartes 2022). - \u003C\u003Cmask>> — aplikovaná statistika řešená v R: náhodné veličiny a rozdělení, popisná statistika, tes …",[1506,6666,11128,15894,20597,26046],{"id":1507,"title":1284,"body":1508,"course":23,"courses":1459,"created":1460,"description":1452,"extension":1461,"meta":6656,"navigation":1464,"path":6657,"seo":6658,"sources":6659,"stem":6662,"tags":6663,"type":6664,"updated":1460,"__hash__":6665},"topics\u002Ftopics\u002Fkontingencni-tabulky.md",{"type":1095,"value":1509,"toc":6646},[1510,1513,1705,1709,1728,1746,1957,2098,2693,2710,2823,2827,2858,2863,3464,3471,3691,3917,3925,4006,4118,4271,4277,4358,4379,4388,4422,4429,4432,4438,4503,4562,4714,4720,4727,4805,4808,4864,5202,5223,5327,5436,5439,5460,5463,5718,5799,5806,5810,6040,6054,6203,6337,6343,6401,6405,6424,6439,6445,6490,6509,6524,6530,6589,6593,6631,6634,6642],[1098,1511,1284],{"id":1512},"kontingenční-tabulky",[1514,1515,1520,1532],"aside",{"className":1516,"dataCallout":1519},[1517,1518],"callout","callout-default","tldr",[1148,1521,1524,1531],{"className":1522},[1523],"callout-title",[1296,1525],{"className":1526,"ariaHidden":1530},[1527,1528,1529],"iconify","i-lucide:info","callout-icon","true","V kostce",[1102,1533,1534,1541,1606,1627,1666,1694],{},[1105,1535,1536,1537,1540],{},"Kontingenční tabulka zaznamenává ",[1108,1538,1539],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1105,1542,1543,1546,1547,1568,1569,1590,1591,1605],{},[1108,1544,1545],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1296,1548,1550],{"className":1549},[1299],[1301,1551,1552],{"xmlns":1303},[1305,1553,1554,1565],{},[1308,1555,1556],{},[1311,1557,1558,1561],{},[1314,1559,1560],{},"H",[1562,1563,1564],"mn",{},"0",[1319,1566,1567],{"encoding":1321},"H_0"," pomocí statistiky ",[1296,1570,1572],{"className":1571},[1299],[1301,1573,1574],{"xmlns":1303},[1305,1575,1576,1587],{},[1308,1577,1578],{},[1579,1580,1581,1584],"msup",{},[1314,1582,1583],{},"χ",[1562,1585,1586],{},"2",[1319,1588,1589],{"encoding":1321},"\\chi^2","; rozhoduje kritický obor ",[1296,1592,1594],{"className":1593},[1299],[1301,1595,1596],{"xmlns":1303},[1305,1597,1598,1603],{},[1308,1599,1600],{},[1314,1601,1602],{},"W",[1319,1604,1602],{"encoding":1321},", prakticky p-hodnota.",[1105,1607,1608,1609,1626],{},"Aproximace ",[1296,1610,1612],{"className":1611},[1299],[1301,1613,1614],{"xmlns":1303},[1305,1615,1616,1624],{},[1308,1617,1618],{},[1579,1619,1620,1622],{},[1314,1621,1583],{},[1562,1623,1586],{},[1319,1625,1589],{"encoding":1321}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1105,1628,1629,1630,1647,1648,1651,1652,1395],{},"Zamítnutí ",[1296,1631,1633],{"className":1632},[1299],[1301,1634,1635],{"xmlns":1303},[1305,1636,1637,1645],{},[1308,1638,1639],{},[1311,1640,1641,1643],{},[1314,1642,1560],{},[1562,1644,1564],{},[1319,1646,1567],{"encoding":1321}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1108,1649,1650],{},"Cramérův koeficient kontingence"," ",[1296,1653,1655],{"className":1654},[1299],[1301,1656,1657],{"xmlns":1303},[1305,1658,1659,1664],{},[1308,1660,1661],{},[1314,1662,1663],{},"V",[1319,1665,1663],{"encoding":1321},[1105,1667,1668,1671,1672,1395],{},[1108,1669,1670],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1296,1673,1675],{"className":1674},[1299],[1301,1676,1677],{"xmlns":1303},[1305,1678,1679,1691],{},[1308,1680,1681,1684,1688],{},[1314,1682,1683],{},"n",[1685,1686,1687],"mo",{},">",[1562,1689,1690],{},"40",[1319,1692,1693],{"encoding":1321},"n>40",[1105,1695,1696,1697,1700,1701,1704],{},"Pro ",[1108,1698,1699],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1108,1702,1703],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1143,1706,1708],{"id":1707},"kontingenční-tabulka","Kontingenční tabulka",[1148,1710,1711,1712,1718,1719,1723,1724,1727],{},"V rámci ",[1242,1713,1717],{"className":1714,"dataFsResolvedFilePath":1715,"href":1716},[1245],"courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky"," navazují kontingenční tabulky na\n",[1242,1720,1722],{"className":1721,"dataFsResolvedFilePath":1264,"href":1265},[1245],"testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1108,1725,1726],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1148,1729,1730,1731,1734,1735,1737,1738,1741,1742,1745],{},"Znak je ",[1108,1732,1733],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1108,1736,1726],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1108,1739,1740],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1108,1743,1744],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1148,1747,1748,1749,1762,1763,1776,1777,1810,1811,1824,1825,1856,1857,1860,1861,1888,1889,1651,1892,1914,1915,1933,1934,1952,1953,1956],{},"Mějme ",[1296,1750,1752],{"className":1751},[1299],[1301,1753,1754],{"xmlns":1303},[1305,1755,1756,1760],{},[1308,1757,1758],{},[1314,1759,1683],{},[1319,1761,1683],{"encoding":1321}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1296,1764,1766],{"className":1765},[1299],[1301,1767,1768],{"xmlns":1303},[1305,1769,1770,1774],{},[1308,1771,1772],{},[1314,1773,1185],{},[1319,1775,1185],{"encoding":1321}," (varianty ",[1296,1778,1780],{"className":1779},[1299],[1301,1781,1782],{"xmlns":1303},[1305,1783,1784,1807],{},[1308,1785,1786,1793,1796,1799,1801],{},[1311,1787,1788,1790],{},[1314,1789,1185],{},[1562,1791,1792],{},"1",[1685,1794,1795],{"separator":1530},",",[1685,1797,1798],{},"…",[1685,1800,1795],{"separator":1530},[1311,1802,1803,1805],{},[1314,1804,1185],{},[1314,1806,71],{},[1319,1808,1809],{"encoding":1321},"A_1,\\dots,A_r",") a ",[1296,1812,1814],{"className":1813},[1299],[1301,1815,1816],{"xmlns":1303},[1305,1817,1818,1822],{},[1308,1819,1820],{},[1314,1821,1193],{},[1319,1823,1193],{"encoding":1321},"\n(varianty ",[1296,1826,1828],{"className":1827},[1299],[1301,1829,1830],{"xmlns":1303},[1305,1831,1832,1853],{},[1308,1833,1834,1840,1842,1844,1846],{},[1311,1835,1836,1838],{},[1314,1837,1193],{},[1562,1839,1792],{},[1685,1841,1795],{"separator":1530},[1685,1843,1798],{},[1685,1845,1795],{"separator":1530},[1311,1847,1848,1850],{},[1314,1849,1193],{},[1314,1851,1852],{},"s",[1319,1854,1855],{"encoding":1321},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1108,1858,1859],{},"kontingenční tabulky",": v políčku ",[1296,1862,1864],{"className":1863},[1299],[1301,1865,1866],{"xmlns":1303},[1305,1867,1868,1885],{},[1308,1869,1870,1874,1877,1879,1882],{},[1685,1871,1873],{"stretchy":1872},"false","(",[1314,1875,1876],{},"i",[1685,1878,1795],{"separator":1530},[1314,1880,1881],{},"j",[1685,1883,1884],{"stretchy":1872},")",[1319,1886,1887],{"encoding":1321},"(i,j)"," je ",[1108,1890,1891],{},"simultánní\nčetnost",[1296,1893,1895],{"className":1894},[1299],[1301,1896,1897],{"xmlns":1303},[1305,1898,1899,1911],{},[1308,1900,1901],{},[1311,1902,1903,1905],{},[1314,1904,1683],{},[1308,1906,1907,1909],{},[1314,1908,1876],{},[1314,1910,1881],{},[1319,1912,1913],{"encoding":1321},"n_{ij}",", tedy počet pokusů s variantou ",[1296,1916,1918],{"className":1917},[1299],[1301,1919,1920],{"xmlns":1303},[1305,1921,1922,1930],{},[1308,1923,1924],{},[1311,1925,1926,1928],{},[1314,1927,1185],{},[1314,1929,1876],{},[1319,1931,1932],{"encoding":1321},"A_i"," zároveň s variantou ",[1296,1935,1937],{"className":1936},[1299],[1301,1938,1939],{"xmlns":1303},[1305,1940,1941,1949],{},[1308,1942,1943],{},[1311,1944,1945,1947],{},[1314,1946,1193],{},[1314,1948,1881],{},[1319,1950,1951],{"encoding":1321},"B_j",". Řádkové a sloupcové součty\njsou ",[1108,1954,1955],{},"marginální četnosti",":",[1296,1958,1960],{"className":1959},[1299],[1301,1961,1963],{"xmlns":1303,"display":1962},"block",[1305,1964,1965,2095],{},[1308,1966,1967,1978,1981,1997,2007,2009,2013,2023,2025,2039,2049,2051,2053,2055,2057,2071,2085],{},[1311,1968,1969,1971],{},[1314,1970,1683],{},[1308,1972,1973,1975],{},[1314,1974,1876],{},[1685,1976,1977],{},"∙",[1685,1979,1980],{},"=",[1982,1983,1984,1987,1995],"munderover",{},[1685,1985,1986],{},"∑",[1308,1988,1989,1991,1993],{},[1314,1990,1881],{},[1685,1992,1980],{},[1562,1994,1792],{},[1314,1996,1852],{},[1311,1998,1999,2001],{},[1314,2000,1683],{},[1308,2002,2003,2005],{},[1314,2004,1876],{},[1314,2006,1881],{},[1685,2008,1795],{"separator":1530},[2010,2011],"mspace",{"width":2012},"2em",[1311,2014,2015,2017],{},[1314,2016,1683],{},[1308,2018,2019,2021],{},[1685,2020,1977],{},[1314,2022,1881],{},[1685,2024,1980],{},[1982,2026,2027,2029,2037],{},[1685,2028,1986],{},[1308,2030,2031,2033,2035],{},[1314,2032,1876],{},[1685,2034,1980],{},[1562,2036,1792],{},[1314,2038,71],{},[1311,2040,2041,2043],{},[1314,2042,1683],{},[1308,2044,2045,2047],{},[1314,2046,1876],{},[1314,2048,1881],{},[1685,2050,1795],{"separator":1530},[2010,2052],{"width":2012},[1314,2054,1683],{},[1685,2056,1980],{},[1982,2058,2059,2061,2069],{},[1685,2060,1986],{},[1308,2062,2063,2065,2067],{},[1314,2064,1876],{},[1685,2066,1980],{},[1562,2068,1792],{},[1314,2070,71],{},[1982,2072,2073,2075,2083],{},[1685,2074,1986],{},[1308,2076,2077,2079,2081],{},[1314,2078,1881],{},[1685,2080,1980],{},[1562,2082,1792],{},[1314,2084,1852],{},[1311,2086,2087,2089],{},[1314,2088,1683],{},[1308,2090,2091,2093],{},[1314,2092,1876],{},[1314,2094,1881],{},[1319,2096,2097],{"encoding":1321},"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}",[1162,2099,2100,2212],{},[1165,2101,2102],{},[1168,2103,2104,2126,2146,2166,2168,2188],{},[1171,2105,2106],{},[1296,2107,2109],{"className":2108},[1299],[1301,2110,2111],{"xmlns":1303},[1305,2112,2113,2123],{},[1308,2114,2115,2117,2121],{},[1314,2116,1185],{},[1314,2118,2120],{"mathvariant":2119},"normal","\\",[1314,2122,1193],{},[1319,2124,2125],{"encoding":1321},"A \\backslash B",[1171,2127,2128],{},[1296,2129,2131],{"className":2130},[1299],[1301,2132,2133],{"xmlns":1303},[1305,2134,2135,2143],{},[1308,2136,2137],{},[1311,2138,2139,2141],{},[1314,2140,1193],{},[1562,2142,1792],{},[1319,2144,2145],{"encoding":1321},"B_1",[1171,2147,2148],{},[1296,2149,2151],{"className":2150},[1299],[1301,2152,2153],{"xmlns":1303},[1305,2154,2155,2163],{},[1308,2156,2157],{},[1311,2158,2159,2161],{},[1314,2160,1193],{},[1562,2162,1586],{},[1319,2164,2165],{"encoding":1321},"B_2",[1171,2167,1798],{},[1171,2169,2170],{},[1296,2171,2173],{"className":2172},[1299],[1301,2174,2175],{"xmlns":1303},[1305,2176,2177,2185],{},[1308,2178,2179],{},[1311,2180,2181,2183],{},[1314,2182,1193],{},[1314,2184,1852],{},[1319,2186,2187],{"encoding":1321},"B_s",[1171,2189,2190],{},[1296,2191,2193],{"className":2192},[1299],[1301,2194,2195],{"xmlns":1303},[1305,2196,2197,2209],{},[1308,2198,2199],{},[1311,2200,2201,2203],{},[1314,2202,1683],{},[1308,2204,2205,2207],{},[1314,2206,1876],{},[1685,2208,1977],{},[1319,2210,2211],{"encoding":1321},"n_{i\\bullet}",[1178,2213,2214,2328,2442,2458,2578],{},[1168,2215,2216,2236,2257,2278,2280,2304],{},[1183,2217,2218],{},[1296,2219,2221],{"className":2220},[1299],[1301,2222,2223],{"xmlns":1303},[1305,2224,2225,2233],{},[1308,2226,2227],{},[1311,2228,2229,2231],{},[1314,2230,1185],{},[1562,2232,1792],{},[1319,2234,2235],{"encoding":1321},"A_1",[1183,2237,2238],{},[1296,2239,2241],{"className":2240},[1299],[1301,2242,2243],{"xmlns":1303},[1305,2244,2245,2254],{},[1308,2246,2247],{},[1311,2248,2249,2251],{},[1314,2250,1683],{},[1562,2252,2253],{},"11",[1319,2255,2256],{"encoding":1321},"n_{11}",[1183,2258,2259],{},[1296,2260,2262],{"className":2261},[1299],[1301,2263,2264],{"xmlns":1303},[1305,2265,2266,2275],{},[1308,2267,2268],{},[1311,2269,2270,2272],{},[1314,2271,1683],{},[1562,2273,2274],{},"12",[1319,2276,2277],{"encoding":1321},"n_{12}",[1183,2279,1798],{},[1183,2281,2282],{},[1296,2283,2285],{"className":2284},[1299],[1301,2286,2287],{"xmlns":1303},[1305,2288,2289,2301],{},[1308,2290,2291],{},[1311,2292,2293,2295],{},[1314,2294,1683],{},[1308,2296,2297,2299],{},[1562,2298,1792],{},[1314,2300,1852],{},[1319,2302,2303],{"encoding":1321},"n_{1s}",[1183,2305,2306],{},[1296,2307,2309],{"className":2308},[1299],[1301,2310,2311],{"xmlns":1303},[1305,2312,2313,2325],{},[1308,2314,2315],{},[1311,2316,2317,2319],{},[1314,2318,1683],{},[1308,2320,2321,2323],{},[1562,2322,1792],{},[1685,2324,1977],{},[1319,2326,2327],{"encoding":1321},"n_{1\\bullet}",[1168,2329,2330,2350,2371,2392,2394,2418],{},[1183,2331,2332],{},[1296,2333,2335],{"className":2334},[1299],[1301,2336,2337],{"xmlns":1303},[1305,2338,2339,2347],{},[1308,2340,2341],{},[1311,2342,2343,2345],{},[1314,2344,1185],{},[1562,2346,1586],{},[1319,2348,2349],{"encoding":1321},"A_2",[1183,2351,2352],{},[1296,2353,2355],{"className":2354},[1299],[1301,2356,2357],{"xmlns":1303},[1305,2358,2359,2368],{},[1308,2360,2361],{},[1311,2362,2363,2365],{},[1314,2364,1683],{},[1562,2366,2367],{},"21",[1319,2369,2370],{"encoding":1321},"n_{21}",[1183,2372,2373],{},[1296,2374,2376],{"className":2375},[1299],[1301,2377,2378],{"xmlns":1303},[1305,2379,2380,2389],{},[1308,2381,2382],{},[1311,2383,2384,2386],{},[1314,2385,1683],{},[1562,2387,2388],{},"22",[1319,2390,2391],{"encoding":1321},"n_{22}",[1183,2393,1798],{},[1183,2395,2396],{},[1296,2397,2399],{"className":2398},[1299],[1301,2400,2401],{"xmlns":1303},[1305,2402,2403,2415],{},[1308,2404,2405],{},[1311,2406,2407,2409],{},[1314,2408,1683],{},[1308,2410,2411,2413],{},[1562,2412,1586],{},[1314,2414,1852],{},[1319,2416,2417],{"encoding":1321},"n_{2s}",[1183,2419,2420],{},[1296,2421,2423],{"className":2422},[1299],[1301,2424,2425],{"xmlns":1303},[1305,2426,2427,2439],{},[1308,2428,2429],{},[1311,2430,2431,2433],{},[1314,2432,1683],{},[1308,2434,2435,2437],{},[1562,2436,1586],{},[1685,2438,1977],{},[1319,2440,2441],{"encoding":1321},"n_{2\\bullet}",[1168,2443,2444,2447,2449,2451,2454,2456],{},[1183,2445,2446],{},"⋮",[1183,2448,2446],{},[1183,2450,2446],{},[1183,2452,2453],{},"⋱",[1183,2455,2446],{},[1183,2457,2446],{},[1168,2459,2460,2480,2504,2528,2530,2554],{},[1183,2461,2462],{},[1296,2463,2465],{"className":2464},[1299],[1301,2466,2467],{"xmlns":1303},[1305,2468,2469,2477],{},[1308,2470,2471],{},[1311,2472,2473,2475],{},[1314,2474,1185],{},[1314,2476,71],{},[1319,2478,2479],{"encoding":1321},"A_r",[1183,2481,2482],{},[1296,2483,2485],{"className":2484},[1299],[1301,2486,2487],{"xmlns":1303},[1305,2488,2489,2501],{},[1308,2490,2491],{},[1311,2492,2493,2495],{},[1314,2494,1683],{},[1308,2496,2497,2499],{},[1314,2498,71],{},[1562,2500,1792],{},[1319,2502,2503],{"encoding":1321},"n_{r1}",[1183,2505,2506],{},[1296,2507,2509],{"className":2508},[1299],[1301,2510,2511],{"xmlns":1303},[1305,2512,2513,2525],{},[1308,2514,2515],{},[1311,2516,2517,2519],{},[1314,2518,1683],{},[1308,2520,2521,2523],{},[1314,2522,71],{},[1562,2524,1586],{},[1319,2526,2527],{"encoding":1321},"n_{r2}",[1183,2529,1798],{},[1183,2531,2532],{},[1296,2533,2535],{"className":2534},[1299],[1301,2536,2537],{"xmlns":1303},[1305,2538,2539,2551],{},[1308,2540,2541],{},[1311,2542,2543,2545],{},[1314,2544,1683],{},[1308,2546,2547,2549],{},[1314,2548,71],{},[1314,2550,1852],{},[1319,2552,2553],{"encoding":1321},"n_{rs}",[1183,2555,2556],{},[1296,2557,2559],{"className":2558},[1299],[1301,2560,2561],{"xmlns":1303},[1305,2562,2563,2575],{},[1308,2564,2565],{},[1311,2566,2567,2569],{},[1314,2568,1683],{},[1308,2570,2571,2573],{},[1314,2572,71],{},[1685,2574,1977],{},[1319,2576,2577],{"encoding":1321},"n_{r\\bullet}",[1168,2579,2580,2604,2628,2652,2654,2678],{},[1183,2581,2582],{},[1296,2583,2585],{"className":2584},[1299],[1301,2586,2587],{"xmlns":1303},[1305,2588,2589,2601],{},[1308,2590,2591],{},[1311,2592,2593,2595],{},[1314,2594,1683],{},[1308,2596,2597,2599],{},[1685,2598,1977],{},[1314,2600,1881],{},[1319,2602,2603],{"encoding":1321},"n_{\\bullet j}",[1183,2605,2606],{},[1296,2607,2609],{"className":2608},[1299],[1301,2610,2611],{"xmlns":1303},[1305,2612,2613,2625],{},[1308,2614,2615],{},[1311,2616,2617,2619],{},[1314,2618,1683],{},[1308,2620,2621,2623],{},[1685,2622,1977],{},[1562,2624,1792],{},[1319,2626,2627],{"encoding":1321},"n_{\\bullet 1}",[1183,2629,2630],{},[1296,2631,2633],{"className":2632},[1299],[1301,2634,2635],{"xmlns":1303},[1305,2636,2637,2649],{},[1308,2638,2639],{},[1311,2640,2641,2643],{},[1314,2642,1683],{},[1308,2644,2645,2647],{},[1685,2646,1977],{},[1562,2648,1586],{},[1319,2650,2651],{"encoding":1321},"n_{\\bullet 2}",[1183,2653,1798],{},[1183,2655,2656],{},[1296,2657,2659],{"className":2658},[1299],[1301,2660,2661],{"xmlns":1303},[1305,2662,2663,2675],{},[1308,2664,2665],{},[1311,2666,2667,2669],{},[1314,2668,1683],{},[1308,2670,2671,2673],{},[1685,2672,1977],{},[1314,2674,1852],{},[1319,2676,2677],{"encoding":1321},"n_{\\bullet s}",[1183,2679,2680],{},[1296,2681,2683],{"className":2682},[1299],[1301,2684,2685],{"xmlns":1303},[1305,2686,2687,2691],{},[1308,2688,2689],{},[1314,2690,1683],{},[1319,2692,1683],{"encoding":1321},[1148,2694,2695,2696,2709],{},"Vydělením četností počtem opakování ",[1296,2697,2699],{"className":2698},[1299],[1301,2700,2701],{"xmlns":1303},[1305,2702,2703,2707],{},[1308,2704,2705],{},[1314,2706,1683],{},[1319,2708,1683],{"encoding":1321}," dostaneme odhady pravděpodobností:",[1296,2711,2713],{"className":2712},[1299],[1301,2714,2715],{"xmlns":1303,"display":1962},[1305,2716,2717,2820],{},[1308,2718,2719,2735,2737,2752,2754,2756,2770,2772,2786,2788,2790,2804,2806],{},[1311,2720,2721,2729],{},[2722,2723,2724,2726],"mover",{"accent":1530},[1314,2725,1148],{},[1685,2727,2728],{},"^",[1308,2730,2731,2733],{},[1314,2732,1876],{},[1314,2734,1881],{},[1685,2736,1980],{},[2738,2739,2740,2750],"mfrac",{},[1311,2741,2742,2744],{},[1314,2743,1683],{},[1308,2745,2746,2748],{},[1314,2747,1876],{},[1314,2749,1881],{},[1314,2751,1683],{},[1685,2753,1795],{"separator":1530},[2010,2755],{"width":2012},[1311,2757,2758,2764],{},[2722,2759,2760,2762],{"accent":1530},[1314,2761,1148],{},[1685,2763,2728],{},[1308,2765,2766,2768],{},[1314,2767,1876],{},[1685,2769,1977],{},[1685,2771,1980],{},[2738,2773,2774,2784],{},[1311,2775,2776,2778],{},[1314,2777,1683],{},[1308,2779,2780,2782],{},[1314,2781,1876],{},[1685,2783,1977],{},[1314,2785,1683],{},[1685,2787,1795],{"separator":1530},[2010,2789],{"width":2012},[1311,2791,2792,2798],{},[2722,2793,2794,2796],{"accent":1530},[1314,2795,1148],{},[1685,2797,2728],{},[1308,2799,2800,2802],{},[1685,2801,1977],{},[1314,2803,1881],{},[1685,2805,1980],{},[2738,2807,2808,2818],{},[1311,2809,2810,2812],{},[1314,2811,1683],{},[1308,2813,2814,2816],{},[1685,2815,1977],{},[1314,2817,1881],{},[1314,2819,1683],{},[1319,2821,2822],{"encoding":1321},"\\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}",[1143,2824,2826],{"id":2825},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1148,2828,2829,2830,2843,2844,2857],{},"Test ověřuje, zda varianty znaku ",[1296,2831,2833],{"className":2832},[1299],[1301,2834,2835],{"xmlns":1303},[1305,2836,2837,2841],{},[1308,2838,2839],{},[1314,2840,1185],{},[1319,2842,1185],{"encoding":1321}," a varianty znaku ",[1296,2845,2847],{"className":2846},[1299],[1301,2848,2849],{"xmlns":1303},[1305,2850,2851,2855],{},[1308,2852,2853],{},[1314,2854,1193],{},[1319,2856,1193],{"encoding":1321}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1148,2859,2860],{},[1108,2861,2862],{},"Postup testu:",[1237,2864,2865,2996,3314,3396],{},[1105,2866,2867,2923,2924,1323,2950,2976,2977,2995],{},[1296,2868,2870],{"className":2869},[1299],[1301,2871,2872],{"xmlns":1303},[1305,2873,2874,2920],{},[1308,2875,2876,2882,2884,2894,2896,2906,2910],{},[1311,2877,2878,2880],{},[1314,2879,1560],{},[1562,2881,1564],{},[1685,2883,1956],{},[1311,2885,2886,2888],{},[1314,2887,1148],{},[1308,2889,2890,2892],{},[1314,2891,1876],{},[1314,2893,1881],{},[1685,2895,1980],{},[1311,2897,2898,2900],{},[1314,2899,1148],{},[1308,2901,2902,2904],{},[1314,2903,1876],{},[1685,2905,1977],{},[2907,2908,2909],"mtext",{}," ",[1311,2911,2912,2914],{},[1314,2913,1148],{},[1308,2915,2916,2918],{},[1685,2917,1977],{},[1314,2919,1881],{},[1319,2921,2922],{"encoding":1321},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1296,2925,2927],{"className":2926},[1299],[1301,2928,2929],{"xmlns":1303},[1305,2930,2931,2947],{},[1308,2932,2933,2935,2937,2939,2941,2943,2945],{},[1314,2934,1876],{},[1685,2936,1980],{},[1562,2938,1792],{},[1685,2940,1795],{"separator":1530},[1685,2942,1798],{},[1685,2944,1795],{"separator":1530},[1314,2946,71],{},[1319,2948,2949],{"encoding":1321},"i = 1,\\dots,r",[1296,2951,2953],{"className":2952},[1299],[1301,2954,2955],{"xmlns":1303},[1305,2956,2957,2973],{},[1308,2958,2959,2961,2963,2965,2967,2969,2971],{},[1314,2960,1881],{},[1685,2962,1980],{},[1562,2964,1792],{},[1685,2966,1795],{"separator":1530},[1685,2968,1798],{},[1685,2970,1795],{"separator":1530},[1314,2972,1852],{},[1319,2974,2975],{"encoding":1321},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1296,2978,2980],{"className":2979},[1299],[1301,2981,2982],{"xmlns":1303},[1305,2983,2984,2992],{},[1308,2985,2986],{},[1311,2987,2988,2990],{},[1314,2989,1560],{},[1562,2991,1792],{},[1319,2993,2994],{"encoding":1321},"H_1",": znaky jsou závislé.",[1105,2997,2998,2999,3156,3159,3160,3177,3178,3210,3211,1888,3270,3273,3274,3295,3296,3313],{},"Testové kritérium",[1296,3000,3002],{"className":3001},[1299],[1301,3003,3004],{"xmlns":1303,"display":1962},[1305,3005,3006,3153],{},[1308,3007,3008,3014,3016,3030,3044,3103,3105,3107,3121,3123,3137,3139],{},[1579,3009,3010,3012],{},[1314,3011,1583],{},[1562,3013,1586],{},[1685,3015,1980],{},[1982,3017,3018,3020,3028],{},[1685,3019,1986],{},[1308,3021,3022,3024,3026],{},[1314,3023,1876],{},[1685,3025,1980],{},[1562,3027,1792],{},[1314,3029,71],{},[1982,3031,3032,3034,3042],{},[1685,3033,1986],{},[1308,3035,3036,3038,3040],{},[1314,3037,1881],{},[1685,3039,1980],{},[1562,3041,1792],{},[1314,3043,1852],{},[2738,3045,3046,3085],{},[1308,3047,3048,3050,3060,3063,3065,3079],{},[1685,3049,1873],{"stretchy":1872},[1311,3051,3052,3054],{},[1314,3053,1683],{},[1308,3055,3056,3058],{},[1314,3057,1876],{},[1314,3059,1881],{},[1685,3061,3062],{},"−",[1314,3064,1683],{},[1311,3066,3067,3073],{},[2722,3068,3069,3071],{"accent":1530},[1314,3070,1148],{},[1685,3072,2728],{},[1308,3074,3075,3077],{},[1314,3076,1876],{},[1314,3078,1881],{},[1579,3080,3081,3083],{},[1685,3082,1884],{"stretchy":1872},[1562,3084,1586],{},[1308,3086,3087,3089],{},[1314,3088,1683],{},[1311,3090,3091,3097],{},[2722,3092,3093,3095],{"accent":1530},[1314,3094,1148],{},[1685,3096,2728],{},[1308,3098,3099,3101],{},[1314,3100,1876],{},[1314,3102,1881],{},[1685,3104,1795],{"separator":1530},[2010,3106],{"width":2012},[1311,3108,3109,3115],{},[2722,3110,3111,3113],{"accent":1530},[1314,3112,1148],{},[1685,3114,2728],{},[1308,3116,3117,3119],{},[1314,3118,1876],{},[1314,3120,1881],{},[1685,3122,1980],{},[1311,3124,3125,3131],{},[2722,3126,3127,3129],{"accent":1530},[1314,3128,1148],{},[1685,3130,2728],{},[1308,3132,3133,3135],{},[1314,3134,1876],{},[1685,3136,1977],{},[2907,3138,2909],{},[1311,3140,3141,3147],{},[2722,3142,3143,3145],{"accent":1530},[1314,3144,1148],{},[1685,3146,2728],{},[1308,3148,3149,3151],{},[1685,3150,1977],{},[1314,3152,1881],{},[1319,3154,3155],{"encoding":1321},"\\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}",[3157,3158],"br",{},"má asymptoticky Pearsonovo (",[1296,3161,3163],{"className":3162},[1299],[1301,3164,3165],{"xmlns":1303},[1305,3166,3167,3175],{},[1308,3168,3169],{},[1579,3170,3171,3173],{},[1314,3172,1583],{},[1562,3174,1586],{},[1319,3176,1589],{"encoding":1321},") rozdělení o ",[1296,3179,3181],{"className":3180},[1299],[1301,3182,3183],{"xmlns":1303},[1305,3184,3185,3207],{},[1308,3186,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205],{},[1685,3188,1873],{"stretchy":1872},[1314,3190,71],{},[1685,3192,3062],{},[1562,3194,1792],{},[1685,3196,1884],{"stretchy":1872},[1685,3198,1873],{"stretchy":1872},[1314,3200,1852],{},[1685,3202,3062],{},[1562,3204,1792],{},[1685,3206,1884],{"stretchy":1872},[1319,3208,3209],{"encoding":1321},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1296,3212,3214],{"className":3213},[1299],[1301,3215,3216],{"xmlns":1303},[1305,3217,3218,3267],{},[1308,3219,3220,3222,3236,3238],{},[1314,3221,1683],{},[1311,3223,3224,3230],{},[2722,3225,3226,3228],{"accent":1530},[1314,3227,1148],{},[1685,3229,2728],{},[1308,3231,3232,3234],{},[1314,3233,1876],{},[1314,3235,1881],{},[1685,3237,1980],{},[3239,3240,3241],"mstyle",{"scriptlevel":1564,"displaystyle":1530},[2738,3242,3243,3265],{},[1308,3244,3245,3255],{},[1311,3246,3247,3249],{},[1314,3248,1683],{},[1308,3250,3251,3253],{},[1314,3252,1876],{},[1685,3254,1977],{},[1311,3256,3257,3259],{},[1314,3258,1683],{},[1308,3260,3261,3263],{},[1685,3262,1977],{},[1314,3264,1881],{},[1314,3266,1683],{},[1319,3268,3269],{"encoding":1321},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1108,3271,3272],{},"očekávaná četnost"," políčka ",[1296,3275,3277],{"className":3276},[1299],[1301,3278,3279],{"xmlns":1303},[1305,3280,3281,3293],{},[1308,3282,3283,3285,3287,3289,3291],{},[1685,3284,1873],{"stretchy":1872},[1314,3286,1876],{},[1685,3288,1795],{"separator":1530},[1314,3290,1881],{},[1685,3292,1884],{"stretchy":1872},[1319,3294,1887],{"encoding":1321}," — četnost, kterou bychom čekali, kdyby ",[1296,3297,3299],{"className":3298},[1299],[1301,3300,3301],{"xmlns":1303},[1305,3302,3303,3311],{},[1308,3304,3305],{},[1311,3306,3307,3309],{},[1314,3308,1560],{},[1562,3310,1564],{},[1319,3312,1567],{"encoding":1321}," platila.",[1105,3315,3316,3317,1395],{},"Kritický obor: ",[1296,3318,3320],{"className":3319},[1299],[1301,3321,3322],{"xmlns":1303},[1305,3323,3324,3393],{},[1308,3325,3326,3328,3330,3333,3339,3341,3347,3350,3366,3368,3370,3372,3374,3376,3378,3380,3382,3384,3386,3388,3390],{},[1314,3327,1602],{},[1685,3329,1980],{},[1685,3331,3332],{"stretchy":1872},"{",[1579,3334,3335,3337],{},[1314,3336,1583],{},[1562,3338,1586],{},[1685,3340,1956],{},[1579,3342,3343,3345],{},[1314,3344,1583],{},[1562,3346,1586],{},[1685,3348,3349],{},"≥",[3351,3352,3353,3355,3364],"msubsup",{},[1314,3354,1583],{},[1308,3356,3357,3359,3361],{},[1562,3358,1792],{},[1685,3360,3062],{},[1314,3362,3363],{},"α",[1562,3365,1586],{},[1685,3367,1873],{"stretchy":1872},[1685,3369,1873],{"stretchy":1872},[1314,3371,71],{},[1685,3373,3062],{},[1562,3375,1792],{},[1685,3377,1884],{"stretchy":1872},[1685,3379,1873],{"stretchy":1872},[1314,3381,1852],{},[1685,3383,3062],{},[1562,3385,1792],{},[1685,3387,1884],{"stretchy":1872},[1685,3389,1884],{"stretchy":1872},[1685,3391,3392],{"stretchy":1872},"}",[1319,3394,3395],{"encoding":1321},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1105,3397,3398,3399,3412,3413,3427,3428,3445,3446,3463],{},"Padne-li testové kritérium do ",[1296,3400,3402],{"className":3401},[1299],[1301,3403,3404],{"xmlns":1303},[1305,3405,3406,3410],{},[1308,3407,3408],{},[1314,3409,1602],{},[1319,3411,1602],{"encoding":1321},", zamítáme na hladině ",[1296,3414,3416],{"className":3415},[1299],[1301,3417,3418],{"xmlns":1303},[1305,3419,3420,3424],{},[1308,3421,3422],{},[1314,3423,3363],{},[1319,3425,3426],{"encoding":1321},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1296,3429,3431],{"className":3430},[1299],[1301,3432,3433],{"xmlns":1303},[1305,3434,3435,3443],{},[1308,3436,3437],{},[1311,3438,3439,3441],{},[1314,3440,1560],{},[1562,3442,1792],{},[1319,3444,2994],{"encoding":1321},"; jinak nemáme důvod ",[1296,3447,3449],{"className":3448},[1299],[1301,3450,3451],{"xmlns":1303},[1305,3452,3453,3461],{},[1308,3454,3455],{},[1311,3456,3457,3459],{},[1314,3458,1560],{},[1562,3460,1564],{},[1319,3462,1567],{"encoding":1321}," zamítnout.",[1148,3465,3466,3467,1395],{},"V R počítá test i očekávané četnosti funkce ",[3468,3469,3470],"code",{},"chisq.test()",[1514,3472,3476,3484,3487,3490,3636],{"className":3473,"dataCallout":3475},[1517,3474],"callout-example","example",[1148,3477,3479,3483],{"className":3478},[1523],[1296,3480],{"className":3481,"ariaHidden":1530},[1527,3482,1529],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1148,3485,3486],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1148,3488,3489],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1162,3491,3492,3531],{},[1165,3493,3494],{},[1168,3495,3496,3499,3502,3505,3508],{},[1171,3497,3498],{},"vzdělání \\ nákup",[1171,3500,3501],{},"ano",[1171,3503,3504],{},"ne, ale plánuji",[1171,3506,3507],{},"ne, neplánuji",[1171,3509,3510],{},[1296,3511,3513],{"className":3512},[1299],[1301,3514,3515],{"xmlns":1303},[1305,3516,3517,3529],{},[1308,3518,3519],{},[1311,3520,3521,3523],{},[1314,3522,1683],{},[1308,3524,3525,3527],{},[1314,3526,1876],{},[1685,3528,1977],{},[1319,3530,2211],{"encoding":1321},[1178,3532,3533,3549,3566,3583,3599],{},[1168,3534,3535,3538,3541,3544,3546],{},[1183,3536,3537],{},"SŠ bez maturity",[1183,3539,3540],{},"4",[1183,3542,3543],{},"13",[1183,3545,2274],{},[1183,3547,3548],{},"29",[1168,3550,3551,3554,3557,3560,3563],{},[1183,3552,3553],{},"SŠ s maturitou, VOŠ",[1183,3555,3556],{},"31",[1183,3558,3559],{},"62",[1183,3561,3562],{},"71",[1183,3564,3565],{},"164",[1168,3567,3568,3571,3574,3577,3580],{},[1183,3569,3570],{},"VŠ",[1183,3572,3573],{},"44",[1183,3575,3576],{},"58",[1183,3578,3579],{},"66",[1183,3581,3582],{},"168",[1168,3584,3585,3588,3591,3594,3596],{},[1183,3586,3587],{},"ZŠ",[1183,3589,3590],{},"3",[1183,3592,3593],{},"9",[1183,3595,2274],{},[1183,3597,3598],{},"24",[1168,3600,3601,3624,3627,3630,3633],{},[1183,3602,3603],{},[1296,3604,3606],{"className":3605},[1299],[1301,3607,3608],{"xmlns":1303},[1305,3609,3610,3622],{},[1308,3611,3612],{},[1311,3613,3614,3616],{},[1314,3615,1683],{},[1308,3617,3618,3620],{},[1685,3619,1977],{},[1314,3621,1881],{},[1319,3623,2603],{"encoding":1321},[1183,3625,3626],{},"82",[1183,3628,3629],{},"142",[1183,3631,3632],{},"161",[1183,3634,3635],{},"385",[1148,3637,3638,3690],{},[1296,3639,3641],{"className":3640},[1299],[1301,3642,3643],{"xmlns":1303},[1305,3644,3645,3687],{},[1308,3646,3647,3653,3655,3665,3667,3677],{},[1311,3648,3649,3651],{},[1314,3650,1560],{},[1562,3652,1564],{},[1685,3654,1956],{},[1311,3656,3657,3659],{},[1314,3658,1148],{},[1308,3660,3661,3663],{},[1314,3662,1876],{},[1314,3664,1881],{},[1685,3666,1980],{},[1311,3668,3669,3671],{},[1314,3670,1148],{},[1308,3672,3673,3675],{},[1314,3674,1876],{},[1685,3676,1977],{},[1311,3678,3679,3681],{},[1314,3680,1148],{},[1308,3682,3683,3685],{},[1685,3684,1977],{},[1314,3686,1881],{},[1319,3688,3689],{"encoding":1321},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3692,3693,3696],"pre",{"className":3694,"code":3695,"language":71,"meta":1452,"style":1452},"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",[3468,3697,3698,3737,3754,3771,3789,3812,3825,3860,3888,3901],{"__ignoreMap":1452},[1296,3699,3701,3705,3709,3713,3716,3719,3721,3724,3726,3729,3731,3734],{"class":3700,"line":10},"line",[1296,3702,3704],{"class":3703},"sP4rz","tab1",[1296,3706,3708],{"class":3707},"s8jYJ"," \u003C-",[1296,3710,3712],{"class":3711},"snPdu"," matrix",[1296,3714,1873],{"class":3715},"sxrX7",[1296,3717,3718],{"class":3711},"c",[1296,3720,1873],{"class":3715},[1296,3722,3540],{"class":3723},"sBjJW",[1296,3725,1795],{"class":3707},[1296,3727,3728],{"class":3723}," 13",[1296,3730,1795],{"class":3707},[1296,3732,3733],{"class":3723}," 12",[1296,3735,3736],{"class":3707},",\n",[1296,3738,3739,3742,3744,3747,3749,3752],{"class":3700,"line":27},[1296,3740,3741],{"class":3723},"                 31",[1296,3743,1795],{"class":3707},[1296,3745,3746],{"class":3723}," 62",[1296,3748,1795],{"class":3707},[1296,3750,3751],{"class":3723}," 71",[1296,3753,3736],{"class":3707},[1296,3755,3756,3759,3761,3764,3766,3769],{"class":3700,"line":148},[1296,3757,3758],{"class":3723},"                 44",[1296,3760,1795],{"class":3707},[1296,3762,3763],{"class":3723}," 58",[1296,3765,1795],{"class":3707},[1296,3767,3768],{"class":3723}," 66",[1296,3770,3736],{"class":3707},[1296,3772,3773,3776,3778,3781,3783,3785,3787],{"class":3700,"line":111},[1296,3774,3775],{"class":3723},"                 3",[1296,3777,1795],{"class":3707},[1296,3779,3780],{"class":3723},"  9",[1296,3782,1795],{"class":3707},[1296,3784,3733],{"class":3723},[1296,3786,1884],{"class":3715},[1296,3788,3736],{"class":3707},[1296,3790,3791,3794,3797,3800,3802,3805,3807,3810],{"class":3700,"line":96},[1296,3792,3793],{"class":3703},"               nrow",[1296,3795,3796],{"class":3707}," =",[1296,3798,3799],{"class":3723}," 4",[1296,3801,1795],{"class":3707},[1296,3803,3804],{"class":3703}," byrow",[1296,3806,3796],{"class":3707},[1296,3808,3809],{"class":3723}," TRUE",[1296,3811,3736],{"class":3707},[1296,3813,3814,3817,3819,3822],{"class":3700,"line":89},[1296,3815,3816],{"class":3703},"               dimnames",[1296,3818,3796],{"class":3707},[1296,3820,3821],{"class":3711}," list",[1296,3823,3824],{"class":3715},"(\n",[1296,3826,3827,3830,3832,3835,3837,3841,3843,3846,3848,3851,3853,3856,3858],{"class":3700,"line":82},[1296,3828,3829],{"class":3703},"                 vzdelani",[1296,3831,3796],{"class":3707},[1296,3833,3834],{"class":3711}," c",[1296,3836,1873],{"class":3715},[1296,3838,3840],{"class":3839},"sIIMD","\"SS bez maturity\"",[1296,3842,1795],{"class":3707},[1296,3844,3845],{"class":3839}," \"SS s maturitou nebo VOS\"",[1296,3847,1795],{"class":3707},[1296,3849,3850],{"class":3839}," \"VS\"",[1296,3852,1795],{"class":3707},[1296,3854,3855],{"class":3839}," \"ZS\"",[1296,3857,1884],{"class":3715},[1296,3859,3736],{"class":3707},[1296,3861,3862,3865,3868,3870,3872,3875,3877,3880,3882,3885],{"class":3700,"line":75},[1296,3863,3864],{"class":3703},"                 nakup",[1296,3866,3867],{"class":3707},"    =",[1296,3869,3834],{"class":3711},[1296,3871,1873],{"class":3715},[1296,3873,3874],{"class":3839},"\"ano\"",[1296,3876,1795],{"class":3707},[1296,3878,3879],{"class":3839}," \"ne, ale planuji\"",[1296,3881,1795],{"class":3707},[1296,3883,3884],{"class":3839}," \"ne, neplanuji\"",[1296,3886,3887],{"class":3715},")))\n",[1296,3889,3891,3894,3896,3898],{"class":3700,"line":3890},9,[1296,3892,3893],{"class":3711},"chisq.test",[1296,3895,1873],{"class":3715},[1296,3897,3704],{"class":3703},[1296,3899,3900],{"class":3715},")\n",[1296,3902,3903,3905,3907,3909,3911,3914],{"class":3700,"line":72},[1296,3904,3893],{"class":3711},[1296,3906,1873],{"class":3715},[1296,3908,3704],{"class":3703},[1296,3910,1884],{"class":3715},[1296,3912,3913],{"class":3707},"$",[1296,3915,3916],{"class":3703},"expected\n",[3692,3918,3923],{"className":3919,"code":3921,"language":3922,"meta":1452},[3920],"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",[3468,3924,3921],{"__ignoreMap":1452},[1148,3926,3927,3928,3951,3952,3966,3967,3987,3988,4005],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1296,3929,3931],{"className":3930},[1299],[1301,3932,3933],{"xmlns":1303},[1305,3934,3935,3948],{},[1308,3936,3937,3943,3945],{},[1579,3938,3939,3941],{},[1314,3940,1583],{},[1562,3942,1586],{},[1685,3944,1980],{},[1562,3946,3947],{},"5,49",[1319,3949,3950],{"encoding":1321},"\\chi^2 = 5{,}49"," s ",[1296,3953,3955],{"className":3954},[1299],[1301,3956,3957],{"xmlns":1303},[1305,3958,3959,3964],{},[1308,3960,3961],{},[1562,3962,3963],{},"6",[1319,3965,3963],{"encoding":1321}," stupni\nvolnosti dává p-hodnotu ",[1296,3968,3970],{"className":3969},[1299],[1301,3971,3972],{"xmlns":1303},[1305,3973,3974,3984],{},[1308,3975,3976,3979,3981],{},[1562,3977,3978],{},"0,483",[1685,3980,1687],{},[1562,3982,3983],{},"0,05",[1319,3985,3986],{"encoding":1321},"0{,}483 > 0{,}05",": ",[1296,3989,3991],{"className":3990},[1299],[1301,3992,3993],{"xmlns":1303},[1305,3994,3995,4003],{},[1308,3996,3997],{},[1311,3998,3999,4001],{},[1314,4000,1560],{},[1562,4002,1564],{},[1319,4004,1567],{"encoding":1321}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1514,4007,4009,4016,4019,4064],{"className":4008,"dataCallout":3475},[1517,3474],[1148,4010,4012,4015],{"className":4011},[1523],[1296,4013],{"className":4014,"ariaHidden":1530},[1527,3482,1529],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1148,4017,4018],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1162,4020,4021,4035],{},[1165,4022,4023],{},[1168,4024,4025,4028,4031,4033],{},[1171,4026,4027],{},"zveřejňuje \\ vzdělání",[1171,4029,4030],{},"SŠ",[1171,4032,3570],{},[1171,4034,3587],{},[1178,4036,4037,4051],{},[1168,4038,4039,4042,4045,4048],{},[1183,4040,4041],{},"ne",[1183,4043,4044],{},"20",[1183,4046,4047],{},"33",[1183,4049,4050],{},"39",[1168,4052,4053,4055,4058,4061],{},[1183,4054,3501],{},[1183,4056,4057],{},"25",[1183,4059,4060],{},"28",[1183,4062,4063],{},"76",[1148,4065,4066,4117],{},[1296,4067,4069],{"className":4068},[1299],[1301,4070,4071],{"xmlns":1303},[1305,4072,4073,4115],{},[1308,4074,4075,4081,4083,4093,4095,4105],{},[1311,4076,4077,4079],{},[1314,4078,1560],{},[1562,4080,1564],{},[1685,4082,1956],{},[1311,4084,4085,4087],{},[1314,4086,1148],{},[1308,4088,4089,4091],{},[1314,4090,1876],{},[1314,4092,1881],{},[1685,4094,1980],{},[1311,4096,4097,4099],{},[1314,4098,1148],{},[1308,4100,4101,4103],{},[1314,4102,1876],{},[1685,4104,1977],{},[1311,4106,4107,4109],{},[1314,4108,1148],{},[1308,4110,4111,4113],{},[1685,4112,1977],{},[1314,4114,1881],{},[1319,4116,3689],{"encoding":1321}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3692,4119,4121],{"className":3694,"code":4120,"language":71,"meta":1452,"style":1452},"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",[3468,4122,4123,4152,4171,4190,4200,4223,4247,4257],{"__ignoreMap":1452},[1296,4124,4125,4128,4130,4132,4134,4136,4138,4140,4142,4145,4147,4150],{"class":3700,"line":10},[1296,4126,4127],{"class":3703},"tab2",[1296,4129,3708],{"class":3707},[1296,4131,3712],{"class":3711},[1296,4133,1873],{"class":3715},[1296,4135,3718],{"class":3711},[1296,4137,1873],{"class":3715},[1296,4139,4044],{"class":3723},[1296,4141,1795],{"class":3707},[1296,4143,4144],{"class":3723}," 33",[1296,4146,1795],{"class":3707},[1296,4148,4149],{"class":3723}," 39",[1296,4151,3736],{"class":3707},[1296,4153,4154,4157,4159,4162,4164,4167,4169],{"class":3700,"line":27},[1296,4155,4156],{"class":3723},"                 25",[1296,4158,1795],{"class":3707},[1296,4160,4161],{"class":3723}," 28",[1296,4163,1795],{"class":3707},[1296,4165,4166],{"class":3723}," 76",[1296,4168,1884],{"class":3715},[1296,4170,3736],{"class":3707},[1296,4172,4173,4175,4177,4180,4182,4184,4186,4188],{"class":3700,"line":148},[1296,4174,3793],{"class":3703},[1296,4176,3796],{"class":3707},[1296,4178,4179],{"class":3723}," 2",[1296,4181,1795],{"class":3707},[1296,4183,3804],{"class":3703},[1296,4185,3796],{"class":3707},[1296,4187,3809],{"class":3723},[1296,4189,3736],{"class":3707},[1296,4191,4192,4194,4196,4198],{"class":3700,"line":111},[1296,4193,3816],{"class":3703},[1296,4195,3796],{"class":3707},[1296,4197,3821],{"class":3711},[1296,4199,3824],{"class":3715},[1296,4201,4202,4205,4207,4209,4211,4214,4216,4219,4221],{"class":3700,"line":96},[1296,4203,4204],{"class":3703},"                 zverejnuje",[1296,4206,3796],{"class":3707},[1296,4208,3834],{"class":3711},[1296,4210,1873],{"class":3715},[1296,4212,4213],{"class":3839},"\"ne\"",[1296,4215,1795],{"class":3707},[1296,4217,4218],{"class":3839}," \"ano\"",[1296,4220,1884],{"class":3715},[1296,4222,3736],{"class":3707},[1296,4224,4225,4227,4230,4232,4234,4237,4239,4241,4243,4245],{"class":3700,"line":89},[1296,4226,3829],{"class":3703},[1296,4228,4229],{"class":3707},"   =",[1296,4231,3834],{"class":3711},[1296,4233,1873],{"class":3715},[1296,4235,4236],{"class":3839},"\"SS\"",[1296,4238,1795],{"class":3707},[1296,4240,3850],{"class":3839},[1296,4242,1795],{"class":3707},[1296,4244,3855],{"class":3839},[1296,4246,3887],{"class":3715},[1296,4248,4249,4251,4253,4255],{"class":3700,"line":82},[1296,4250,3893],{"class":3711},[1296,4252,1873],{"class":3715},[1296,4254,4127],{"class":3703},[1296,4256,3900],{"class":3715},[1296,4258,4259,4261,4263,4265,4267,4269],{"class":3700,"line":75},[1296,4260,3893],{"class":3711},[1296,4262,1873],{"class":3715},[1296,4264,4127],{"class":3703},[1296,4266,1884],{"class":3715},[1296,4268,3913],{"class":3707},[1296,4270,3916],{"class":3703},[3692,4272,4275],{"className":4273,"code":4274,"language":3922,"meta":1452},[3920],"    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",[3468,4276,4274],{"__ignoreMap":1452},[1148,4278,4279,4280,3951,4303,4316,4317,3987,4337,4354,4355,1395],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1296,4281,4283],{"className":4282},[1299],[1301,4284,4285],{"xmlns":1303},[1305,4286,4287,4300],{},[1308,4288,4289,4295,4297],{},[1579,4290,4291,4293],{},[1314,4292,1583],{},[1562,4294,1586],{},[1685,4296,1980],{},[1562,4298,4299],{},"6,87",[1319,4301,4302],{"encoding":1321},"\\chi^2 = 6{,}87",[1296,4304,4306],{"className":4305},[1299],[1301,4307,4308],{"xmlns":1303},[1305,4309,4310,4314],{},[1308,4311,4312],{},[1562,4313,1586],{},[1319,4315,1586],{"encoding":1321}," stupni volnosti dává\np-hodnotu ",[1296,4318,4320],{"className":4319},[1299],[1301,4321,4322],{"xmlns":1303},[1305,4323,4324,4334],{},[1308,4325,4326,4329,4332],{},[1562,4327,4328],{},"0,032",[1685,4330,4331],{},"\u003C",[1562,4333,3983],{},[1319,4335,4336],{"encoding":1321},"0{,}032 \u003C 0{,}05",[1296,4338,4340],{"className":4339},[1299],[1301,4341,4342],{"xmlns":1303},[1305,4343,4344,4352],{},[1308,4345,4346],{},[1311,4347,4348,4350],{},[1314,4349,1560],{},[1562,4351,1564],{},[1319,4353,1567],{"encoding":1321}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1108,4356,4357],{},"závisí",[1148,4359,4360,4361,4378],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1296,4362,4364],{"className":4363},[1299],[1301,4365,4366],{"xmlns":1303},[1305,4367,4368,4376],{},[1308,4369,4370],{},[1311,4371,4372,4374],{},[1314,4373,1560],{},[1562,4375,1564],{},[1319,4377,1567],{"encoding":1321}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1148,4380,4381],{},[4382,4383],"img",{"alt":4384,"className":4385,"src":4387},"mask-kt-observed-expected",[1245,4386],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1148,4389,4390,4391,4408,4409,1956],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1296,4392,4394],{"className":4393},[1299],[1301,4395,4396],{"xmlns":1303},[1305,4397,4398,4406],{},[1308,4399,4400],{},[1579,4401,4402,4404],{},[1314,4403,1583],{},[1562,4405,1586],{},[1319,4407,1589],{"encoding":1321}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1296,4410,4412],{"className":4411},[1299],[1301,4413,4414],{"xmlns":1303},[1305,4415,4416,4420],{},[1308,4417,4418],{},[1314,4419,1602],{},[1319,4421,1602],{"encoding":1321},[1148,4423,4424],{},[4382,4425],{"alt":4426,"className":4427,"src":4428},"mask-kt-chi2-kriticky-obor",[1245,4386],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1143,4430,1650],{"id":4431},"cramérův-koeficient-kontingence",[1148,4433,4434,4435,1956],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1108,4436,4437],{},"Cramérův koeficient\nkontingence",[1296,4439,4441],{"className":4440},[1299],[1301,4442,4443],{"xmlns":1303,"display":1962},[1305,4444,4445,4500],{},[1308,4446,4447,4449,4451,4476,4478,4480,4482,4484,4487,4490,4492,4494,4496,4498],{},[1314,4448,1663],{},[1685,4450,1980],{},[4452,4453,4454],"msqrt",{},[2738,4455,4456,4462],{},[1579,4457,4458,4460],{},[1314,4459,1583],{},[1562,4461,1586],{},[1308,4463,4464,4466,4468,4470,4472,4474],{},[1314,4465,1683],{},[1685,4467,1873],{"stretchy":1872},[1314,4469,1366],{},[1685,4471,3062],{},[1562,4473,1792],{},[1685,4475,1884],{"stretchy":1872},[1685,4477,1795],{"separator":1530},[2010,4479],{"width":2012},[1314,4481,1366],{},[1685,4483,1980],{},[1314,4485,4486],{},"min",[1685,4488,4489],{},"⁡",[1685,4491,1873],{"stretchy":1872},[1314,4493,71],{},[1685,4495,1795],{"separator":1530},[1314,4497,1852],{},[1685,4499,1884],{"stretchy":1872},[1319,4501,4502],{"encoding":1321},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1148,4504,4505,4506,4523,4524,4542,4543,4561],{},"kde ",[1296,4507,4509],{"className":4508},[1299],[1301,4510,4511],{"xmlns":1303},[1305,4512,4513,4521],{},[1308,4514,4515],{},[1579,4516,4517,4519],{},[1314,4518,1583],{},[1562,4520,1586],{},[1319,4522,1589],{"encoding":1321}," je hodnota testového kritéria z testu nezávislosti. ",[1296,4525,4527],{"className":4526},[1299],[1301,4528,4529],{"xmlns":1303},[1305,4530,4531,4539],{},[1308,4532,4533,4535,4537],{},[1314,4534,1663],{},[1685,4536,1980],{},[1562,4538,1564],{},[1319,4540,4541],{"encoding":1321},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1296,4544,4546],{"className":4545},[1299],[1301,4547,4548],{"xmlns":1303},[1305,4549,4550,4558],{},[1308,4551,4552,4554,4556],{},[1314,4553,1663],{},[1685,4555,1980],{},[1562,4557,1792],{},[1319,4559,4560],{"encoding":1321},"V = 1"," jejich úplné závislosti.",[3692,4563,4565],{"className":3694,"code":4564,"language":71,"meta":1452,"style":1452},"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",[3468,4566,4567,4641,4704,4709],{"__ignoreMap":1452},[1296,4568,4569,4572,4574,4577,4579,4582,4584,4586,4588,4590,4592,4594,4597,4600,4602,4605,4608,4610,4612,4614,4617,4619,4621,4623,4626,4628,4630,4633,4636,4639],{"class":3700,"line":10},[1296,4570,4571],{"class":3703},"V1",[1296,4573,3708],{"class":3707},[1296,4575,4576],{"class":3711}," sqrt",[1296,4578,1873],{"class":3715},[1296,4580,4581],{"class":3711},"as.numeric",[1296,4583,1873],{"class":3715},[1296,4585,3893],{"class":3711},[1296,4587,1873],{"class":3715},[1296,4589,3704],{"class":3703},[1296,4591,1884],{"class":3715},[1296,4593,3913],{"class":3707},[1296,4595,4596],{"class":3703},"statistic",[1296,4598,4599],{"class":3715},") ",[1296,4601,1502],{"class":3707},[1296,4603,4604],{"class":3715}," (",[1296,4606,4607],{"class":3711},"sum",[1296,4609,1873],{"class":3715},[1296,4611,3704],{"class":3703},[1296,4613,4599],{"class":3715},[1296,4615,4616],{"class":3707},"*",[1296,4618,4604],{"class":3715},[1296,4620,4486],{"class":3711},[1296,4622,1873],{"class":3715},[1296,4624,4625],{"class":3711},"dim",[1296,4627,1873],{"class":3715},[1296,4629,3704],{"class":3703},[1296,4631,4632],{"class":3715},")) ",[1296,4634,4635],{"class":3707},"-",[1296,4637,4638],{"class":3723}," 1",[1296,4640,3887],{"class":3715},[1296,4642,4643,4646,4648,4650,4652,4654,4656,4658,4660,4662,4664,4666,4668,4670,4672,4674,4676,4678,4680,4682,4684,4686,4688,4690,4692,4694,4696,4698,4700,4702],{"class":3700,"line":27},[1296,4644,4645],{"class":3703},"V2",[1296,4647,3708],{"class":3707},[1296,4649,4576],{"class":3711},[1296,4651,1873],{"class":3715},[1296,4653,4581],{"class":3711},[1296,4655,1873],{"class":3715},[1296,4657,3893],{"class":3711},[1296,4659,1873],{"class":3715},[1296,4661,4127],{"class":3703},[1296,4663,1884],{"class":3715},[1296,4665,3913],{"class":3707},[1296,4667,4596],{"class":3703},[1296,4669,4599],{"class":3715},[1296,4671,1502],{"class":3707},[1296,4673,4604],{"class":3715},[1296,4675,4607],{"class":3711},[1296,4677,1873],{"class":3715},[1296,4679,4127],{"class":3703},[1296,4681,4599],{"class":3715},[1296,4683,4616],{"class":3707},[1296,4685,4604],{"class":3715},[1296,4687,4486],{"class":3711},[1296,4689,1873],{"class":3715},[1296,4691,4625],{"class":3711},[1296,4693,1873],{"class":3715},[1296,4695,4127],{"class":3703},[1296,4697,4632],{"class":3715},[1296,4699,4635],{"class":3707},[1296,4701,4638],{"class":3723},[1296,4703,3887],{"class":3715},[1296,4705,4706],{"class":3700,"line":148},[1296,4707,4708],{"class":3703},"V1\n",[1296,4710,4711],{"class":3700,"line":111},[1296,4712,4713],{"class":3703},"V2\n",[3692,4715,4718],{"className":4716,"code":4717,"language":3922,"meta":1452},[3920],"[1] 0.08441958\n[1] 0.1762822\n",[3468,4719,4717],{"__ignoreMap":1452},[1148,4721,4722],{},[4382,4723],{"alt":4724,"className":4725,"src":4726},"mask-kt-cramerovo-v",[1245,4386],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1148,4728,4729,4730,4749,4750,4767,4768,3987,4787,4804],{},"U nákupu potravin je ",[1296,4731,4733],{"className":4732},[1299],[1301,4734,4735],{"xmlns":1303},[1305,4736,4737,4746],{},[1308,4738,4739,4741,4743],{},[1314,4740,1663],{},[1685,4742,1980],{},[1562,4744,4745],{},"0,084",[1319,4747,4748],{"encoding":1321},"V = 0{,}084"," zanedbatelné — ostatně ",[1296,4751,4753],{"className":4752},[1299],[1301,4754,4755],{"xmlns":1303},[1305,4756,4757,4765],{},[1308,4758,4759],{},[1311,4760,4761,4763],{},[1314,4762,1560],{},[1562,4764,1564],{},[1319,4766,1567],{"encoding":1321}," jsme ani nezamítli. U zveřejňování údajů je ",[1296,4769,4771],{"className":4770},[1299],[1301,4772,4773],{"xmlns":1303},[1305,4774,4775,4784],{},[1308,4776,4777,4779,4781],{},[1314,4778,1663],{},[1685,4780,1980],{},[1562,4782,4783],{},"0,176",[1319,4785,4786],{"encoding":1321},"V = 0{,}176",[1296,4788,4790],{"className":4789},[1299],[1301,4791,4792],{"xmlns":1303},[1305,4793,4794,4802],{},[1308,4795,4796],{},[1311,4797,4798,4800],{},[1314,4799,1560],{},[1562,4801,1564],{},[1319,4803,1567],{"encoding":1321},"\njsme zamítli, ale samotná závislost je stále slabá.",[1143,4806,1670],{"id":4807},"čtyřpolní-tabulka",[1148,4809,4810,4812,4813,4826,4827,4840,4841,4863],{},[1108,4811,1670],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1296,4814,4816],{"className":4815},[1299],[1301,4817,4818],{"xmlns":1303},[1305,4819,4820,4824],{},[1308,4821,4822],{},[1314,4823,1185],{},[1319,4825,1185],{"encoding":1321}," i ",[1296,4828,4830],{"className":4829},[1299],[1301,4831,4832],{"xmlns":1303},[1305,4833,4834,4838],{},[1308,4835,4836],{},[1314,4837,1193],{},[1319,4839,1193],{"encoding":1321}," mají jen dvě varianty\n(",[1296,4842,4844],{"className":4843},[1299],[1301,4845,4846],{"xmlns":1303},[1305,4847,4848,4860],{},[1308,4849,4850,4852,4854,4856,4858],{},[1314,4851,71],{},[1685,4853,1980],{},[1314,4855,1852],{},[1685,4857,1980],{},[1562,4859,1586],{},[1319,4861,4862],{"encoding":1321},"r = s = 2","):",[1162,4865,4866,4950],{},[1165,4867,4868],{},[1168,4869,4870,4889,4908,4927],{},[1171,4871,4872],{},[1296,4873,4875],{"className":4874},[1299],[1301,4876,4877],{"xmlns":1303},[1305,4878,4879,4887],{},[1308,4880,4881,4883,4885],{},[1314,4882,1185],{},[1314,4884,2120],{"mathvariant":2119},[1314,4886,1193],{},[1319,4888,2125],{"encoding":1321},[1171,4890,4891],{},[1296,4892,4894],{"className":4893},[1299],[1301,4895,4896],{"xmlns":1303},[1305,4897,4898,4906],{},[1308,4899,4900],{},[1311,4901,4902,4904],{},[1314,4903,1193],{},[1562,4905,1792],{},[1319,4907,2145],{"encoding":1321},[1171,4909,4910],{},[1296,4911,4913],{"className":4912},[1299],[1301,4914,4915],{"xmlns":1303},[1305,4916,4917,4925],{},[1308,4918,4919],{},[1311,4920,4921,4923],{},[1314,4922,1193],{},[1562,4924,1586],{},[1319,4926,2165],{"encoding":1321},[1171,4928,4929],{},[1296,4930,4932],{"className":4931},[1299],[1301,4933,4934],{"xmlns":1303},[1305,4935,4936,4948],{},[1308,4937,4938],{},[1311,4939,4940,4942],{},[1314,4941,1683],{},[1308,4943,4944,4946],{},[1314,4945,1876],{},[1685,4947,1977],{},[1319,4949,2211],{"encoding":1321},[1178,4951,4952,5034,5116],{},[1168,4953,4954,4973,4992,5011],{},[1183,4955,4956],{},[1296,4957,4959],{"className":4958},[1299],[1301,4960,4961],{"xmlns":1303},[1305,4962,4963,4971],{},[1308,4964,4965],{},[1311,4966,4967,4969],{},[1314,4968,1185],{},[1562,4970,1792],{},[1319,4972,2235],{"encoding":1321},[1183,4974,4975],{},[1296,4976,4978],{"className":4977},[1299],[1301,4979,4980],{"xmlns":1303},[1305,4981,4982,4990],{},[1308,4983,4984],{},[1311,4985,4986,4988],{},[1314,4987,1683],{},[1562,4989,2253],{},[1319,4991,2256],{"encoding":1321},[1183,4993,4994],{},[1296,4995,4997],{"className":4996},[1299],[1301,4998,4999],{"xmlns":1303},[1305,5000,5001,5009],{},[1308,5002,5003],{},[1311,5004,5005,5007],{},[1314,5006,1683],{},[1562,5008,2274],{},[1319,5010,2277],{"encoding":1321},[1183,5012,5013],{},[1296,5014,5016],{"className":5015},[1299],[1301,5017,5018],{"xmlns":1303},[1305,5019,5020,5032],{},[1308,5021,5022],{},[1311,5023,5024,5026],{},[1314,5025,1683],{},[1308,5027,5028,5030],{},[1562,5029,1792],{},[1685,5031,1977],{},[1319,5033,2327],{"encoding":1321},[1168,5035,5036,5055,5074,5093],{},[1183,5037,5038],{},[1296,5039,5041],{"className":5040},[1299],[1301,5042,5043],{"xmlns":1303},[1305,5044,5045,5053],{},[1308,5046,5047],{},[1311,5048,5049,5051],{},[1314,5050,1185],{},[1562,5052,1586],{},[1319,5054,2349],{"encoding":1321},[1183,5056,5057],{},[1296,5058,5060],{"className":5059},[1299],[1301,5061,5062],{"xmlns":1303},[1305,5063,5064,5072],{},[1308,5065,5066],{},[1311,5067,5068,5070],{},[1314,5069,1683],{},[1562,5071,2367],{},[1319,5073,2370],{"encoding":1321},[1183,5075,5076],{},[1296,5077,5079],{"className":5078},[1299],[1301,5080,5081],{"xmlns":1303},[1305,5082,5083,5091],{},[1308,5084,5085],{},[1311,5086,5087,5089],{},[1314,5088,1683],{},[1562,5090,2388],{},[1319,5092,2391],{"encoding":1321},[1183,5094,5095],{},[1296,5096,5098],{"className":5097},[1299],[1301,5099,5100],{"xmlns":1303},[1305,5101,5102,5114],{},[1308,5103,5104],{},[1311,5105,5106,5108],{},[1314,5107,1683],{},[1308,5109,5110,5112],{},[1562,5111,1586],{},[1685,5113,1977],{},[1319,5115,2441],{"encoding":1321},[1168,5117,5118,5141,5164,5187],{},[1183,5119,5120],{},[1296,5121,5123],{"className":5122},[1299],[1301,5124,5125],{"xmlns":1303},[1305,5126,5127,5139],{},[1308,5128,5129],{},[1311,5130,5131,5133],{},[1314,5132,1683],{},[1308,5134,5135,5137],{},[1685,5136,1977],{},[1314,5138,1881],{},[1319,5140,2603],{"encoding":1321},[1183,5142,5143],{},[1296,5144,5146],{"className":5145},[1299],[1301,5147,5148],{"xmlns":1303},[1305,5149,5150,5162],{},[1308,5151,5152],{},[1311,5153,5154,5156],{},[1314,5155,1683],{},[1308,5157,5158,5160],{},[1685,5159,1977],{},[1562,5161,1792],{},[1319,5163,2627],{"encoding":1321},[1183,5165,5166],{},[1296,5167,5169],{"className":5168},[1299],[1301,5170,5171],{"xmlns":1303},[1305,5172,5173,5185],{},[1308,5174,5175],{},[1311,5176,5177,5179],{},[1314,5178,1683],{},[1308,5180,5181,5183],{},[1685,5182,1977],{},[1562,5184,1586],{},[1319,5186,2651],{"encoding":1321},[1183,5188,5189],{},[1296,5190,5192],{"className":5191},[1299],[1301,5193,5194],{"xmlns":1303},[1305,5195,5196,5200],{},[1308,5197,5198],{},[1314,5199,1683],{},[1319,5201,1683],{"encoding":1321},[1148,5203,1696,5204,5222],{},[1296,5205,5207],{"className":5206},[1299],[1301,5208,5209],{"xmlns":1303},[1305,5210,5211,5219],{},[1308,5212,5213,5215,5217],{},[1314,5214,1683],{},[1685,5216,1687],{},[1562,5218,1690],{},[1319,5220,5221],{"encoding":1321},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1296,5224,5226],{"className":5225},[1299],[1301,5227,5228],{"xmlns":1303,"display":1962},[1305,5229,5230,5324],{},[1308,5231,5232,5238,5240,5242,5244],{},[1579,5233,5234,5236],{},[1314,5235,1583],{},[1562,5237,1586],{},[1685,5239,1980],{},[1314,5241,1683],{},[2907,5243,2909],{},[2738,5245,5246,5282],{},[1308,5247,5248,5250,5256,5262,5264,5270,5276],{},[1685,5249,1873],{"stretchy":1872},[1311,5251,5252,5254],{},[1314,5253,1683],{},[1562,5255,2253],{},[1311,5257,5258,5260],{},[1314,5259,1683],{},[1562,5261,2388],{},[1685,5263,3062],{},[1311,5265,5266,5268],{},[1314,5267,1683],{},[1562,5269,2274],{},[1311,5271,5272,5274],{},[1314,5273,1683],{},[1562,5275,2367],{},[1579,5277,5278,5280],{},[1685,5279,1884],{"stretchy":1872},[1562,5281,1586],{},[1308,5283,5284,5294,5304,5314],{},[1311,5285,5286,5288],{},[1314,5287,1683],{},[1308,5289,5290,5292],{},[1562,5291,1792],{},[1685,5293,1977],{},[1311,5295,5296,5298],{},[1314,5297,1683],{},[1308,5299,5300,5302],{},[1562,5301,1586],{},[1685,5303,1977],{},[1311,5305,5306,5308],{},[1314,5307,1683],{},[1308,5309,5310,5312],{},[1685,5311,1977],{},[1562,5313,1792],{},[1311,5315,5316,5318],{},[1314,5317,1683],{},[1308,5319,5320,5322],{},[1685,5321,1977],{},[1562,5323,1586],{},[1319,5325,5326],{"encoding":1321},"\\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}}",[1148,5328,5329,5330,5390,5391,5427,5428,5431,5432,5435],{},"s kritickým oborem ",[1296,5331,5333],{"className":5332},[1299],[1301,5334,5335],{"xmlns":1303},[1305,5336,5337,5387],{},[1308,5338,5339,5345,5347,5349,5355,5357,5363,5365,5379,5381,5383,5385],{},[1311,5340,5341,5343],{},[1314,5342,1602],{},[1314,5344,3363],{},[1685,5346,1980],{},[1685,5348,3332],{"stretchy":1872},[1579,5350,5351,5353],{},[1314,5352,1583],{},[1562,5354,1586],{},[1685,5356,1956],{},[1579,5358,5359,5361],{},[1314,5360,1583],{},[1562,5362,1586],{},[1685,5364,3349],{},[3351,5366,5367,5369,5377],{},[1314,5368,1583],{},[1308,5370,5371,5373,5375],{},[1562,5372,1792],{},[1685,5374,3062],{},[1314,5376,3363],{},[1562,5378,1586],{},[1685,5380,1873],{"stretchy":1872},[1562,5382,1792],{},[1685,5384,1884],{"stretchy":1872},[1685,5386,3392],{"stretchy":1872},[1319,5388,5389],{"encoding":1321},"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 ",[1296,5392,5394],{"className":5393},[1299],[1301,5395,5396],{"xmlns":1303},[1305,5397,5398,5424],{},[1308,5399,5400,5402,5404,5406,5408,5410,5412,5414,5416,5418,5420,5422],{},[1685,5401,1873],{"stretchy":1872},[1314,5403,71],{},[1685,5405,3062],{},[1562,5407,1792],{},[1685,5409,1884],{"stretchy":1872},[1685,5411,1873],{"stretchy":1872},[1314,5413,1852],{},[1685,5415,3062],{},[1562,5417,1792],{},[1685,5419,1884],{"stretchy":1872},[1685,5421,1980],{},[1562,5423,1792],{},[1319,5425,5426],{"encoding":1321},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3468,5429,5430],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3468,5433,5434],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1143,5437,1703],{"id":5438},"mcnemarův-test",[1148,5440,5441,5442,5445,5446,5448,5449,5452,5453,5456,5457,5459],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1108,5443,5444],{},"různé"," znaky na stejném souboru. ",[1108,5447,1703],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1108,5450,5451],{},"jeden"," alternativní znak, a to ",[1108,5454,5455],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1108,5458,1699],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1148,5461,5462],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1162,5464,5465,5500],{},[1165,5466,5467],{},[1168,5468,5469,5472,5475,5477],{},[1171,5470,5471],{},"před \\ po",[1171,5473,5474],{},"+",[1171,5476,3062],{},[1171,5478,5479],{},[1296,5480,5482],{"className":5481},[1299],[1301,5483,5484],{"xmlns":1303},[1305,5485,5486,5498],{},[1308,5487,5488],{},[1311,5489,5490,5492],{},[1314,5491,1683],{},[1308,5493,5494,5496],{},[1314,5495,1876],{},[1685,5497,1977],{},[1319,5499,2211],{"encoding":1321},[1178,5501,5502,5567,5632],{},[1168,5503,5504,5506,5525,5544],{},[1183,5505,5474],{},[1183,5507,5508],{},[1296,5509,5511],{"className":5510},[1299],[1301,5512,5513],{"xmlns":1303},[1305,5514,5515,5523],{},[1308,5516,5517],{},[1311,5518,5519,5521],{},[1314,5520,1683],{},[1562,5522,2253],{},[1319,5524,2256],{"encoding":1321},[1183,5526,5527],{},[1296,5528,5530],{"className":5529},[1299],[1301,5531,5532],{"xmlns":1303},[1305,5533,5534,5542],{},[1308,5535,5536],{},[1311,5537,5538,5540],{},[1314,5539,1683],{},[1562,5541,2274],{},[1319,5543,2277],{"encoding":1321},[1183,5545,5546],{},[1296,5547,5549],{"className":5548},[1299],[1301,5550,5551],{"xmlns":1303},[1305,5552,5553,5565],{},[1308,5554,5555],{},[1311,5556,5557,5559],{},[1314,5558,1683],{},[1308,5560,5561,5563],{},[1562,5562,1792],{},[1685,5564,1977],{},[1319,5566,2327],{"encoding":1321},[1168,5568,5569,5571,5590,5609],{},[1183,5570,3062],{},[1183,5572,5573],{},[1296,5574,5576],{"className":5575},[1299],[1301,5577,5578],{"xmlns":1303},[1305,5579,5580,5588],{},[1308,5581,5582],{},[1311,5583,5584,5586],{},[1314,5585,1683],{},[1562,5587,2367],{},[1319,5589,2370],{"encoding":1321},[1183,5591,5592],{},[1296,5593,5595],{"className":5594},[1299],[1301,5596,5597],{"xmlns":1303},[1305,5598,5599,5607],{},[1308,5600,5601],{},[1311,5602,5603,5605],{},[1314,5604,1683],{},[1562,5606,2388],{},[1319,5608,2391],{"encoding":1321},[1183,5610,5611],{},[1296,5612,5614],{"className":5613},[1299],[1301,5615,5616],{"xmlns":1303},[1305,5617,5618,5630],{},[1308,5619,5620],{},[1311,5621,5622,5624],{},[1314,5623,1683],{},[1308,5625,5626,5628],{},[1562,5627,1586],{},[1685,5629,1977],{},[1319,5631,2441],{"encoding":1321},[1168,5633,5634,5657,5680,5703],{},[1183,5635,5636],{},[1296,5637,5639],{"className":5638},[1299],[1301,5640,5641],{"xmlns":1303},[1305,5642,5643,5655],{},[1308,5644,5645],{},[1311,5646,5647,5649],{},[1314,5648,1683],{},[1308,5650,5651,5653],{},[1685,5652,1977],{},[1314,5654,1881],{},[1319,5656,2603],{"encoding":1321},[1183,5658,5659],{},[1296,5660,5662],{"className":5661},[1299],[1301,5663,5664],{"xmlns":1303},[1305,5665,5666,5678],{},[1308,5667,5668],{},[1311,5669,5670,5672],{},[1314,5671,1683],{},[1308,5673,5674,5676],{},[1685,5675,1977],{},[1562,5677,1792],{},[1319,5679,2627],{"encoding":1321},[1183,5681,5682],{},[1296,5683,5685],{"className":5684},[1299],[1301,5686,5687],{"xmlns":1303},[1305,5688,5689,5701],{},[1308,5690,5691],{},[1311,5692,5693,5695],{},[1314,5694,1683],{},[1308,5696,5697,5699],{},[1685,5698,1977],{},[1562,5700,1586],{},[1319,5702,2651],{"encoding":1321},[1183,5704,5705],{},[1296,5706,5708],{"className":5707},[1299],[1301,5709,5710],{"xmlns":1303},[1305,5711,5712,5716],{},[1308,5713,5714],{},[1314,5715,1683],{},[1319,5717,1683],{"encoding":1321},[1148,5719,5720,5721,1370,5738,5755,5756,5759,5760,1370,5777,5794,5795,5798],{},"Pole ",[1296,5722,5724],{"className":5723},[1299],[1301,5725,5726],{"xmlns":1303},[1305,5727,5728,5736],{},[1308,5729,5730],{},[1311,5731,5732,5734],{},[1314,5733,1683],{},[1562,5735,2253],{},[1319,5737,2256],{"encoding":1321},[1296,5739,5741],{"className":5740},[1299],[1301,5742,5743],{"xmlns":1303},[1305,5744,5745,5753],{},[1308,5746,5747],{},[1311,5748,5749,5751],{},[1314,5750,1683],{},[1562,5752,2388],{},[1319,5754,2391],{"encoding":1321}," jsou ",[1108,5757,5758],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1296,5761,5763],{"className":5762},[1299],[1301,5764,5765],{"xmlns":1303},[1305,5766,5767,5775],{},[1308,5768,5769],{},[1311,5770,5771,5773],{},[1314,5772,1683],{},[1562,5774,2274],{},[1319,5776,2277],{"encoding":1321},[1296,5778,5780],{"className":5779},[1299],[1301,5781,5782],{"xmlns":1303},[1305,5783,5784,5792],{},[1308,5785,5786],{},[1311,5787,5788,5790],{},[1314,5789,1683],{},[1562,5791,2367],{},[1319,5793,2370],{"encoding":1321}," jsou\n",[1108,5796,5797],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1148,5800,5801],{},[4382,5802],{"alt":5803,"className":5804,"src":5805},"mask-kt-mcnemar-tabulka",[1245,4386],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1148,5807,5808],{},[1108,5809,2862],{},[1237,5811,5812,5849,5930,5988],{},[1105,5813,5814,5848],{},[1296,5815,5817],{"className":5816},[1299],[1301,5818,5819],{"xmlns":1303},[1305,5820,5821,5845],{},[1308,5822,5823,5829,5831,5837,5839],{},[1311,5824,5825,5827],{},[1314,5826,1560],{},[1562,5828,1564],{},[1685,5830,1956],{},[1311,5832,5833,5835],{},[1314,5834,1148],{},[1562,5836,2274],{},[1685,5838,1980],{},[1311,5840,5841,5843],{},[1314,5842,1148],{},[1562,5844,2367],{},[1319,5846,5847],{"encoding":1321},"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.",[1105,5850,2998,5851,5913,5915,5916,5929],{},[1296,5852,5854],{"className":5853},[1299],[1301,5855,5856],{"xmlns":1303,"display":1962},[1305,5857,5858,5910],{},[1308,5859,5860,5866,5868],{},[1579,5861,5862,5864],{},[1314,5863,1583],{},[1562,5865,1586],{},[1685,5867,1980],{},[2738,5869,5870,5894],{},[1308,5871,5872,5874,5880,5882,5888],{},[1685,5873,1873],{"stretchy":1872},[1311,5875,5876,5878],{},[1314,5877,1683],{},[1562,5879,2274],{},[1685,5881,3062],{},[1311,5883,5884,5886],{},[1314,5885,1683],{},[1562,5887,2367],{},[1579,5889,5890,5892],{},[1685,5891,1884],{"stretchy":1872},[1562,5893,1586],{},[1308,5895,5896,5902,5904],{},[1311,5897,5898,5900],{},[1314,5899,1683],{},[1562,5901,2274],{},[1685,5903,5474],{},[1311,5905,5906,5908],{},[1314,5907,1683],{},[1562,5909,2367],{},[1319,5911,5912],{"encoding":1321},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[3157,5914],{},"má asymptoticky Pearsonovo rozdělení o ",[1296,5917,5919],{"className":5918},[1299],[1301,5920,5921],{"xmlns":1303},[1305,5922,5923,5927],{},[1308,5924,5925],{},[1562,5926,1792],{},[1319,5928,1792],{"encoding":1321}," stupni volnosti.",[1105,5931,3316,5932,1395],{},[1296,5933,5935],{"className":5934},[1299],[1301,5936,5937],{"xmlns":1303},[1305,5938,5939,5985],{},[1308,5940,5941,5943,5945,5947,5953,5955,5961,5963,5977,5979,5981,5983],{},[1314,5942,1602],{},[1685,5944,1980],{},[1685,5946,3332],{"stretchy":1872},[1579,5948,5949,5951],{},[1314,5950,1583],{},[1562,5952,1586],{},[1685,5954,1956],{},[1579,5956,5957,5959],{},[1314,5958,1583],{},[1562,5960,1586],{},[1685,5962,3349],{},[3351,5964,5965,5967,5975],{},[1314,5966,1583],{},[1308,5968,5969,5971,5973],{},[1562,5970,1792],{},[1685,5972,3062],{},[1314,5974,3363],{},[1562,5976,1586],{},[1685,5978,1873],{"stretchy":1872},[1562,5980,1792],{},[1685,5982,1884],{"stretchy":1872},[1685,5984,3392],{"stretchy":1872},[1319,5986,5987],{"encoding":1321},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1105,5989,3398,5990,6003,6004,6021,6022,6039],{},[1296,5991,5993],{"className":5992},[1299],[1301,5994,5995],{"xmlns":1303},[1305,5996,5997,6001],{},[1308,5998,5999],{},[1314,6000,1602],{},[1319,6002,1602],{"encoding":1321},", zamítáme ",[1296,6005,6007],{"className":6006},[1299],[1301,6008,6009],{"xmlns":1303},[1305,6010,6011,6019],{},[1308,6012,6013],{},[1311,6014,6015,6017],{},[1314,6016,1560],{},[1562,6018,1564],{},[1319,6020,1567],{"encoding":1321}," a přijímáme ",[1296,6023,6025],{"className":6024},[1299],[1301,6026,6027],{"xmlns":1303},[1305,6028,6029,6037],{},[1308,6030,6031],{},[1311,6032,6033,6035],{},[1314,6034,1560],{},[1562,6036,1792],{},[1319,6038,2994],{"encoding":1321},": zásah rozdělení variant změnil.",[1148,6041,6042,6043,6046,6047,6050,6051,6053],{},"V R počítá tento test funkce ",[3468,6044,6045],{},"mcnemar.test()",". Vzorec výše ",[1108,6048,6049],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3468,6052,5434],{}," (viz Časté chyby níže).",[1514,6055,6057,6064,6067,6070,6167],{"className":6056,"dataCallout":3475},[1517,3474],[1148,6058,6060,6063],{"className":6059},[1523],[1296,6061],{"className":6062,"ariaHidden":1530},[1527,3482,1529],"Příklad: informační kampaň a zveřejňování na Facebooku",[1148,6065,6066],{},"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.",[1148,6068,6069],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1162,6071,6072,6107],{},[1165,6073,6074],{},[1168,6075,6076,6078,6081,6084],{},[1171,6077,5471],{},[1171,6079,6080],{},"nezveřejňuje",[1171,6082,6083],{},"zveřejňuje",[1171,6085,6086],{},[1296,6087,6089],{"className":6088},[1299],[1301,6090,6091],{"xmlns":1303},[1305,6092,6093,6105],{},[1308,6094,6095],{},[1311,6096,6097,6099],{},[1314,6098,1683],{},[1308,6100,6101,6103],{},[1314,6102,1876],{},[1685,6104,1977],{},[1319,6106,2211],{"encoding":1321},[1178,6108,6109,6121,6133],{},[1168,6110,6111,6113,6115,6118],{},[1183,6112,6080],{},[1183,6114,3598],{},[1183,6116,6117],{},"68",[1183,6119,6120],{},"92",[1168,6122,6123,6125,6127,6130],{},[1183,6124,6083],{},[1183,6126,4060],{},[1183,6128,6129],{},"50",[1183,6131,6132],{},"78",[1168,6134,6135,6158,6161,6164],{},[1183,6136,6137],{},[1296,6138,6140],{"className":6139},[1299],[1301,6141,6142],{"xmlns":1303},[1305,6143,6144,6156],{},[1308,6145,6146],{},[1311,6147,6148,6150],{},[1314,6149,1683],{},[1308,6151,6152,6154],{},[1685,6153,1977],{},[1314,6155,1881],{},[1319,6157,2603],{"encoding":1321},[1183,6159,6160],{},"52",[1183,6162,6163],{},"118",[1183,6165,6166],{},"170",[1148,6168,6169,6202],{},[1296,6170,6172],{"className":6171},[1299],[1301,6173,6174],{"xmlns":1303},[1305,6175,6176,6200],{},[1308,6177,6178,6184,6186,6192,6194],{},[1311,6179,6180,6182],{},[1314,6181,1560],{},[1562,6183,1564],{},[1685,6185,1956],{},[1311,6187,6188,6190],{},[1314,6189,1148],{},[1562,6191,2274],{},[1685,6193,1980],{},[1311,6195,6196,6198],{},[1314,6197,1148],{},[1562,6199,2367],{},[1319,6201,5847],{"encoding":1321}," — informační kampaň nemá na chování vliv.",[3692,6204,6206],{"className":3694,"code":6205,"language":71,"meta":1452,"style":1452},"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",[3468,6207,6208,6232,6246,6264,6274,6297,6316],{"__ignoreMap":1452},[1296,6209,6210,6213,6215,6217,6219,6221,6223,6225,6227,6230],{"class":3700,"line":10},[1296,6211,6212],{"class":3703},"tab3",[1296,6214,3708],{"class":3707},[1296,6216,3712],{"class":3711},[1296,6218,1873],{"class":3715},[1296,6220,3718],{"class":3711},[1296,6222,1873],{"class":3715},[1296,6224,3598],{"class":3723},[1296,6226,1795],{"class":3707},[1296,6228,6229],{"class":3723}," 68",[1296,6231,3736],{"class":3707},[1296,6233,6234,6237,6239,6242,6244],{"class":3700,"line":27},[1296,6235,6236],{"class":3723},"                 28",[1296,6238,1795],{"class":3707},[1296,6240,6241],{"class":3723}," 50",[1296,6243,1884],{"class":3715},[1296,6245,3736],{"class":3707},[1296,6247,6248,6250,6252,6254,6256,6258,6260,6262],{"class":3700,"line":148},[1296,6249,3793],{"class":3703},[1296,6251,3796],{"class":3707},[1296,6253,4179],{"class":3723},[1296,6255,1795],{"class":3707},[1296,6257,3804],{"class":3703},[1296,6259,3796],{"class":3707},[1296,6261,3809],{"class":3723},[1296,6263,3736],{"class":3707},[1296,6265,6266,6268,6270,6272],{"class":3700,"line":111},[1296,6267,3816],{"class":3703},[1296,6269,3796],{"class":3707},[1296,6271,3821],{"class":3711},[1296,6273,3824],{"class":3715},[1296,6275,6276,6279,6281,6283,6285,6288,6290,6293,6295],{"class":3700,"line":96},[1296,6277,6278],{"class":3703},"                 pred",[1296,6280,3796],{"class":3707},[1296,6282,3834],{"class":3711},[1296,6284,1873],{"class":3715},[1296,6286,6287],{"class":3839},"\"nezverejnuje\"",[1296,6289,1795],{"class":3707},[1296,6291,6292],{"class":3839}," \"zverejnuje\"",[1296,6294,1884],{"class":3715},[1296,6296,3736],{"class":3707},[1296,6298,6299,6302,6304,6306,6308,6310,6312,6314],{"class":3700,"line":89},[1296,6300,6301],{"class":3703},"                 po",[1296,6303,4229],{"class":3707},[1296,6305,3834],{"class":3711},[1296,6307,1873],{"class":3715},[1296,6309,6287],{"class":3839},[1296,6311,1795],{"class":3707},[1296,6313,6292],{"class":3839},[1296,6315,3887],{"class":3715},[1296,6317,6318,6321,6323,6325,6327,6330,6332,6335],{"class":3700,"line":82},[1296,6319,6320],{"class":3711},"mcnemar.test",[1296,6322,1873],{"class":3715},[1296,6324,6212],{"class":3703},[1296,6326,1795],{"class":3707},[1296,6328,6329],{"class":3703}," correct",[1296,6331,3796],{"class":3707},[1296,6333,6334],{"class":3723}," FALSE",[1296,6336,3900],{"class":3715},[3692,6338,6341],{"className":6339,"code":6340,"language":3922,"meta":1452},[3920],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3468,6342,6340],{"__ignoreMap":1452},[1148,6344,6345,6346,3987,6365,6382,6383,6400],{},"P-hodnota ",[1296,6347,6349],{"className":6348},[1299],[1301,6350,6351],{"xmlns":1303},[1305,6352,6353,6362],{},[1308,6354,6355,6358,6360],{},[1562,6356,6357],{},"0,00004456",[1685,6359,4331],{},[1562,6361,3983],{},[1319,6363,6364],{"encoding":1321},"0{,}00004456 \u003C 0{,}05",[1296,6366,6368],{"className":6367},[1299],[1301,6369,6370],{"xmlns":1303},[1305,6371,6372,6380],{},[1308,6373,6374],{},[1311,6375,6376,6378],{},[1314,6377,1560],{},[1562,6379,1564],{},[1319,6381,1567],{"encoding":1321}," zamítáme, přijímáme ",[1296,6384,6386],{"className":6385},[1299],[1301,6387,6388],{"xmlns":1303},[1305,6389,6390,6398],{},[1308,6391,6392],{},[1311,6393,6394,6396],{},[1314,6395,1560],{},[1562,6397,1792],{},[1319,6399,2994],{"encoding":1321}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1143,6402,6404],{"id":6403},"časté-chyby","Časté chyby",[1514,6406,6410,6418],{"className":6407,"dataCallout":6409},[1517,6408],"callout-warning","warning",[1148,6411,6413,6417],{"className":6412},[1523],[1296,6414],{"className":6415,"ariaHidden":1530},[1527,6416,1529],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1148,6419,6420,6421,6423],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3468,6422,3470],{}," 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.",[3692,6425,6427],{"className":3694,"code":6426,"language":71,"meta":1452,"style":1452},"chisq.test(tab3)\n",[3468,6428,6429],{"__ignoreMap":1452},[1296,6430,6431,6433,6435,6437],{"class":3700,"line":10},[1296,6432,3893],{"class":3711},[1296,6434,1873],{"class":3715},[1296,6436,6212],{"class":3703},[1296,6438,3900],{"class":3715},[3692,6440,6443],{"className":6441,"code":6442,"language":3922,"meta":1452},[3920],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3468,6444,6442],{"__ignoreMap":1452},[1148,6446,6345,6447,6466,6467,6484,6485,6487,6488,1395],{},[1296,6448,6450],{"className":6449},[1299],[1301,6451,6452],{"xmlns":1303},[1305,6453,6454,6463],{},[1308,6455,6456,6459,6461],{},[1562,6457,6458],{},"0,224",[1685,6460,1687],{},[1562,6462,3983],{},[1319,6464,6465],{"encoding":1321},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1296,6468,6470],{"className":6469},[1299],[1301,6471,6472],{"xmlns":1303},[1305,6473,6474,6482],{},[1308,6475,6476],{},[1311,6477,6478,6480],{},[1314,6479,1560],{},[1562,6481,1564],{},[1319,6483,1567],{"encoding":1321}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3468,6486,6045],{},", nikdy ",[3468,6489,3470],{},[1514,6491,6493,6502],{"className":6492,"dataCallout":6409},[1517,6408],[1148,6494,6496,6499,6500],{"className":6495},[1523],[1296,6497],{"className":6498,"ariaHidden":1530},[1527,6416,1529],"Výchozí korekce na kontinuitu v ",[3468,6501,6045],{},[1148,6503,6504,6505,6508],{},"Bez argumentu ",[3468,6506,6507],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3692,6510,6512],{"className":3694,"code":6511,"language":71,"meta":1452,"style":1452},"mcnemar.test(tab3)\n",[3468,6513,6514],{"__ignoreMap":1452},[1296,6515,6516,6518,6520,6522],{"class":3700,"line":10},[1296,6517,6320],{"class":3711},[1296,6519,1873],{"class":3715},[1296,6521,6212],{"class":3703},[1296,6523,3900],{"class":3715},[3692,6525,6528],{"className":6526,"code":6527,"language":3922,"meta":1452},[3920],"    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",[3468,6529,6527],{"__ignoreMap":1452},[1148,6531,6532,6533,6551,6552,6571,6572,6585,6586,1395],{},"Oproti nekorigované hodnotě ",[1296,6534,6536],{"className":6535},[1299],[1301,6537,6538],{"xmlns":1303},[1305,6539,6540,6548],{},[1308,6541,6542,6544,6546],{},[1314,6543,1148],{},[1685,6545,1980],{},[1562,6547,6357],{},[1319,6549,6550],{"encoding":1321},"p = 0{,}00004456"," vyjde ",[1296,6553,6555],{"className":6554},[1299],[1301,6556,6557],{"xmlns":1303},[1305,6558,6559,6568],{},[1308,6560,6561,6563,6565],{},[1314,6562,1148],{},[1685,6564,1980],{},[1562,6566,6567],{},"0,00006879",[1319,6569,6570],{"encoding":1321},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1296,6573,6575],{"className":6574},[1299],[1301,6576,6577],{"xmlns":1303},[1305,6578,6579,6583],{},[1308,6580,6581],{},[1314,6582,3363],{},[1319,6584,3426],{"encoding":1321}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3468,6587,6588],{},"mcnemar.test(x, correct = FALSE)",[1143,6590,6592],{"id":6591},"související-stránky","Související stránky",[1102,6594,6595,6600,6605,6610,6615,6620,6625],{},[1105,6596,6597],{},[1242,6598,1717],{"className":6599,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,6601,6602],{},[1242,6603,1266],{"className":6604,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1105,6606,6607],{},[1242,6608,1257],{"className":6609,"dataFsResolvedFilePath":1255,"href":1256},[1245],[1105,6611,6612],{},[1242,6613,1248],{"className":6614,"dataFsResolvedFilePath":1246,"href":1247},[1245],[1105,6616,6617],{},[1242,6618,1275],{"className":6619,"dataFsResolvedFilePath":1273,"href":1274},[1245],[1105,6621,6622],{},[1242,6623,1293],{"className":6624,"dataFsResolvedFilePath":1291,"href":1292},[1245],[1105,6626,6627],{},[1242,6628,6630],{"className":6629,"dataFsResolvedFilePath":1447,"href":1448},[1245],"Tahák pro R",[1143,6632,6633],{"id":934},"Reference",[1148,6635,6636,6637,6641],{},"KROPÁČ, J. ",[6638,6639,6640],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[6643,6644,6645],"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 .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":1452,"searchDepth":27,"depth":27,"links":6647},[6648,6649,6650,6651,6652,6653,6654,6655],{"id":1707,"depth":27,"text":1708},{"id":2825,"depth":27,"text":2826},{"id":4431,"depth":27,"text":1650},{"id":4807,"depth":27,"text":1670},{"id":5438,"depth":27,"text":1703},{"id":6403,"depth":27,"text":6404},{"id":6591,"depth":27,"text":6592},{"id":934,"depth":27,"text":6633},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":1284,"description":1452},[6660,6661],"raw\u002Fmask\u002F05 kontingenční tabulky.pdf","raw\u002Fmask\u002Fpříklady 04 a 05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":6667,"title":1248,"body":6668,"course":23,"courses":1459,"created":1460,"description":1452,"extension":1461,"meta":11118,"navigation":1464,"path":11119,"seo":11120,"sources":11121,"stem":11125,"tags":11126,"type":6664,"updated":1460,"__hash__":11127},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1095,"value":6669,"toc":11106},[6670,6673,6959,6963,7196,7199,7266,7270,7277,7284,7443,7482,7485,7719,7722,7800,7854,7952,7956,8058,8061,8065,8071,8126,8129,8137,8287,8294,8347,8377,8496,8499,8547,8709,8764,8771,8878,8940,8944,9047,9050,9087,9093,9152,9201,9208,9244,9250,9253,9301,9308,9370,9376,9379,9443,9450,9489,9495,9498,9502,9528,9859,9897,9952,10082,10088,10092,10099,10118,10224,10268,10287,10382,10399,10441,10616,10623,10626,10629,10783,10786,10862,10868,10870,11056,11058,11097,11099,11103],[1098,6671,1248],{"id":6672},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1514,6674,6676,6682],{"className":6675,"dataCallout":1519},[1517,1518],[1148,6677,6679,1531],{"className":6678},[1523],[1296,6680],{"className":6681,"ariaHidden":1530},[1527,1528,1529],[1102,6683,6684,6695,6799,6866,6947],{},[1105,6685,6686,6687,6690,6691,6694],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1108,6688,6689],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1108,6692,6693],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1105,6696,6697,6698,1651,6701,6739,6740,6777,6778,6798],{},"Každou náhodnou veličinu popisuje ",[1108,6699,6700],{},"distribuční funkce",[1296,6702,6704],{"className":6703},[1299],[1301,6705,6706],{"xmlns":1303},[1305,6707,6708,6736],{},[1308,6709,6710,6712,6714,6717,6719,6721,6724,6726,6729,6732,6734],{},[1314,6711,1225],{},[1685,6713,1873],{"stretchy":1872},[1314,6715,6716],{},"x",[1685,6718,1884],{"stretchy":1872},[1685,6720,1980],{},[1314,6722,6723],{},"P",[1685,6725,1873],{"stretchy":1872},[1314,6727,6728],{},"X",[1685,6730,6731],{},"≤",[1314,6733,6716],{},[1685,6735,1884],{"stretchy":1872},[1319,6737,6738],{"encoding":1321},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1296,6741,6743],{"className":6742},[1299],[1301,6744,6745],{"xmlns":1303},[1305,6746,6747,6774],{},[1308,6748,6749,6757,6759,6761,6763,6765,6768,6770,6772],{},[1579,6750,6751,6753],{},[1314,6752,1225],{},[1685,6754,6756],{"mathvariant":2119,"lspace":6755,"rspace":6755},"0em","′",[1685,6758,1873],{"stretchy":1872},[1314,6760,6716],{},[1685,6762,1884],{"stretchy":1872},[1685,6764,1980],{},[1314,6766,6767],{},"f",[1685,6769,1873],{"stretchy":1872},[1314,6771,6716],{},[1685,6773,1884],{"stretchy":1872},[1319,6775,6776],{"encoding":1321},"F'(x) = f(x)",", kde ",[1296,6779,6781],{"className":6780},[1299],[1301,6782,6783],{"xmlns":1303},[1305,6784,6785,6795],{},[1308,6786,6787,6789,6791,6793],{},[1314,6788,6767],{},[1685,6790,1873],{"stretchy":1872},[1314,6792,6716],{},[1685,6794,1884],{"stretchy":1872},[1319,6796,6797],{"encoding":1321},"f(x)"," je hustota pravděpodobnosti.",[1105,6800,6801,6802,1395],{},"Pravděpodobnost na intervalu se počítá jako ",[1296,6803,6805],{"className":6804},[1299],[1301,6806,6807],{"xmlns":1303},[1305,6808,6809,6863],{},[1308,6810,6811,6813,6815,6821,6823,6825,6827,6833,6835,6837,6839,6841,6847,6849,6851,6853,6855,6861],{},[1314,6812,6723],{},[1685,6814,1873],{"stretchy":1872},[1311,6816,6817,6819],{},[1314,6818,6716],{},[1562,6820,1792],{},[1685,6822,4331],{},[1314,6824,6728],{},[1685,6826,4331],{},[1311,6828,6829,6831],{},[1314,6830,6716],{},[1562,6832,1586],{},[1685,6834,1884],{"stretchy":1872},[1685,6836,1980],{},[1314,6838,1225],{},[1685,6840,1873],{"stretchy":1872},[1311,6842,6843,6845],{},[1314,6844,6716],{},[1562,6846,1586],{},[1685,6848,1884],{"stretchy":1872},[1685,6850,3062],{},[1314,6852,1225],{},[1685,6854,1873],{"stretchy":1872},[1311,6856,6857,6859],{},[1314,6858,6716],{},[1562,6860,1792],{},[1685,6862,1884],{"stretchy":1872},[1319,6864,6865],{"encoding":1321},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1105,6867,6868,1651,6871,6903,6904,1323,6907,1323,6910,6913,6914,6928,6929,1395],{},[1108,6869,6870],{},"Normální rozdělení",[1296,6872,6874],{"className":6873},[1299],[1301,6875,6876],{"xmlns":1303},[1305,6877,6878,6900],{},[1308,6879,6880,6883,6885,6888,6891,6898],{},[1314,6881,6882],{},"N",[1685,6884,1873],{"stretchy":1872},[1314,6886,6887],{},"μ",[1685,6889,6890],{"separator":1530},";",[1579,6892,6893,6896],{},[1314,6894,6895],{},"σ",[1562,6897,1586],{},[1685,6899,1884],{"stretchy":1872},[1319,6901,6902],{"encoding":1321},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3468,6905,6906],{},"dnorm",[3468,6908,6909],{},"pnorm",[3468,6911,6912],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1296,6915,6917],{"className":6916},[1299],[1301,6918,6919],{"xmlns":1303},[1305,6920,6921,6925],{},[1308,6922,6923],{},[1314,6924,6895],{},[1319,6926,6927],{"encoding":1321},"\\sigma",", ne rozptyl ",[1296,6930,6932],{"className":6931},[1299],[1301,6933,6934],{"xmlns":1303},[1305,6935,6936,6944],{},[1308,6937,6938],{},[1579,6939,6940,6942],{},[1314,6941,6895],{},[1562,6943,1586],{},[1319,6945,6946],{"encoding":1321},"\\sigma^2",[1105,6948,6949,1323,6952,1370,6955,6958],{},[1108,6950,6951],{},"Studentovo",[1108,6953,6954],{},"Pearsonovo (χ²)",[1108,6956,6957],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1143,6960,6962],{"id":6961},"náhodná-veličina","Náhodná veličina",[1148,6964,6965,6968,6969,6984,6985,1651,6987,7000,7001,7021,7022,6777,7035,7059,7060,1323,7073,1323,7087,7101,7102,1323,7115,1323,7129,7143,7144,7157,7158,7171,7172,1395],{},[1242,6966,1717],{"className":6967,"dataFsResolvedFilePath":1715,"href":1716},[1245]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1296,6970,6972],{"className":6971},[1299],[1301,6973,6974],{"xmlns":1303},[1305,6975,6976,6981],{},[1308,6977,6978],{},[1314,6979,6980],{"mathvariant":2119},"Ω",[1319,6982,6983],{"encoding":1321},"\\Omega"," přiřazený výsledkům pokusu. ",[1108,6986,6962],{},[1296,6988,6990],{"className":6989},[1299],[1301,6991,6992],{"xmlns":1303},[1305,6993,6994,6998],{},[1308,6995,6996],{},[1314,6997,6728],{},[1319,6999,6728],{"encoding":1321}," je funkce, která prvkům ",[1296,7002,7004],{"className":7003},[1299],[1301,7005,7006],{"xmlns":1303},[1305,7007,7008,7018],{},[1308,7009,7010,7013,7016],{},[1314,7011,7012],{},"ω",[1685,7014,7015],{},"∈",[1314,7017,6980],{"mathvariant":2119},[1319,7019,7020],{"encoding":1321},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1296,7023,7025],{"className":7024},[1299],[1301,7026,7027],{"xmlns":1303},[1305,7028,7029,7033],{},[1308,7030,7031],{},[1314,7032,6716],{},[1319,7034,6716],{"encoding":1321},[1296,7036,7038],{"className":7037},[1299],[1301,7039,7040],{"xmlns":1303},[1305,7041,7042,7056],{},[1308,7043,7044,7046,7048,7050,7052,7054],{},[1314,7045,6716],{},[1685,7047,1980],{},[1314,7049,6728],{},[1685,7051,1873],{"stretchy":1872},[1314,7053,7012],{},[1685,7055,1884],{"stretchy":1872},[1319,7057,7058],{"encoding":1321},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1296,7061,7063],{"className":7062},[1299],[1301,7064,7065],{"xmlns":1303},[1305,7066,7067,7071],{},[1308,7068,7069],{},[1314,7070,6728],{},[1319,7072,6728],{"encoding":1321},[1296,7074,7076],{"className":7075},[1299],[1301,7077,7078],{"xmlns":1303},[1305,7079,7080,7085],{},[1308,7081,7082],{},[1314,7083,7084],{},"Y",[1319,7086,7084],{"encoding":1321},[1296,7088,7090],{"className":7089},[1299],[1301,7091,7092],{"xmlns":1303},[1305,7093,7094,7099],{},[1308,7095,7096],{},[1314,7097,7098],{},"T",[1319,7100,7098],{"encoding":1321},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1296,7103,7105],{"className":7104},[1299],[1301,7106,7107],{"xmlns":1303},[1305,7108,7109,7113],{},[1308,7110,7111],{},[1314,7112,6716],{},[1319,7114,6716],{"encoding":1321},[1296,7116,7118],{"className":7117},[1299],[1301,7119,7120],{"xmlns":1303},[1305,7121,7122,7127],{},[1308,7123,7124],{},[1314,7125,7126],{},"y",[1319,7128,7126],{"encoding":1321},[1296,7130,7132],{"className":7131},[1299],[1301,7133,7134],{"xmlns":1303},[1305,7135,7136,7141],{},[1308,7137,7138],{},[1314,7139,7140],{},"t",[1319,7142,7140],{"encoding":1321},"); pravděpodobnost, že ",[1296,7145,7147],{"className":7146},[1299],[1301,7148,7149],{"xmlns":1303},[1305,7150,7151,7155],{},[1308,7152,7153],{},[1314,7154,6728],{},[1319,7156,6728],{"encoding":1321}," nabyla hodnoty ",[1296,7159,7161],{"className":7160},[1299],[1301,7162,7163],{"xmlns":1303},[1305,7164,7165,7169],{},[1308,7166,7167],{},[1314,7168,6716],{},[1319,7170,6716],{"encoding":1321},", zapisujeme ",[1296,7173,7175],{"className":7174},[1299],[1301,7176,7177],{"xmlns":1303},[1305,7178,7179,7193],{},[1308,7180,7181,7183,7185,7187,7189,7191],{},[1314,7182,6723],{},[1685,7184,1873],{"stretchy":1872},[1314,7186,6728],{},[1685,7188,1980],{},[1314,7190,6716],{},[1685,7192,1884],{"stretchy":1872},[1319,7194,7195],{"encoding":1321},"P(X = x)",[1148,7197,7198],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1102,7200,7201,7260],{},[1105,7202,7203,7206,7207,7220,7221,7259],{},[1108,7204,7205],{},"Diskrétní náhodná veličina"," — prvky ",[1296,7208,7210],{"className":7209},[1299],[1301,7211,7212],{"xmlns":1303},[1305,7213,7214,7218],{},[1308,7215,7216],{},[1314,7217,6980],{"mathvariant":2119},[1319,7219,6983],{"encoding":1321}," se zobrazí na osu reálných čísel jako izolované body ",[1296,7222,7224],{"className":7223},[1299],[1301,7225,7226],{"xmlns":1303},[1305,7227,7228,7256],{},[1308,7229,7230,7236,7238,7244,7246,7248,7250],{},[1311,7231,7232,7234],{},[1314,7233,6716],{},[1562,7235,1792],{},[1685,7237,1795],{"separator":1530},[1311,7239,7240,7242],{},[1314,7241,6716],{},[1562,7243,1586],{},[1685,7245,1795],{"separator":1530},[1685,7247,1798],{},[1685,7249,1795],{"separator":1530},[1311,7251,7252,7254],{},[1314,7253,6716],{},[1314,7255,1343],{},[1319,7257,7258],{"encoding":1321},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1105,7261,7262,7265],{},[1108,7263,7264],{},"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.",[1143,7267,7269],{"id":7268},"distribuční-funkce","Distribuční funkce",[1148,7271,7272,7273,7276],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1108,7274,7275],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1148,7278,7279],{},[4382,7280],{"alt":7281,"className":7282,"src":7283},"mask-nv-distribucni-funkce",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1514,7285,7288,7295],{"className":7286,"dataCallout":654},[1517,7287],"callout-info",[1148,7289,7291,7294],{"className":7290},[1523],[1296,7292],{"className":7293,"ariaHidden":1530},[1527,1528,1529],"Definice",[1148,7296,7297,7298,7311,7312,7332,7333,7346,7347,7383,7402,7403,7416,7417,1395],{},"Distribuční funkcí náhodné veličiny ",[1296,7299,7301],{"className":7300},[1299],[1301,7302,7303],{"xmlns":1303},[1305,7304,7305,7309],{},[1308,7306,7307],{},[1314,7308,6728],{},[1319,7310,6728],{"encoding":1321}," nazýváme reálnou funkci ",[1296,7313,7315],{"className":7314},[1299],[1301,7316,7317],{"xmlns":1303},[1305,7318,7319,7329],{},[1308,7320,7321,7323,7325,7327],{},[1314,7322,1225],{},[1685,7324,1873],{"stretchy":1872},[1314,7326,6716],{},[1685,7328,1884],{"stretchy":1872},[1319,7330,7331],{"encoding":1321},"F(x)"," definovanou pro každé reálné číslo ",[1296,7334,7336],{"className":7335},[1299],[1301,7337,7338],{"xmlns":1303},[1305,7339,7340,7344],{},[1308,7341,7342],{},[1314,7343,6716],{},[1319,7345,6716],{"encoding":1321}," jako\n",[1296,7348,7350],{"className":7349},[1299],[1301,7351,7352],{"xmlns":1303},[1305,7353,7354,7380],{},[1308,7355,7356,7358,7360,7362,7364,7366,7368,7370,7372,7374,7376,7378],{},[1314,7357,1225],{},[1685,7359,1873],{"stretchy":1872},[1314,7361,6716],{},[1685,7363,1884],{"stretchy":1872},[1685,7365,1980],{},[1314,7367,6723],{},[1685,7369,1873],{"stretchy":1872},[1314,7371,6728],{},[1685,7373,6731],{},[1314,7375,6716],{},[1685,7377,1884],{"stretchy":1872},[1314,7379,1395],{"mathvariant":2119},[1319,7381,7382],{"encoding":1321},"F(x) = P(X \\le x).",[1296,7384,7386],{"className":7385},[1299],[1301,7387,7388],{"xmlns":1303},[1305,7389,7390,7400],{},[1308,7391,7392,7394,7396,7398],{},[1314,7393,1225],{},[1685,7395,1873],{"stretchy":1872},[1314,7397,6716],{},[1685,7399,1884],{"stretchy":1872},[1319,7401,7331],{"encoding":1321}," tedy vyjadřuje pravděpodobnost, s jakou ",[1296,7404,7406],{"className":7405},[1299],[1301,7407,7408],{"xmlns":1303},[1305,7409,7410,7414],{},[1308,7411,7412],{},[1314,7413,6728],{},[1319,7415,6728],{"encoding":1321}," nabude hodnoty z intervalu ",[1296,7418,7420],{"className":7419},[1299],[1301,7421,7422],{"xmlns":1303},[1305,7423,7424,7440],{},[1308,7425,7426,7428,7430,7433,7435,7437],{},[1685,7427,1873],{"stretchy":1872},[1685,7429,3062],{},[1314,7431,7432],{"mathvariant":2119},"∞",[1685,7434,1795],{"separator":1530},[1314,7436,6716],{},[1685,7438,7439],{"stretchy":1872},"⟩",[1319,7441,7442],{"encoding":1321},"(-\\infty, x\\rangle",[1148,7444,7445,7446,7459,7460,7481],{},"Značí-li například ",[1296,7447,7449],{"className":7448},[1299],[1301,7450,7451],{"xmlns":1303},[1305,7452,7453,7457],{},[1308,7454,7455],{},[1314,7456,6728],{},[1319,7458,6728],{"encoding":1321}," výšku mužů v populaci, pak ",[1296,7461,7463],{"className":7462},[1299],[1301,7464,7465],{"xmlns":1303},[1305,7466,7467,7478],{},[1308,7468,7469,7471,7473,7476],{},[1314,7470,1225],{},[1685,7472,1873],{"stretchy":1872},[1562,7474,7475],{},"175",[1685,7477,1884],{"stretchy":1872},[1319,7479,7480],{"encoding":1321},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1148,7483,7484],{},"Pro distribuční funkci vždy platí:",[1102,7486,7487,7517,7575,7635],{},[1105,7488,7489,1795],{},[1296,7490,7492],{"className":7491},[1299],[1301,7493,7494],{"xmlns":1303},[1305,7495,7496,7514],{},[1308,7497,7498,7500,7502,7504,7506,7508,7510,7512],{},[1562,7499,1564],{},[1685,7501,6731],{},[1314,7503,1225],{},[1685,7505,1873],{"stretchy":1872},[1314,7507,6716],{},[1685,7509,1884],{"stretchy":1872},[1685,7511,6731],{},[1562,7513,1792],{},[1319,7515,7516],{"encoding":1321},"0 \\le F(x) \\le 1",[1105,7518,7519,7520,1795],{},"je neklesající: ",[1296,7521,7523],{"className":7522},[1299],[1301,7524,7525],{"xmlns":1303},[1305,7526,7527,7572],{},[1308,7528,7529,7535,7537,7543,7546,7548,7550,7556,7558,7560,7562,7564,7570],{},[1311,7530,7531,7533],{},[1314,7532,6716],{},[1562,7534,1792],{},[1685,7536,6731],{},[1311,7538,7539,7541],{},[1314,7540,6716],{},[1562,7542,1586],{},[1685,7544,7545],{},"⇒",[1314,7547,1225],{},[1685,7549,1873],{"stretchy":1872},[1311,7551,7552,7554],{},[1314,7553,6716],{},[1562,7555,1792],{},[1685,7557,1884],{"stretchy":1872},[1685,7559,6731],{},[1314,7561,1225],{},[1685,7563,1873],{"stretchy":1872},[1311,7565,7566,7568],{},[1314,7567,6716],{},[1562,7569,1586],{},[1685,7571,1884],{"stretchy":1872},[1319,7573,7574],{"encoding":1321},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1105,7576,7577,7578,1795],{},"je spojitá zprava: ",[1296,7579,7581],{"className":7580},[1299],[1301,7582,7583],{"xmlns":1303},[1305,7584,7585,7632],{},[1308,7586,7587,7610,7612,7614,7616,7618,7620,7622,7624,7626,7628,7630],{},[1311,7588,7589,7596],{},[1308,7590,7591,7594],{},[1314,7592,7593],{},"lim",[1685,7595,4489],{},[1308,7597,7598,7601,7604],{},[1314,7599,7600],{},"h",[1685,7602,7603],{},"→",[1579,7605,7606,7608],{},[1562,7607,1564],{},[1685,7609,5474],{},[1314,7611,1225],{},[1685,7613,1873],{"stretchy":1872},[1314,7615,6716],{},[1685,7617,5474],{},[1314,7619,7600],{},[1685,7621,1884],{"stretchy":1872},[1685,7623,1980],{},[1314,7625,1225],{},[1685,7627,1873],{"stretchy":1872},[1314,7629,6716],{},[1685,7631,1884],{"stretchy":1872},[1319,7633,7634],{"encoding":1321},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1105,7636,7637,1323,7679,1395],{},[1296,7638,7640],{"className":7639},[1299],[1301,7641,7642],{"xmlns":1303},[1305,7643,7644,7676],{},[1308,7645,7646,7664,7666,7668,7670,7672,7674],{},[1311,7647,7648,7654],{},[1308,7649,7650,7652],{},[1314,7651,7593],{},[1685,7653,4489],{},[1308,7655,7656,7658,7660,7662],{},[1314,7657,6716],{},[1685,7659,7603],{},[1685,7661,3062],{},[1314,7663,7432],{"mathvariant":2119},[1314,7665,1225],{},[1685,7667,1873],{"stretchy":1872},[1314,7669,6716],{},[1685,7671,1884],{"stretchy":1872},[1685,7673,1980],{},[1562,7675,1564],{},[1319,7677,7678],{"encoding":1321},"\\lim_{x \\to -\\infty} F(x) = 0",[1296,7680,7682],{"className":7681},[1299],[1301,7683,7684],{"xmlns":1303},[1305,7685,7686,7716],{},[1308,7687,7688,7704,7706,7708,7710,7712,7714],{},[1311,7689,7690,7696],{},[1308,7691,7692,7694],{},[1314,7693,7593],{},[1685,7695,4489],{},[1308,7697,7698,7700,7702],{},[1314,7699,6716],{},[1685,7701,7603],{},[1314,7703,7432],{"mathvariant":2119},[1314,7705,1225],{},[1685,7707,1873],{"stretchy":1872},[1314,7709,6716],{},[1685,7711,1884],{"stretchy":1872},[1685,7713,1980],{},[1562,7715,1792],{},[1319,7717,7718],{"encoding":1321},"\\lim_{x \\to \\infty} F(x) = 1",[1148,7720,7721],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1296,7723,7725],{"className":7724},[1299],[1301,7726,7727],{"xmlns":1303,"display":1962},[1305,7728,7729,7797],{},[1308,7730,7731,7737,7739,7741,7743,7745,7747,7749,7751,7753,7755,7757,7759,7761,7763,7765,7767,7780,7782,7784,7786,7788,7790,7793,7795],{},[1579,7732,7733,7735],{},[1314,7734,1225],{},[1685,7736,6756],{"mathvariant":2119,"lspace":6755,"rspace":6755},[1685,7738,1873],{"stretchy":1872},[1314,7740,6716],{},[1685,7742,1884],{"stretchy":1872},[1685,7744,1980],{},[1314,7746,6767],{},[1685,7748,1873],{"stretchy":1872},[1314,7750,6716],{},[1685,7752,1884],{"stretchy":1872},[1685,7754,1795],{"separator":1530},[2010,7756],{"width":2012},[1314,7758,1225],{},[1685,7760,1873],{"stretchy":1872},[1314,7762,6716],{},[1685,7764,1884],{"stretchy":1872},[1685,7766,1980],{},[3351,7768,7769,7772,7778],{},[1685,7770,7771],{},"∫",[1308,7773,7774,7776],{},[1685,7775,3062],{},[1314,7777,7432],{"mathvariant":2119},[1314,7779,6716],{},[1314,7781,6767],{},[1685,7783,1873],{"stretchy":1872},[1314,7785,7140],{},[1685,7787,1884],{"stretchy":1872},[2907,7789,2909],{},[1314,7791,7792],{},"d",[1314,7794,7140],{},[1314,7796,1395],{"mathvariant":2119},[1319,7798,7799],{"encoding":1321},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1148,7801,7802,7803,7816,7817,1370,7835,7853],{},"Pravděpodobnost, že ",[1296,7804,7806],{"className":7805},[1299],[1301,7807,7808],{"xmlns":1303},[1305,7809,7810,7814],{},[1308,7811,7812],{},[1314,7813,6728],{},[1319,7815,6728],{"encoding":1321}," padne mezi body ",[1296,7818,7820],{"className":7819},[1299],[1301,7821,7822],{"xmlns":1303},[1305,7823,7824,7832],{},[1308,7825,7826],{},[1311,7827,7828,7830],{},[1314,7829,6716],{},[1562,7831,1792],{},[1319,7833,7834],{"encoding":1321},"x_1",[1296,7836,7838],{"className":7837},[1299],[1301,7839,7840],{"xmlns":1303},[1305,7841,7842,7850],{},[1308,7843,7844],{},[1311,7845,7846,7848],{},[1314,7847,6716],{},[1562,7849,1586],{},[1319,7851,7852],{"encoding":1321},"x_2",", se pak počítá jako",[1296,7855,7857],{"className":7856},[1299],[1301,7858,7859],{"xmlns":1303,"display":1962},[1305,7860,7861,7949],{},[1308,7862,7863,7865,7867,7873,7875,7877,7879,7885,7887,7889,7905,7907,7909,7911,7913,7915,7917,7919,7921,7923,7925,7931,7933,7935,7937,7939,7945,7947],{},[1314,7864,6723],{},[1685,7866,1873],{"stretchy":1872},[1311,7868,7869,7871],{},[1314,7870,6716],{},[1562,7872,1792],{},[1685,7874,4331],{},[1314,7876,6728],{},[1685,7878,4331],{},[1311,7880,7881,7883],{},[1314,7882,6716],{},[1562,7884,1586],{},[1685,7886,1884],{"stretchy":1872},[1685,7888,1980],{},[3351,7890,7891,7893,7899],{},[1685,7892,7771],{},[1311,7894,7895,7897],{},[1314,7896,6716],{},[1562,7898,1792],{},[1311,7900,7901,7903],{},[1314,7902,6716],{},[1562,7904,1586],{},[1314,7906,6767],{},[1685,7908,1873],{"stretchy":1872},[1314,7910,7140],{},[1685,7912,1884],{"stretchy":1872},[2907,7914,2909],{},[1314,7916,7792],{},[1314,7918,7140],{},[1685,7920,1980],{},[1314,7922,1225],{},[1685,7924,1873],{"stretchy":1872},[1311,7926,7927,7929],{},[1314,7928,6716],{},[1562,7930,1586],{},[1685,7932,1884],{"stretchy":1872},[1685,7934,3062],{},[1314,7936,1225],{},[1685,7938,1873],{"stretchy":1872},[1311,7940,7941,7943],{},[1314,7942,6716],{},[1562,7944,1792],{},[1685,7946,1884],{"stretchy":1872},[1314,7948,1395],{"mathvariant":2119},[1319,7950,7951],{"encoding":1321},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1143,7953,7955],{"id":7954},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1514,7957,7959,7965],{"className":7958,"dataCallout":654},[1517,7287],[1148,7960,7962,7294],{"className":7961},[1523],[1296,7963],{"className":7964,"ariaHidden":1530},[1527,1528,1529],[1148,7966,7967,7968,7987,7988,8001,8002,8015,8016,1395],{},"Hustota pravděpodobnosti ",[1296,7969,7971],{"className":7970},[1299],[1301,7972,7973],{"xmlns":1303},[1305,7974,7975,7985],{},[1308,7976,7977,7979,7981,7983],{},[1314,7978,6767],{},[1685,7980,1873],{"stretchy":1872},[1314,7982,6716],{},[1685,7984,1884],{"stretchy":1872},[1319,7986,6797],{"encoding":1321}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1296,7989,7991],{"className":7990},[1299],[1301,7992,7993],{"xmlns":1303},[1305,7994,7995,7999],{},[1308,7996,7997],{},[1314,7998,6728],{},[1319,8000,6728],{"encoding":1321}," nahuštěny v okolí bodu ",[1296,8003,8005],{"className":8004},[1299],[1301,8006,8007],{"xmlns":1303},[1305,8008,8009,8013],{},[1308,8010,8011],{},[1314,8012,6716],{},[1319,8014,6716],{"encoding":1321},". Je vždy nezáporná a platí pro ni ",[1296,8017,8019],{"className":8018},[1299],[1301,8020,8021],{"xmlns":1303},[1305,8022,8023,8055],{},[1308,8024,8025,8037,8039,8041,8043,8045,8047,8049,8051,8053],{},[3351,8026,8027,8029,8035],{},[1685,8028,7771],{},[1308,8030,8031,8033],{},[1685,8032,3062],{},[1314,8034,7432],{"mathvariant":2119},[1314,8036,7432],{"mathvariant":2119},[1314,8038,6767],{},[1685,8040,1873],{"stretchy":1872},[1314,8042,6716],{},[1685,8044,1884],{"stretchy":1872},[2907,8046,2909],{},[1314,8048,7792],{},[1314,8050,6716],{},[1685,8052,1980],{},[1562,8054,1792],{},[1319,8056,8057],{"encoding":1321},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1148,8059,8060],{},"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.",[1143,8062,8064],{"id":8063},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1148,8066,8067,8070],{},[1108,8068,8069],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1296,8072,8074],{"className":8073},[1299],[1301,8075,8076],{"xmlns":1303,"display":1962},[1305,8077,8078,8123],{},[1308,8079,8080,8082,8084,8086,8088,8090,8102,8104,8107,8109,8111,8113,8115,8117,8119,8121],{},[1314,8081,1217],{},[1685,8083,1873],{"stretchy":1872},[1314,8085,6728],{},[1685,8087,1884],{"stretchy":1872},[1685,8089,1980],{},[3351,8091,8092,8094,8100],{},[1685,8093,7771],{},[1308,8095,8096,8098],{},[1685,8097,3062],{},[1314,8099,7432],{"mathvariant":2119},[1314,8101,7432],{"mathvariant":2119},[1314,8103,6716],{},[1685,8105,8106],{},"⋅",[1314,8108,6767],{},[1685,8110,1873],{"stretchy":1872},[1314,8112,6716],{},[1685,8114,1884],{"stretchy":1872},[2907,8116,2909],{},[1314,8118,7792],{},[1314,8120,6716],{},[1314,8122,1395],{"mathvariant":2119},[1319,8124,8125],{"encoding":1321},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1148,8127,8128],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1148,8130,8131,1370,8134,1956],{},[1108,8132,8133],{},"Rozptyl",[1108,8135,8136],{},"směrodatná odchylka",[1296,8138,8140],{"className":8139},[1299],[1301,8141,8142],{"xmlns":1303,"display":1962},[1305,8143,8144,8284],{},[1308,8145,8146,8148,8150,8152,8154,8156,8168,8171,8173,8175,8177,8179,8181,8183,8190,8192,8194,8196,8198,8200,8202,8204,8206,8218,8224,8226,8228,8230,8232,8234,8236,8238,8240,8242,8244,8246,8248,8250,8256,8258,8260,8262,8264,8266,8268,8270,8282],{},[1314,8147,1209],{},[1685,8149,1873],{"stretchy":1872},[1314,8151,6728],{},[1685,8153,1884],{"stretchy":1872},[1685,8155,1980],{},[3351,8157,8158,8160,8166],{},[1685,8159,7771],{},[1308,8161,8162,8164],{},[1685,8163,3062],{},[1314,8165,7432],{"mathvariant":2119},[1314,8167,7432],{"mathvariant":2119},[1685,8169,8170],{"stretchy":1872},"[",[1314,8172,6716],{},[1685,8174,3062],{},[1314,8176,1217],{},[1685,8178,1873],{"stretchy":1872},[1314,8180,6728],{},[1685,8182,1884],{"stretchy":1872},[1579,8184,8185,8188],{},[1685,8186,8187],{"stretchy":1872},"]",[1562,8189,1586],{},[1314,8191,6767],{},[1685,8193,1873],{"stretchy":1872},[1314,8195,6716],{},[1685,8197,1884],{"stretchy":1872},[2907,8199,2909],{},[1314,8201,7792],{},[1314,8203,6716],{},[1685,8205,1980],{},[3351,8207,8208,8210,8216],{},[1685,8209,7771],{},[1308,8211,8212,8214],{},[1685,8213,3062],{},[1314,8215,7432],{"mathvariant":2119},[1314,8217,7432],{"mathvariant":2119},[1579,8219,8220,8222],{},[1314,8221,6716],{},[1562,8223,1586],{},[1314,8225,6767],{},[1685,8227,1873],{"stretchy":1872},[1314,8229,6716],{},[1685,8231,1884],{"stretchy":1872},[2907,8233,2909],{},[1314,8235,7792],{},[1314,8237,6716],{},[1685,8239,3062],{},[1685,8241,8170],{"stretchy":1872},[1314,8243,1217],{},[1685,8245,1873],{"stretchy":1872},[1314,8247,6728],{},[1685,8249,1884],{"stretchy":1872},[1579,8251,8252,8254],{},[1685,8253,8187],{"stretchy":1872},[1562,8255,1586],{},[1685,8257,1795],{"separator":1530},[2010,8259],{"width":2012},[1314,8261,6895],{},[1685,8263,1873],{"stretchy":1872},[1314,8265,6728],{},[1685,8267,1884],{"stretchy":1872},[1685,8269,1980],{},[4452,8271,8272],{},[1308,8273,8274,8276,8278,8280],{},[1314,8275,1209],{},[1685,8277,1873],{"stretchy":1872},[1314,8279,6728],{},[1685,8281,1884],{"stretchy":1872},[1314,8283,1395],{"mathvariant":2119},[1319,8285,8286],{"encoding":1321},"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)}.",[1148,8288,8289,8290,8293],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1242,8291,886],{"className":8292,"dataFsResolvedFilePath":1255,"href":1256},[1245],".)",[1148,8295,8296,8299,8300,8313,8314,8332,8333,8346],{},[1108,8297,8298],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1296,8301,8303],{"className":8302},[1299],[1301,8304,8305],{"xmlns":1303},[1305,8306,8307,8311],{},[1308,8308,8309],{},[1314,8310,6728],{},[1319,8312,6728],{"encoding":1321}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1296,8315,8317],{"className":8316},[1299],[1301,8318,8319],{"xmlns":1303},[1305,8320,8321,8329],{},[1308,8322,8323],{},[1311,8324,8325,8327],{},[1314,8326,6716],{},[1314,8328,1148],{},[1319,8330,8331],{"encoding":1321},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1296,8334,8336],{"className":8335},[1299],[1301,8337,8338],{"xmlns":1303},[1305,8339,8340,8344],{},[1308,8341,8342],{},[1314,8343,1148],{},[1319,8345,1148],{"encoding":1321}," platí",[1296,8348,8350],{"className":8349},[1299],[1301,8351,8352],{"xmlns":1303,"display":1962},[1305,8353,8354,8374],{},[1308,8355,8356,8358,8360,8366,8368,8370,8372],{},[1314,8357,1225],{},[1685,8359,1873],{"stretchy":1872},[1311,8361,8362,8364],{},[1314,8363,6716],{},[1314,8365,1148],{},[1685,8367,1884],{"stretchy":1872},[1685,8369,1980],{},[1314,8371,1148],{},[1314,8373,1395],{"mathvariant":2119},[1319,8375,8376],{"encoding":1321},"F(x_p) = p.",[1148,8378,8379,8380,8408,8409,8436,8437,8456,8457,8476,8477,1395],{},"V intervalu ",[1296,8381,8383],{"className":8382},[1299],[1301,8384,8385],{"xmlns":1303},[1305,8386,8387,8405],{},[1308,8388,8389,8391,8393,8395,8397,8403],{},[1685,8390,1873],{"stretchy":1872},[1685,8392,3062],{},[1314,8394,7432],{"mathvariant":2119},[1685,8396,6890],{"separator":1530},[1311,8398,8399,8401],{},[1314,8400,6716],{},[1314,8402,1148],{},[1685,8404,1884],{"stretchy":1872},[1319,8406,8407],{"encoding":1321},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1296,8410,8412],{"className":8411},[1299],[1301,8413,8414],{"xmlns":1303},[1305,8415,8416,8433],{},[1308,8417,8418,8421,8427,8429,8431],{},[1685,8419,8420],{"stretchy":1872},"⟨",[1311,8422,8423,8425],{},[1314,8424,6716],{},[1314,8426,1148],{},[1685,8428,6890],{"separator":1530},[1314,8430,7432],{"mathvariant":2119},[1685,8432,1884],{"stretchy":1872},[1319,8434,8435],{"encoding":1321},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1296,8438,8440],{"className":8439},[1299],[1301,8441,8442],{"xmlns":1303},[1305,8443,8444,8453],{},[1308,8445,8446],{},[1311,8447,8448,8450],{},[1314,8449,6716],{},[1562,8451,8452],{},"0,5",[1319,8454,8455],{"encoding":1321},"x_{0{,}5}",", dolní kvartil ",[1296,8458,8460],{"className":8459},[1299],[1301,8461,8462],{"xmlns":1303},[1305,8463,8464,8473],{},[1308,8465,8466],{},[1311,8467,8468,8470],{},[1314,8469,6716],{},[1562,8471,8472],{},"0,25",[1319,8474,8475],{"encoding":1321},"x_{0{,}25}"," a horní kvartil ",[1296,8478,8480],{"className":8479},[1299],[1301,8481,8482],{"xmlns":1303},[1305,8483,8484,8493],{},[1308,8485,8486],{},[1311,8487,8488,8490],{},[1314,8489,6716],{},[1562,8491,8492],{},"0,75",[1319,8494,8495],{"encoding":1321},"x_{0{,}75}",[1143,8497,6870],{"id":8498},"normální-rozdělení",[1148,8500,8501,8502,8515,8516,1651,8519,8546],{},"Spojitá náhodná veličina ",[1296,8503,8505],{"className":8504},[1299],[1301,8506,8507],{"xmlns":1303},[1305,8508,8509,8513],{},[1308,8510,8511],{},[1314,8512,6728],{},[1319,8514,6728],{"encoding":1321}," má ",[1108,8517,8518],{},"normální rozdělení",[1296,8520,8522],{"className":8521},[1299],[1301,8523,8524],{"xmlns":1303},[1305,8525,8526,8544],{},[1308,8527,8528,8530,8532,8534,8536,8542],{},[1314,8529,6882],{},[1685,8531,1873],{"stretchy":1872},[1314,8533,6887],{},[1685,8535,6890],{"separator":1530},[1579,8537,8538,8540],{},[1314,8539,6895],{},[1562,8541,1586],{},[1685,8543,1884],{"stretchy":1872},[1319,8545,6902],{"encoding":1321},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1296,8548,8550],{"className":8549},[1299],[1301,8551,8552],{"xmlns":1303,"display":1962},[1305,8553,8554,8706],{},[1308,8555,8556,8558,8560,8562,8564,8566,8583,8620,8622,8624,8626,8628,8630,8632,8634,8650,8662,8698,8700,8702,8704],{},[1314,8557,6767],{},[1685,8559,1873],{"stretchy":1872},[1314,8561,6716],{},[1685,8563,1884],{"stretchy":1872},[1685,8565,1980],{},[2738,8567,8568,8570],{},[1562,8569,1792],{},[1308,8571,8572,8574],{},[1314,8573,6895],{},[4452,8575,8576],{},[1308,8577,8578,8580],{},[1562,8579,1586],{},[1314,8581,8582],{},"π",[1579,8584,8585,8588],{},[1314,8586,8587],{},"e",[1308,8589,8590,8592],{},[1685,8591,3062],{},[2738,8593,8594,8610],{},[1308,8595,8596,8598,8600,8602,8604],{},[1685,8597,1873],{"stretchy":1872},[1314,8599,6716],{},[1685,8601,3062],{},[1314,8603,6887],{},[1579,8605,8606,8608],{},[1685,8607,1884],{"stretchy":1872},[1562,8609,1586],{},[1308,8611,8612,8614],{},[1562,8613,1586],{},[1579,8615,8616,8618],{},[1314,8617,6895],{},[1562,8619,1586],{},[1685,8621,1795],{"separator":1530},[2010,8623],{"width":2012},[1314,8625,1225],{},[1685,8627,1873],{"stretchy":1872},[1314,8629,6716],{},[1685,8631,1884],{"stretchy":1872},[1685,8633,1980],{},[2738,8635,8636,8638],{},[1562,8637,1792],{},[1308,8639,8640,8642],{},[1314,8641,6895],{},[4452,8643,8644],{},[1308,8645,8646,8648],{},[1562,8647,1586],{},[1314,8649,8582],{},[3351,8651,8652,8654,8660],{},[1685,8653,7771],{},[1308,8655,8656,8658],{},[1685,8657,3062],{},[1314,8659,7432],{"mathvariant":2119},[1314,8661,6716],{},[1579,8663,8664,8666],{},[1314,8665,8587],{},[1308,8667,8668,8670],{},[1685,8669,3062],{},[2738,8671,8672,8688],{},[1308,8673,8674,8676,8678,8680,8682],{},[1685,8675,1873],{"stretchy":1872},[1314,8677,7140],{},[1685,8679,3062],{},[1314,8681,6887],{},[1579,8683,8684,8686],{},[1685,8685,1884],{"stretchy":1872},[1562,8687,1586],{},[1308,8689,8690,8692],{},[1562,8691,1586],{},[1579,8693,8694,8696],{},[1314,8695,6895],{},[1562,8697,1586],{},[2907,8699,2909],{},[1314,8701,7792],{},[1314,8703,7140],{},[1685,8705,1795],{"separator":1530},[1319,8707,8708],{"encoding":1321},"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,",[1148,8710,8711,8712,1323,8736,1395],{},"přičemž ",[1296,8713,8715],{"className":8714},[1299],[1301,8716,8717],{"xmlns":1303},[1305,8718,8719,8733],{},[1308,8720,8721,8723,8725,8727,8729,8731],{},[1314,8722,1217],{},[1685,8724,1873],{"stretchy":1872},[1314,8726,6728],{},[1685,8728,1884],{"stretchy":1872},[1685,8730,1980],{},[1314,8732,6887],{},[1319,8734,8735],{"encoding":1321},"E(X) = \\mu",[1296,8737,8739],{"className":8738},[1299],[1301,8740,8741],{"xmlns":1303},[1305,8742,8743,8761],{},[1308,8744,8745,8747,8749,8751,8753,8755],{},[1314,8746,1209],{},[1685,8748,1873],{"stretchy":1872},[1314,8750,6728],{},[1685,8752,1884],{"stretchy":1872},[1685,8754,1980],{},[1579,8756,8757,8759],{},[1314,8758,6895],{},[1562,8760,1586],{},[1319,8762,8763],{"encoding":1321},"D(X) = \\sigma^2",[1148,8765,8766],{},[4382,8767],{"alt":8768,"className":8769,"src":8770},"mask-nv-normalni",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1148,8772,8773,8774,8777,8778,8792,8793,8812,8813,8829,8830,8843,8844,1395],{},"Křivka hustoty se nazývá ",[1108,8775,8776],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1296,8779,8781],{"className":8780},[1299],[1301,8782,8783],{"xmlns":1303},[1305,8784,8785,8789],{},[1308,8786,8787],{},[1314,8788,6887],{},[1319,8790,8791],{"encoding":1321},"\\mu",", kde má ",[1296,8794,8796],{"className":8795},[1299],[1301,8797,8798],{"xmlns":1303},[1305,8799,8800,8810],{},[1308,8801,8802,8804,8806,8808],{},[1314,8803,6767],{},[1685,8805,1873],{"stretchy":1872},[1314,8807,6716],{},[1685,8809,1884],{"stretchy":1872},[1319,8811,6797],{"encoding":1321}," globální maximum, a ve vzdálenosti ",[1296,8814,8816],{"className":8815},[1299],[1301,8817,8818],{"xmlns":1303},[1305,8819,8820,8826],{},[1308,8821,8822,8824],{},[1562,8823,3590],{},[1314,8825,6895],{},[1319,8827,8828],{"encoding":1321},"3\\sigma"," od ",[1296,8831,8833],{"className":8832},[1299],[1301,8834,8835],{"xmlns":1303},[1305,8836,8837,8841],{},[1308,8838,8839],{},[1314,8840,6887],{},[1319,8842,8791],{"encoding":1321}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1296,8845,8847],{"className":8846},[1299],[1301,8848,8849],{"xmlns":1303},[1305,8850,8851,8875],{},[1308,8852,8853,8855,8857,8859,8861,8863,8865,8867,8869,8871,8873],{},[1685,8854,1873],{"stretchy":1872},[1314,8856,6887],{},[1685,8858,3062],{},[1562,8860,3590],{},[1314,8862,6895],{},[1685,8864,6890],{"separator":1530},[1314,8866,6887],{},[1685,8868,5474],{},[1562,8870,3590],{},[1314,8872,6895],{},[1685,8874,1884],{"stretchy":1872},[1319,8876,8877],{"encoding":1321},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1148,8879,8880,8881,1651,8884,8908,8909,1395],{},"Zvláštní postavení má ",[1108,8882,8883],{},"normované normální rozdělení",[1296,8885,8887],{"className":8886},[1299],[1301,8888,8889],{"xmlns":1303},[1305,8890,8891,8905],{},[1308,8892,8893,8895,8897,8899,8901,8903],{},[1314,8894,6882],{},[1685,8896,1873],{"stretchy":1872},[1562,8898,1564],{},[1685,8900,6890],{"separator":1530},[1562,8902,1792],{},[1685,8904,1884],{"stretchy":1872},[1319,8906,8907],{"encoding":1321},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1296,8910,8912],{"className":8911},[1299],[1301,8913,8914],{"xmlns":1303},[1305,8915,8916,8937],{},[1308,8917,8918,8921,8923,8925,8927,8929,8931,8933,8935],{},[1314,8919,8920],{},"Z",[1685,8922,1980],{},[1685,8924,1873],{"stretchy":1872},[1314,8926,6728],{},[1685,8928,3062],{},[1314,8930,6887],{},[1685,8932,1884],{"stretchy":1872},[1314,8934,1502],{"mathvariant":2119},[1314,8936,6895],{},[1319,8938,8939],{"encoding":1321},"Z = (X-\\mu)\u002F\\sigma",[8941,8942],"graph-mount",{"spec":8943},"{\"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\"}]}",[1514,8945,8947,8954],{"className":8946,"dataCallout":6409},[1517,6408],[1148,8948,8950,8953],{"className":8949},[1523],[1296,8951],{"className":8952,"ariaHidden":1530},[1527,6416,1529],"R očekává směrodatnou odchylku, ne rozptyl",[1148,8955,8956,8957,8984,8985,8988,8989,1323,8991,1370,8993,8995,8996,1651,8999,9012,9013,9039,9040,9043,9044,1395],{},"Zápis ",[1296,8958,8960],{"className":8959},[1299],[1301,8961,8962],{"xmlns":1303},[1305,8963,8964,8982],{},[1308,8965,8966,8968,8970,8972,8974,8980],{},[1314,8967,6882],{},[1685,8969,1873],{"stretchy":1872},[1314,8971,6887],{},[1685,8973,6890],{"separator":1530},[1579,8975,8976,8978],{},[1314,8977,6895],{},[1562,8979,1586],{},[1685,8981,1884],{"stretchy":1872},[1319,8983,6902],{"encoding":1321}," v definici používá ",[1108,8986,8987],{},"rozptyl",". Funkce ",[3468,8990,6906],{},[3468,8992,6909],{},[3468,8994,6912],{}," v R ale jako třetí argument berou ",[1108,8997,8998],{},"směrodatnou odchylku",[1296,9000,9002],{"className":9001},[1299],[1301,9003,9004],{"xmlns":1303},[1305,9005,9006,9010],{},[1308,9007,9008],{},[1314,9009,6895],{},[1319,9011,6927],{"encoding":1321},". Má-li náhodná veličina rozdělení ",[1296,9014,9016],{"className":9015},[1299],[1301,9017,9018],{"xmlns":1303},[1305,9019,9020,9036],{},[1308,9021,9022,9024,9026,9029,9031,9034],{},[1314,9023,6882],{},[1685,9025,1873],{"stretchy":1872},[1562,9027,9028],{},"10",[1685,9030,6890],{"separator":1530},[1562,9032,9033],{},"0,12",[1685,9035,1884],{"stretchy":1872},[1319,9037,9038],{"encoding":1321},"N(10; 0{,}12)",", je ",[3468,9041,9042],{},"sd = sqrt(0.12)",", ne ",[3468,9045,9046],{},"sd = 0.12",[1148,9048,9049],{},"V R:",[3692,9051,9053],{"className":3694,"code":9052,"language":71,"meta":1452,"style":1452},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3468,9054,9055,9065,9076],{"__ignoreMap":1452},[1296,9056,9057,9059,9061,9063],{"class":3700,"line":10},[1296,9058,6906],{"class":3711},[1296,9060,1873],{"class":3715},[1296,9062,1564],{"class":3723},[1296,9064,3900],{"class":3715},[1296,9066,9067,9069,9071,9074],{"class":3700,"line":27},[1296,9068,6909],{"class":3711},[1296,9070,1873],{"class":3715},[1296,9072,9073],{"class":3723},"1.96",[1296,9075,3900],{"class":3715},[1296,9077,9078,9080,9082,9085],{"class":3700,"line":148},[1296,9079,6912],{"class":3711},[1296,9081,1873],{"class":3715},[1296,9083,9084],{"class":3723},"0.975",[1296,9086,3900],{"class":3715},[3692,9088,9091],{"className":9089,"code":9090,"language":3922,"meta":1452},[3920],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3468,9092,9090],{"__ignoreMap":1452},[1148,9094,9095,9098,9099,9123,9124,1888,9127,1370,9148,9151],{},[3468,9096,9097],{},"dnorm(0)"," je hodnota hustoty ",[1296,9100,9102],{"className":9101},[1299],[1301,9103,9104],{"xmlns":1303},[1305,9105,9106,9120],{},[1308,9107,9108,9110,9112,9114,9116,9118],{},[1314,9109,6882],{},[1685,9111,1873],{"stretchy":1872},[1562,9113,1564],{},[1685,9115,6890],{"separator":1530},[1562,9117,1792],{},[1685,9119,1884],{"stretchy":1872},[1319,9121,9122],{"encoding":1321},"N(0;1)"," v bodě 0, ",[3468,9125,9126],{},"pnorm(1.96)",[1296,9128,9130],{"className":9129},[1299],[1301,9131,9132],{"xmlns":1303},[1305,9133,9134,9145],{},[1308,9135,9136,9138,9140,9143],{},[1314,9137,1225],{},[1685,9139,1873],{"stretchy":1872},[1562,9141,9142],{},"1,96",[1685,9144,1884],{"stretchy":1872},[1319,9146,9147],{"encoding":1321},"F(1{,}96)",[3468,9149,9150],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1514,9153,9155,9162],{"className":9154,"dataCallout":3475},[1517,3474],[1148,9156,9158,9161],{"className":9157},[1523],[1296,9159],{"className":9160,"ariaHidden":1530},[1527,3482,1529],"Příklad: Návštěvnost zábavního parku",[1148,9163,9164,9165,9200],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1296,9166,9168],{"className":9167},[1299],[1301,9169,9170],{"xmlns":1303},[1305,9171,9172,9197],{},[1308,9173,9174,9176,9179,9181,9183,9186,9188,9195],{},[1314,9175,6728],{},[1685,9177,9178],{},"∼",[1314,9180,6882],{},[1685,9182,1873],{"stretchy":1872},[1562,9184,9185],{},"230",[1685,9187,6890],{"separator":1530},[1579,9189,9190,9193],{},[1562,9191,9192],{},"27,5",[1562,9194,1586],{},[1685,9196,1884],{"stretchy":1872},[1319,9198,9199],{"encoding":1321},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1148,9202,9203],{},[4382,9204],{"alt":9205,"className":9206,"src":9207},"mask-nv-priklad-park",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3692,9209,9211],{"className":3694,"code":9210,"language":71,"meta":1452,"style":1452},"pnorm(180, mean = 230, sd = 27.5)\n",[3468,9212,9213],{"__ignoreMap":1452},[1296,9214,9215,9217,9219,9222,9224,9227,9229,9232,9234,9237,9239,9242],{"class":3700,"line":10},[1296,9216,6909],{"class":3711},[1296,9218,1873],{"class":3715},[1296,9220,9221],{"class":3723},"180",[1296,9223,1795],{"class":3707},[1296,9225,9226],{"class":3703}," mean",[1296,9228,3796],{"class":3707},[1296,9230,9231],{"class":3723}," 230",[1296,9233,1795],{"class":3707},[1296,9235,9236],{"class":3703}," sd",[1296,9238,3796],{"class":3707},[1296,9240,9241],{"class":3723}," 27.5",[1296,9243,3900],{"class":3715},[3692,9245,9248],{"className":9246,"code":9247,"language":3922,"meta":1452},[3920],"[1] 0.03451817\n",[3468,9249,9247],{"__ignoreMap":1452},[1148,9251,9252],{},"Park je ztrátový přibližně v 3,45 % dní.",[1514,9254,9256,9263],{"className":9255,"dataCallout":3475},[1517,3474],[1148,9257,9259,9262],{"className":9258},[1523],[1296,9260],{"className":9261,"ariaHidden":1530},[1527,3482,1529],"Příklad: Délka výrobku",[1148,9264,9265,9266,9300],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1296,9267,9269],{"className":9268},[1299],[1301,9270,9271],{"xmlns":1303},[1305,9272,9273,9297],{},[1308,9274,9275,9277,9279,9281,9283,9286,9288,9295],{},[1314,9276,6728],{},[1685,9278,9178],{},[1314,9280,6882],{},[1685,9282,1873],{"stretchy":1872},[1562,9284,9285],{},"42",[1685,9287,6890],{"separator":1530},[1579,9289,9290,9293],{},[1562,9291,9292],{},"1,2",[1562,9294,1586],{},[1685,9296,1884],{"stretchy":1872},[1319,9298,9299],{"encoding":1321},"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?",[1148,9302,9303],{},[4382,9304],{"alt":9305,"className":9306,"src":9307},"mask-nv-priklad-delka",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3692,9309,9311],{"className":3694,"code":9310,"language":71,"meta":1452,"style":1452},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3468,9312,9313],{"__ignoreMap":1452},[1296,9314,9315,9317,9319,9322,9324,9326,9328,9331,9333,9335,9337,9340,9342,9344,9347,9349,9352,9354,9356,9358,9360,9362,9364,9366,9368],{"class":3700,"line":10},[1296,9316,6909],{"class":3711},[1296,9318,1873],{"class":3715},[1296,9320,9321],{"class":3723},"43",[1296,9323,1795],{"class":3707},[1296,9325,9226],{"class":3703},[1296,9327,3796],{"class":3707},[1296,9329,9330],{"class":3723}," 42",[1296,9332,1795],{"class":3707},[1296,9334,9236],{"class":3703},[1296,9336,3796],{"class":3707},[1296,9338,9339],{"class":3723}," 1.2",[1296,9341,4599],{"class":3715},[1296,9343,4635],{"class":3707},[1296,9345,9346],{"class":3711}," pnorm",[1296,9348,1873],{"class":3715},[1296,9350,9351],{"class":3723},"41",[1296,9353,1795],{"class":3707},[1296,9355,9226],{"class":3703},[1296,9357,3796],{"class":3707},[1296,9359,9330],{"class":3723},[1296,9361,1795],{"class":3707},[1296,9363,9236],{"class":3703},[1296,9365,3796],{"class":3707},[1296,9367,9339],{"class":3723},[1296,9369,3900],{"class":3715},[3692,9371,9374],{"className":9372,"code":9373,"language":3922,"meta":1452},[3920],"[1] 0.5953432\n",[3468,9375,9373],{"__ignoreMap":1452},[1148,9377,9378],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1514,9380,9382,9389],{"className":9381,"dataCallout":3475},[1517,3474],[1148,9383,9385,9388],{"className":9384},[1523],[1296,9386],{"className":9387,"ariaHidden":1530},[1527,3482,1529],"Příklad: Obsah ampulky",[1148,9390,9391,9392,9415,9416,9442],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1296,9393,9395],{"className":9394},[1299],[1301,9396,9397],{"xmlns":1303},[1305,9398,9399,9413],{},[1308,9400,9401,9403,9405,9407,9409,9411],{},[1314,9402,6882],{},[1685,9404,1873],{"stretchy":1872},[1562,9406,9028],{},[1685,9408,6890],{"separator":1530},[1562,9410,9033],{},[1685,9412,1884],{"stretchy":1872},[1319,9414,9038],{"encoding":1321},", tedy střední hodnota 10 a rozptyl 0,12 (",[1296,9417,9419],{"className":9418},[1299],[1301,9420,9421],{"xmlns":1303},[1305,9422,9423,9439],{},[1308,9424,9425,9427,9429,9433,9436],{},[1314,9426,6895],{},[1685,9428,1980],{},[4452,9430,9431],{},[1562,9432,9033],{},[1685,9434,9435],{},"≈",[1562,9437,9438],{},"0,346",[1319,9440,9441],{"encoding":1321},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1148,9444,9445],{},[4382,9446],{"alt":9447,"className":9448,"src":9449},"mask-nv-priklad-ampulka",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3692,9451,9453],{"className":3694,"code":9452,"language":71,"meta":1452,"style":1452},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3468,9454,9455],{"__ignoreMap":1452},[1296,9456,9457,9459,9461,9464,9466,9468,9470,9473,9475,9477,9479,9481,9483,9486],{"class":3700,"line":10},[1296,9458,6909],{"class":3711},[1296,9460,1873],{"class":3715},[1296,9462,9463],{"class":3723},"9.8",[1296,9465,1795],{"class":3707},[1296,9467,9226],{"class":3703},[1296,9469,3796],{"class":3707},[1296,9471,9472],{"class":3723}," 10",[1296,9474,1795],{"class":3707},[1296,9476,9236],{"class":3703},[1296,9478,3796],{"class":3707},[1296,9480,4576],{"class":3711},[1296,9482,1873],{"class":3715},[1296,9484,9485],{"class":3723},"0.12",[1296,9487,9488],{"class":3715},"))\n",[3692,9490,9493],{"className":9491,"code":9492,"language":3922,"meta":1452},[3920],"[1] 0.2818514\n",[3468,9494,9492],{"__ignoreMap":1452},[1148,9496,9497],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1143,9499,9501],{"id":9500},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1148,9503,9504,9505,9508,9509,9512,9513,9516,9517,1502,9520,9523,9524,9527],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3468,9506,9507],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3468,9510,9511],{},"p*"," distribuční funkce (s ",[3468,9514,9515],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3468,9518,9519],{},"TRUE",[3468,9521,9522],{},"FALSE",", pro horní chvost) a ",[3468,9525,9526],{},"q*"," kvantilová funkce.",[1162,9529,9530,9636],{},[1165,9531,9532],{},[1168,9533,9534,9537,9583,9609],{},[1171,9535,9536],{},"Rozdělení",[1171,9538,9539,9563,9564],{},[1296,9540,9542],{"className":9541},[1299],[1301,9543,9544],{"xmlns":1303},[1305,9545,9546,9560],{},[1308,9547,9548,9550,9552,9554,9556,9558],{},[1314,9549,6723],{},[1685,9551,1873],{"stretchy":1872},[1314,9553,6728],{},[1685,9555,1980],{},[1314,9557,1343],{},[1685,9559,1884],{"stretchy":1872},[1319,9561,9562],{"encoding":1321},"P(X=k)"," \u002F ",[1296,9565,9567],{"className":9566},[1299],[1301,9568,9569],{"xmlns":1303},[1305,9570,9571,9581],{},[1308,9572,9573,9575,9577,9579],{},[1314,9574,6767],{},[1685,9576,1873],{"stretchy":1872},[1314,9578,6716],{},[1685,9580,1884],{"stretchy":1872},[1319,9582,6797],{"encoding":1321},[1171,9584,9585],{},[1296,9586,9588],{"className":9587},[1299],[1301,9589,9590],{"xmlns":1303},[1305,9591,9592,9606],{},[1308,9593,9594,9596,9598,9600,9602,9604],{},[1314,9595,6723],{},[1685,9597,1873],{"stretchy":1872},[1314,9599,6728],{},[1685,9601,6731],{},[1314,9603,1343],{},[1685,9605,1884],{"stretchy":1872},[1319,9607,9608],{"encoding":1321},"P(X \\le k)",[1171,9610,9611,9612],{},"horní chvost ",[1296,9613,9615],{"className":9614},[1299],[1301,9616,9617],{"xmlns":1303},[1305,9618,9619,9633],{},[1308,9620,9621,9623,9625,9627,9629,9631],{},[1314,9622,6723],{},[1685,9624,1873],{"stretchy":1872},[1314,9626,6728],{},[1685,9628,1687],{},[1314,9630,1343],{},[1685,9632,1884],{"stretchy":1872},[1319,9634,9635],{"encoding":1321},"P(X>k)",[1178,9637,9638,9684,9728,9769,9818],{},[1168,9639,9640,9669,9674,9679],{},[1183,9641,9642,9643],{},"Binomické ",[1296,9644,9646],{"className":9645},[1299],[1301,9647,9648],{"xmlns":1303},[1305,9649,9650,9666],{},[1308,9651,9652,9654,9656,9658,9660,9662,9664],{},[1314,9653,1193],{},[1314,9655,1876],{},[1685,9657,1873],{"stretchy":1872},[1314,9659,1683],{},[1685,9661,1795],{"separator":1530},[1314,9663,1148],{},[1685,9665,1884],{"stretchy":1872},[1319,9667,9668],{"encoding":1321},"Bi(n,p)",[1183,9670,9671],{},[3468,9672,9673],{},"dbinom(k, n, p)",[1183,9675,9676],{},[3468,9677,9678],{},"pbinom(k, n, p)",[1183,9680,9681],{},[3468,9682,9683],{},"pbinom(k, n, p, FALSE)",[1168,9685,9686,9713,9718,9723],{},[1183,9687,9688,9689],{},"Poissonovo ",[1296,9690,9692],{"className":9691},[1299],[1301,9693,9694],{"xmlns":1303},[1305,9695,9696,9710],{},[1308,9697,9698,9700,9703,9705,9708],{},[1314,9699,6723],{},[1314,9701,9702],{},"o",[1685,9704,1873],{"stretchy":1872},[1314,9706,9707],{},"λ",[1685,9709,1884],{"stretchy":1872},[1319,9711,9712],{"encoding":1321},"Po(\\lambda)",[1183,9714,9715],{},[3468,9716,9717],{},"dpois(k, lambda)",[1183,9719,9720],{},[3468,9721,9722],{},"ppois(k, lambda)",[1183,9724,9725],{},[3468,9726,9727],{},"ppois(k, lambda, FALSE)",[1168,9729,9730,9754,9759,9764],{},[1183,9731,9732,9733],{},"Geometrické ",[1296,9734,9736],{"className":9735},[1299],[1301,9737,9738],{"xmlns":1303},[1305,9739,9740,9751],{},[1308,9741,9742,9745,9747,9749],{},[1314,9743,9744],{},"G",[1685,9746,1873],{"stretchy":1872},[1314,9748,1148],{},[1685,9750,1884],{"stretchy":1872},[1319,9752,9753],{"encoding":1321},"G(p)",[1183,9755,9756],{},[3468,9757,9758],{},"dgeom(k, p)",[1183,9760,9761],{},[3468,9762,9763],{},"pgeom(k, p)",[1183,9765,9766],{},[3468,9767,9768],{},"pgeom(k, p, FALSE)",[1168,9770,9771,9803,9808,9813],{},[1183,9772,9773,9774],{},"Hypergeometrické ",[1296,9775,9777],{"className":9776},[1299],[1301,9778,9779],{"xmlns":1303},[1305,9780,9781,9800],{},[1308,9782,9783,9785,9787,9789,9791,9794,9796,9798],{},[1314,9784,1560],{},[1685,9786,1873],{"stretchy":1872},[1314,9788,6882],{},[1685,9790,1795],{"separator":1530},[1314,9792,9793],{},"M",[1685,9795,1795],{"separator":1530},[1314,9797,1683],{},[1685,9799,1884],{"stretchy":1872},[1319,9801,9802],{"encoding":1321},"H(N,M,n)",[1183,9804,9805],{},[3468,9806,9807],{},"dhyper(k, M, N-M, n)",[1183,9809,9810],{},[3468,9811,9812],{},"phyper(k, M, N-M, n)",[1183,9814,9815],{},[3468,9816,9817],{},"phyper(k, M, N-M, n, FALSE)",[1168,9819,9820,9844,9849,9854],{},[1183,9821,9822,9823],{},"Exponenciální ",[1296,9824,9826],{"className":9825},[1299],[1301,9827,9828],{"xmlns":1303},[1305,9829,9830,9841],{},[1308,9831,9832,9834,9836,9839],{},[1314,9833,1217],{},[1685,9835,1873],{"stretchy":1872},[1314,9837,9838],{},"δ",[1685,9840,1884],{"stretchy":1872},[1319,9842,9843],{"encoding":1321},"E(\\delta)",[1183,9845,9846],{},[3468,9847,9848],{},"dexp(k, 1\u002Fdelta)",[1183,9850,9851],{},[3468,9852,9853],{},"pexp(k, 1\u002Fdelta)",[1183,9855,9856],{},[3468,9857,9858],{},"pexp(k, 1\u002Fdelta, FALSE)",[1514,9860,9862,9869],{"className":9861,"dataCallout":6409},[1517,6408],[1148,9863,9865,9868],{"className":9864},[1523],[1296,9866],{"className":9867,"ariaHidden":1530},[1527,6416,1529],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1148,9870,9871,9872,9875,9876,9890,9891,9043,9894,1395],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3468,9873,9874],{},"rate","). Je-li ",[1296,9877,9879],{"className":9878},[1299],[1301,9880,9881],{"xmlns":1303},[1305,9882,9883,9887],{},[1308,9884,9885],{},[1314,9886,9838],{},[1319,9888,9889],{"encoding":1321},"\\delta"," střední doba do události, do R se dosazuje ",[3468,9892,9893],{},"1\u002Fdelta",[3468,9895,9896],{},"delta",[1148,9898,9899,9900,9932,9933,9951],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1296,9901,9903],{"className":9902},[1299],[1301,9904,9905],{"xmlns":1303},[1305,9906,9907,9929],{},[1308,9908,9909,9911,9913,9915,9917,9919,9922,9924,9927],{},[1314,9910,6728],{},[1685,9912,9178],{},[1314,9914,1193],{},[1314,9916,1876],{},[1685,9918,1873],{"stretchy":1872},[1562,9920,9921],{},"5",[1685,9923,6890],{"separator":1530},[1562,9925,9926],{},"0,95",[1685,9928,1884],{"stretchy":1872},[1319,9930,9931],{"encoding":1321},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1296,9934,9936],{"className":9935},[1299],[1301,9937,9938],{"xmlns":1303},[1305,9939,9940,9948],{},[1308,9941,9942,9944,9946],{},[1314,9943,9838],{},[1685,9945,1980],{},[1562,9947,9921],{},[1319,9949,9950],{"encoding":1321},"\\delta = 5"," nastane událost do 3 jednotek času):",[3692,9953,9955],{"className":3694,"code":9954,"language":71,"meta":1452,"style":1452},"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",[3468,9956,9957,9971,10003,10032,10037,10046],{"__ignoreMap":1452},[1296,9958,9959,9961,9963,9966,9968],{"class":3700,"line":10},[1296,9960,6716],{"class":3703},[1296,9962,3708],{"class":3707},[1296,9964,9965],{"class":3723}," 0",[1296,9967,1956],{"class":3707},[1296,9969,9970],{"class":3723},"5\n",[1296,9972,9973,9976,9978,9981,9983,9985,9987,9990,9992,9995,9997,9999,10001],{"class":3700,"line":27},[1296,9974,9975],{"class":3711},"round",[1296,9977,1873],{"class":3715},[1296,9979,9980],{"class":3711},"dbinom",[1296,9982,1873],{"class":3715},[1296,9984,6716],{"class":3703},[1296,9986,1795],{"class":3707},[1296,9988,9989],{"class":3723}," 5",[1296,9991,1795],{"class":3707},[1296,9993,9994],{"class":3723}," 0.95",[1296,9996,1884],{"class":3715},[1296,9998,1795],{"class":3707},[1296,10000,3799],{"class":3723},[1296,10002,3900],{"class":3715},[1296,10004,10005,10007,10009,10012,10014,10016,10018,10020,10022,10024,10026,10028,10030],{"class":3700,"line":148},[1296,10006,9975],{"class":3711},[1296,10008,1873],{"class":3715},[1296,10010,10011],{"class":3711},"pbinom",[1296,10013,1873],{"class":3715},[1296,10015,6716],{"class":3703},[1296,10017,1795],{"class":3707},[1296,10019,9989],{"class":3723},[1296,10021,1795],{"class":3707},[1296,10023,9994],{"class":3723},[1296,10025,1884],{"class":3715},[1296,10027,1795],{"class":3707},[1296,10029,3799],{"class":3723},[1296,10031,3900],{"class":3715},[1296,10033,10034],{"class":3700,"line":111},[1296,10035,10036],{"emptyLinePlaceholder":1464},"\n",[1296,10038,10039,10041,10043],{"class":3700,"line":96},[1296,10040,9896],{"class":3703},[1296,10042,3708],{"class":3707},[1296,10044,10045],{"class":3723}," 5\n",[1296,10047,10048,10050,10052,10055,10057,10059,10061,10064,10066,10068,10071,10074,10076,10078,10080],{"class":3700,"line":89},[1296,10049,9975],{"class":3711},[1296,10051,1873],{"class":3715},[1296,10053,10054],{"class":3711},"pexp",[1296,10056,1873],{"class":3715},[1296,10058,3590],{"class":3723},[1296,10060,1795],{"class":3707},[1296,10062,10063],{"class":3703}," rate",[1296,10065,3796],{"class":3707},[1296,10067,4638],{"class":3723},[1296,10069,10070],{"class":3707}," \u002F",[1296,10072,10073],{"class":3703}," delta",[1296,10075,1884],{"class":3715},[1296,10077,1795],{"class":3707},[1296,10079,3799],{"class":3723},[1296,10081,3900],{"class":3715},[3692,10083,10086],{"className":10084,"code":10085,"language":3922,"meta":1452},[3920],"[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",[3468,10087,10085],{"__ignoreMap":1452},[1143,10089,10091],{"id":10090},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1148,10093,10094,10095,10098],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1242,10096,141],{"className":10097,"dataFsResolvedFilePath":1264,"href":1265},[1245],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1148,10100,10101,3951,10104,10117],{},[1108,10102,10103],{},"Studentovo rozdělení",[1296,10105,10107],{"className":10106},[1299],[1301,10108,10109],{"xmlns":1303},[1305,10110,10111,10115],{},[1308,10112,10113],{},[1314,10114,1343],{},[1319,10116,1343],{"encoding":1321}," stupni volnosti má hustotu pravděpodobnosti",[1296,10119,10121],{"className":10120},[1299],[1301,10122,10123],{"xmlns":1303,"display":1962},[1305,10124,10125,10221],{},[1308,10126,10127,10129,10131,10133,10135,10137,10169,10207,10209,10211,10213,10215,10219],{},[1314,10128,6767],{},[1685,10130,1873],{"stretchy":1872},[1314,10132,6716],{},[1685,10134,1884],{"stretchy":1872},[1685,10136,1980],{},[2738,10138,10139,10141],{},[1562,10140,1792],{},[1308,10142,10143,10145,10165],{},[1314,10144,1193],{},[1308,10146,10147,10149,10155,10157,10163],{},[1685,10148,1873],{"fence":1530},[2738,10150,10151,10153],{},[1562,10152,1792],{},[1562,10154,1586],{},[1685,10156,1795],{"separator":1530},[2738,10158,10159,10161],{},[1314,10160,1343],{},[1562,10162,1586],{},[1685,10164,1884],{"fence":1530},[4452,10166,10167],{},[1314,10168,1343],{},[1579,10170,10171,10191],{},[1308,10172,10173,10175,10177,10179,10189],{},[1685,10174,1873],{"fence":1530},[1562,10176,1792],{},[1685,10178,5474],{},[2738,10180,10181,10187],{},[1579,10182,10183,10185],{},[1314,10184,6716],{},[1562,10186,1586],{},[1314,10188,1343],{},[1685,10190,1884],{"fence":1530},[1308,10192,10193,10195],{},[1685,10194,3062],{},[2738,10196,10197,10205],{},[1308,10198,10199,10201,10203],{},[1314,10200,1343],{},[1685,10202,5474],{},[1562,10204,1792],{},[1562,10206,1586],{},[1685,10208,1795],{"separator":1530},[2010,10210],{"width":2012},[1314,10212,6716],{},[1685,10214,7015],{},[1314,10216,10218],{"mathvariant":10217},"double-struck","R",[1685,10220,1795],{"separator":1530},[1319,10222,10223],{"encoding":1321},"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},",[1148,10225,4505,10226,10239,10240,10253,10254,10267],{},[1296,10227,10229],{"className":10228},[1299],[1301,10230,10231],{"xmlns":1303},[1305,10232,10233,10237],{},[1308,10234,10235],{},[1314,10236,1193],{},[1319,10238,1193],{"encoding":1321}," je funkce beta. Je symetrické kolem nuly; číslo ",[1296,10241,10243],{"className":10242},[1299],[1301,10244,10245],{"xmlns":1303},[1305,10246,10247,10251],{},[1308,10248,10249],{},[1314,10250,1343],{},[1319,10252,1343],{"encoding":1321}," určuje tvar křivky — s rostoucím ",[1296,10255,10257],{"className":10256},[1299],[1301,10258,10259],{"xmlns":1303},[1305,10260,10261,10265],{},[1308,10262,10263],{},[1314,10264,1343],{},[1319,10266,1343],{"encoding":1321}," se rozdělení blíží normálnímu.",[1148,10269,10270,3951,10273,10286],{},[1108,10271,10272],{},"Pearsonovo (chí-kvadrát) rozdělení",[1296,10274,10276],{"className":10275},[1299],[1301,10277,10278],{"xmlns":1303},[1305,10279,10280,10284],{},[1308,10281,10282],{},[1314,10283,1343],{},[1319,10285,1343],{"encoding":1321}," stupni volnosti:",[1296,10288,10290],{"className":10289},[1299],[1301,10291,10292],{"xmlns":1303,"display":1962},[1305,10293,10294,10379],{},[1308,10295,10296,10298,10300,10302,10304,10306,10337,10353,10367,10369,10371,10373,10375,10377],{},[1314,10297,6767],{},[1685,10299,1873],{"stretchy":1872},[1314,10301,6716],{},[1685,10303,1884],{"stretchy":1872},[1685,10305,1980],{},[2738,10307,10308,10310],{},[1562,10309,1792],{},[1308,10311,10312,10324,10327,10329,10331,10333,10335],{},[1579,10313,10314,10316],{},[1562,10315,1586],{},[1308,10317,10318,10320,10322],{},[1314,10319,1343],{},[1314,10321,1502],{"mathvariant":2119},[1562,10323,1586],{},[1314,10325,10326],{"mathvariant":2119},"Γ",[1685,10328,1873],{"stretchy":1872},[1314,10330,1343],{},[1314,10332,1502],{"mathvariant":2119},[1562,10334,1586],{},[1685,10336,1884],{"stretchy":1872},[1579,10338,10339,10341],{},[1314,10340,6716],{},[1308,10342,10343,10345,10347,10349,10351],{},[1314,10344,1343],{},[1314,10346,1502],{"mathvariant":2119},[1562,10348,1586],{},[1685,10350,3062],{},[1562,10352,1792],{},[1579,10354,10355,10357],{},[1314,10356,8587],{},[1308,10358,10359,10361,10363,10365],{},[1685,10360,3062],{},[1314,10362,6716],{},[1314,10364,1502],{"mathvariant":2119},[1562,10366,1586],{},[1685,10368,1795],{"separator":1530},[2010,10370],{"width":2012},[1314,10372,6716],{},[1685,10374,1687],{},[1562,10376,1564],{},[1685,10378,1795],{"separator":1530},[1319,10380,10381],{"encoding":1321},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1148,10383,4505,10384,10398],{},[1296,10385,10387],{"className":10386},[1299],[1301,10388,10389],{"xmlns":1303},[1305,10390,10391,10395],{},[1308,10392,10393],{},[1314,10394,10326],{"mathvariant":2119},[1319,10396,10397],{"encoding":1321},"\\Gamma"," je funkce gama.",[1148,10400,10401,10404,10405,1370,10423,1956],{},[1108,10402,10403],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1296,10406,10408],{"className":10407},[1299],[1301,10409,10410],{"xmlns":1303},[1305,10411,10412,10420],{},[1308,10413,10414],{},[1311,10415,10416,10418],{},[1314,10417,1343],{},[1562,10419,1792],{},[1319,10421,10422],{"encoding":1321},"k_1",[1296,10424,10426],{"className":10425},[1299],[1301,10427,10428],{"xmlns":1303},[1305,10429,10430,10438],{},[1308,10431,10432],{},[1311,10433,10434,10436],{},[1314,10435,1343],{},[1562,10437,1586],{},[1319,10439,10440],{"encoding":1321},"k_2",[1296,10442,10444],{"className":10443},[1299],[1301,10445,10446],{"xmlns":1303,"display":1962},[1305,10447,10448,10613],{},[1308,10449,10450,10452,10454,10456,10458,10460,10496,10530,10550,10602,10604,10606,10608,10610],{},[1314,10451,6767],{},[1685,10453,1873],{"stretchy":1872},[1314,10455,6716],{},[1685,10457,1884],{"stretchy":1872},[1685,10459,1980],{},[2738,10461,10462,10464],{},[1562,10463,1792],{},[1308,10465,10466,10468],{},[1314,10467,1193],{},[1308,10469,10470,10472,10482,10484,10494],{},[1685,10471,1873],{"fence":1530},[2738,10473,10474,10480],{},[1311,10475,10476,10478],{},[1314,10477,1343],{},[1562,10479,1792],{},[1562,10481,1586],{},[1685,10483,1795],{"separator":1530},[2738,10485,10486,10492],{},[1311,10487,10488,10490],{},[1314,10489,1343],{},[1562,10491,1586],{},[1562,10493,1586],{},[1685,10495,1884],{"fence":1530},[1579,10497,10498,10518],{},[1308,10499,10500,10502,10516],{},[1685,10501,1873],{"fence":1530},[2738,10503,10504,10510],{},[1311,10505,10506,10508],{},[1314,10507,1343],{},[1562,10509,1792],{},[1311,10511,10512,10514],{},[1314,10513,1343],{},[1562,10515,1586],{},[1685,10517,1884],{"fence":1530},[1308,10519,10520,10526,10528],{},[1311,10521,10522,10524],{},[1314,10523,1343],{},[1562,10525,1792],{},[1314,10527,1502],{"mathvariant":2119},[1562,10529,1586],{},[1579,10531,10532,10534],{},[1314,10533,6716],{},[1308,10535,10536,10542,10544,10546,10548],{},[1311,10537,10538,10540],{},[1314,10539,1343],{},[1562,10541,1792],{},[1314,10543,1502],{"mathvariant":2119},[1562,10545,1586],{},[1685,10547,3062],{},[1562,10549,1792],{},[1579,10551,10552,10578],{},[1308,10553,10554,10556,10558,10560,10574,10576],{},[1685,10555,1873],{"fence":1530},[1562,10557,1792],{},[1685,10559,5474],{},[2738,10561,10562,10568],{},[1311,10563,10564,10566],{},[1314,10565,1343],{},[1562,10567,1792],{},[1311,10569,10570,10572],{},[1314,10571,1343],{},[1562,10573,1586],{},[1314,10575,6716],{},[1685,10577,1884],{"fence":1530},[1308,10579,10580,10582],{},[1685,10581,3062],{},[2738,10583,10584,10600],{},[1308,10585,10586,10592,10594],{},[1311,10587,10588,10590],{},[1314,10589,1343],{},[1562,10591,1792],{},[1685,10593,5474],{},[1311,10595,10596,10598],{},[1314,10597,1343],{},[1562,10599,1586],{},[1562,10601,1586],{},[1685,10603,1795],{"separator":1530},[2010,10605],{"width":2012},[1314,10607,6716],{},[1685,10609,1687],{},[1562,10611,10612],{},"0.",[1319,10614,10615],{"encoding":1321},"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.",[1148,10617,10618],{},[4382,10619],{"alt":10620,"className":10621,"src":10622},"mask-nv-specialni-rozdeleni",[1245,4386],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[8941,10624],{"spec":10625},"{\"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\":[]}",[1148,10627,10628],{},"R funkce pro tato tři rozdělení:",[1162,10630,10631,10645],{},[1165,10632,10633],{},[1168,10634,10635,10637,10640,10642],{},[1171,10636,9536],{},[1171,10638,10639],{},"hustota",[1171,10641,6700],{},[1171,10643,10644],{},"kvantil",[1178,10646,10647,10687,10731],{},[1168,10648,10649,10672,10677,10682],{},[1183,10650,10651,10652],{},"Studentovo ",[1296,10653,10655],{"className":10654},[1299],[1301,10656,10657],{"xmlns":1303},[1305,10658,10659,10669],{},[1308,10660,10661,10663,10665,10667],{},[1314,10662,7140],{},[1685,10664,1873],{"stretchy":1872},[1314,10666,1343],{},[1685,10668,1884],{"stretchy":1872},[1319,10670,10671],{"encoding":1321},"t(k)",[1183,10673,10674],{},[3468,10675,10676],{},"dt(x, df = k)",[1183,10678,10679],{},[3468,10680,10681],{},"pt(x, df = k)",[1183,10683,10684],{},[3468,10685,10686],{},"qt(p, df = k)",[1168,10688,10689,10716,10721,10726],{},[1183,10690,10691,10692],{},"Pearsonovo ",[1296,10693,10695],{"className":10694},[1299],[1301,10696,10697],{"xmlns":1303},[1305,10698,10699,10713],{},[1308,10700,10701,10707,10709,10711],{},[1579,10702,10703,10705],{},[1314,10704,1583],{},[1562,10706,1586],{},[1685,10708,1873],{"stretchy":1872},[1314,10710,1343],{},[1685,10712,1884],{"stretchy":1872},[1319,10714,10715],{"encoding":1321},"\\chi^2(k)",[1183,10717,10718],{},[3468,10719,10720],{},"dchisq(x, df = k)",[1183,10722,10723],{},[3468,10724,10725],{},"pchisq(x, df = k)",[1183,10727,10728],{},[3468,10729,10730],{},"qchisq(p, df = k)",[1168,10732,10733,10768,10773,10778],{},[1183,10734,10735,10736],{},"Fisherovo-Snedecorovo ",[1296,10737,10739],{"className":10738},[1299],[1301,10740,10741],{"xmlns":1303},[1305,10742,10743,10765],{},[1308,10744,10745,10747,10749,10755,10757,10763],{},[1314,10746,1225],{},[1685,10748,1873],{"stretchy":1872},[1311,10750,10751,10753],{},[1314,10752,1343],{},[1562,10754,1792],{},[1685,10756,1795],{"separator":1530},[1311,10758,10759,10761],{},[1314,10760,1343],{},[1562,10762,1586],{},[1685,10764,1884],{"stretchy":1872},[1319,10766,10767],{"encoding":1321},"F(k_1, k_2)",[1183,10769,10770],{},[3468,10771,10772],{},"df(x, df1 = k1, df2 = k2)",[1183,10774,10775],{},[3468,10776,10777],{},"pf(x, df1 = k1, df2 = k2)",[1183,10779,10780],{},[3468,10781,10782],{},"qf(p, df1 = k1, df2 = k2)",[1148,10784,10785],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3692,10787,10789],{"className":3694,"code":10788,"language":71,"meta":1452,"style":1452},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3468,10790,10791,10812,10832],{"__ignoreMap":1452},[1296,10792,10793,10796,10798,10800,10802,10805,10807,10810],{"class":3700,"line":10},[1296,10794,10795],{"class":3711},"qt",[1296,10797,1873],{"class":3715},[1296,10799,9084],{"class":3723},[1296,10801,1795],{"class":3707},[1296,10803,10804],{"class":3703}," df",[1296,10806,3796],{"class":3707},[1296,10808,10809],{"class":3723}," 9",[1296,10811,3900],{"class":3715},[1296,10813,10814,10817,10819,10822,10824,10826,10828,10830],{"class":3700,"line":27},[1296,10815,10816],{"class":3711},"qchisq",[1296,10818,1873],{"class":3715},[1296,10820,10821],{"class":3723},"0.95",[1296,10823,1795],{"class":3707},[1296,10825,10804],{"class":3703},[1296,10827,3796],{"class":3707},[1296,10829,10809],{"class":3723},[1296,10831,3900],{"class":3715},[1296,10833,10834,10837,10839,10841,10843,10846,10848,10851,10853,10856,10858,10860],{"class":3700,"line":148},[1296,10835,10836],{"class":3711},"qf",[1296,10838,1873],{"class":3715},[1296,10840,10821],{"class":3723},[1296,10842,1795],{"class":3707},[1296,10844,10845],{"class":3703}," df1",[1296,10847,3796],{"class":3707},[1296,10849,10850],{"class":3723}," 3",[1296,10852,1795],{"class":3707},[1296,10854,10855],{"class":3703}," df2",[1296,10857,3796],{"class":3707},[1296,10859,9472],{"class":3723},[1296,10861,3900],{"class":3715},[3692,10863,10866],{"className":10864,"code":10865,"language":3922,"meta":1452},[3920],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3468,10867,10865],{"__ignoreMap":1452},[1143,10869,6404],{"id":6403},[1102,10871,10872,10958,11008],{},[1105,10873,10874,10877,10878,10905,10906,1502,10908,1502,10910,10912,10913,10933,10934,10957],{},[1108,10875,10876],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1296,10879,10881],{"className":10880},[1299],[1301,10882,10883],{"xmlns":1303},[1305,10884,10885,10903],{},[1308,10886,10887,10889,10891,10893,10895,10901],{},[1314,10888,6882],{},[1685,10890,1873],{"stretchy":1872},[1314,10892,6887],{},[1685,10894,6890],{"separator":1530},[1579,10896,10897,10899],{},[1314,10898,6895],{},[1562,10900,1586],{},[1685,10902,1884],{"stretchy":1872},[1319,10904,6902],{"encoding":1321}," používá rozptyl, ale ",[3468,10907,6906],{},[3468,10909,6909],{},[3468,10911,6912],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1296,10914,10916],{"className":10915},[1299],[1301,10917,10918],{"xmlns":1303},[1305,10919,10920,10930],{},[1308,10921,10922],{},[4452,10923,10924],{},[1579,10925,10926,10928],{},[1314,10927,6895],{},[1562,10929,1586],{},[1319,10931,10932],{"encoding":1321},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1296,10935,10937],{"className":10936},[1299],[1301,10938,10939],{"xmlns":1303},[1305,10940,10941,10954],{},[1308,10942,10943,10949,10952],{},[1579,10944,10945,10947],{},[1314,10946,6895],{},[1562,10948,1586],{},[1685,10950,10951],{"mathvariant":2119},"≠",[1562,10953,1792],{},[1319,10955,10956],{"encoding":1321},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1105,10959,10960,10987,10988,11007],{},[1108,10961,10962,10986],{},[1296,10963,10965],{"className":10964},[1299],[1301,10966,10967],{"xmlns":1303},[1305,10968,10969,10983],{},[1308,10970,10971,10973,10975,10977,10979,10981],{},[1314,10972,6723],{},[1685,10974,1873],{"stretchy":1872},[1314,10976,6728],{},[1685,10978,1980],{},[1314,10980,6716],{},[1685,10982,1884],{"stretchy":1872},[1319,10984,10985],{"encoding":1321},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1296,10989,10991],{"className":10990},[1299],[1301,10992,10993],{"xmlns":1303},[1305,10994,10995,11005],{},[1308,10996,10997,10999,11001,11003],{},[1314,10998,6767],{},[1685,11000,1873],{"stretchy":1872},[1314,11002,6716],{},[1685,11004,1884],{"stretchy":1872},[1319,11006,6797],{"encoding":1321}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1105,11009,11010,1651,11013,11030,11031,11048,11049,11052,11053,1395],{},[1108,11011,11012],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1296,11014,11016],{"className":11015},[1299],[1301,11017,11018],{"xmlns":1303},[1305,11019,11020,11028],{},[1308,11021,11022],{},[1311,11023,11024,11026],{},[1314,11025,1343],{},[1562,11027,1792],{},[1319,11029,10422],{"encoding":1321}," (čitatel) a ",[1296,11032,11034],{"className":11033},[1299],[1301,11035,11036],{"xmlns":1303},[1305,11037,11038,11046],{},[1308,11039,11040],{},[1311,11041,11042,11044],{},[1314,11043,1343],{},[1562,11045,1586],{},[1319,11047,10440],{"encoding":1321}," (jmenovatel) nejsou zaměnitelné — ",[3468,11050,11051],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3468,11054,11055],{},"qf(p, df2, df1)",[1143,11057,6592],{"id":6591},[1102,11059,11060,11065,11070,11075,11081,11086,11092],{},[1105,11061,11062],{},[1242,11063,1717],{"className":11064,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,11066,11067],{},[1242,11068,886],{"className":11069,"dataFsResolvedFilePath":1255,"href":1256},[1245],[1105,11071,11072],{},[1242,11073,141],{"className":11074,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1105,11076,11077],{},[1242,11078,11080],{"className":11079,"dataFsResolvedFilePath":1273,"href":1274},[1245],"regresni-a-korelacni-analyza",[1105,11082,11083],{},[1242,11084,716],{"className":11085,"dataFsResolvedFilePath":1282,"href":1283},[1245],[1105,11087,11088],{},[1242,11089,11091],{"className":11090,"dataFsResolvedFilePath":1291,"href":1292},[1245],"regulacni-diagramy-a-indexy-zpusobilosti",[1105,11093,11094],{},[1242,11095,6630],{"className":11096,"dataFsResolvedFilePath":1447,"href":1448},[1245],[1143,11098,6633],{"id":934},[1148,11100,6636,11101,6641],{},[6638,11102,6640],{},[6643,11104,11105],{},"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":1452,"searchDepth":27,"depth":27,"links":11107},[11108,11109,11110,11111,11112,11113,11114,11115,11116,11117],{"id":6961,"depth":27,"text":6962},{"id":7268,"depth":27,"text":7269},{"id":7954,"depth":27,"text":7955},{"id":8063,"depth":27,"text":8064},{"id":8498,"depth":27,"text":6870},{"id":9500,"depth":27,"text":9501},{"id":10090,"depth":27,"text":10091},{"id":6403,"depth":27,"text":6404},{"id":6591,"depth":27,"text":6592},{"id":934,"depth":27,"text":6633},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":1248,"description":1452},[11122,11123,11124],"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":11129,"title":1257,"body":11130,"course":23,"courses":1459,"created":1460,"description":1452,"extension":1461,"meta":15881,"navigation":1464,"path":15882,"seo":15883,"sources":15884,"stem":15891,"tags":15892,"type":6664,"updated":1460,"__hash__":15893},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1095,"value":11131,"toc":15872},[11132,11135,11229,11233,11243,11369,11376,11387,11391,11434,11439,11541,11551,11556,11695,11771,11775,11876,11957,11964,12035,12054,12056,12272,12278,12288,12295,12298,12352,12358,12368,12381,12527,12530,12543,12862,12868,12871,12875,12954,12988,13017,13019,13097,13103,13164,13171,13184,13261,13377,13427,13440,13595,13601,13628,13632,13657,13660,13873,13941,14042,14049,14062,14565,14571,14603,14863,15016,15127,15156,15162,15169,15175,15188,15618,15624,15627,15629,15824,15826,15863,15865,15869],[1098,11133,1257],{"id":11134},"popisná-statistika-a-datové-soubory",[1514,11136,11138,11144],{"className":11137,"dataCallout":1519},[1517,1518],[1148,11139,11141,1531],{"className":11140},[1523],[1296,11142],{"className":11143,"ariaHidden":1530},[1527,1528,1529],[1102,11145,11146,11149,11152,11179,11226],{},[1105,11147,11148],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1105,11150,11151],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1105,11153,11154,11155,1395],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1296,11156,11158],{"className":11157},[1299],[1301,11159,11160],{"xmlns":1303},[1305,11161,11162,11176],{},[1308,11163,11164,11170,11172,11174],{},[1311,11165,11166,11168],{},[1314,11167,1225],{},[1314,11169,1683],{},[1685,11171,1873],{"stretchy":1872},[1314,11173,6716],{},[1685,11175,1884],{"stretchy":1872},[1319,11177,11178],{"encoding":1321},"F_n(x)",[1105,11180,11181,11182,11225],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1296,11183,11185],{"className":11184},[1299],[1301,11186,11187],{"xmlns":1303},[1305,11188,11189,11222],{},[1308,11190,11191,11198,11200,11206,11208,11214,11216],{},[1311,11192,11193,11196],{},[1314,11194,11195],{},"I",[1314,11197,1881],{},[1685,11199,1795],{"separator":1530},[1311,11201,11202,11204],{},[1314,11203,8920],{},[1314,11205,1881],{},[1685,11207,1795],{"separator":1530},[1311,11209,11210,11212],{},[1314,11211,6767],{},[1314,11213,1881],{},[1685,11215,1795],{"separator":1530},[1311,11217,11218,11220],{},[1314,11219,1148],{},[1314,11221,1881],{},[1319,11223,11224],{"encoding":1321},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1105,11227,11228],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1143,11230,11232],{"id":11231},"základní-pojmy","Základní pojmy",[1148,11234,11235,11238,11239,11242],{},[1242,11236,1717],{"className":11237,"dataFsResolvedFilePath":1715,"href":1716},[1245]," pracuje s ",[1108,11240,11241],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1102,11244,11245,11251,11275,11281,11356],{},[1105,11246,11247,11250],{},[1108,11248,11249],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1105,11252,11253,11256,11257],{},[1108,11254,11255],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1102,11258,11259,11270],{},[1105,11260,11261,11263,11264,11266,11267,11269],{},[1108,11262,1733],{}," (vyjádřitelné číslem) — dále ",[1108,11265,6689],{}," (spočetně mnoho hodnot) nebo ",[1108,11268,6693],{}," (libovolná hodnota v intervalu);",[1105,11271,11272,11274],{},[1108,11273,1726],{}," (vyjádřitelné slovně).",[1105,11276,11277,11280],{},[1108,11278,11279],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1105,11282,11283,11286,11287,1395],{},[1108,11284,11285],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1296,11288,11290],{"className":11289},[1299],[1301,11291,11292],{"xmlns":1303},[1305,11293,11294,11353],{},[1308,11295,11296,11298,11300,11302,11305,11307,11310,11313,11315,11318,11320,11322,11325,11327,11330,11332,11334,11336,11338,11340,11342,11344,11346,11348,11351],{},[1685,11297,1873],{"stretchy":1872},[1562,11299,3548],{},[2907,11301,2909],{},[1562,11303,11304],{},"500",[1685,11306,1795],{"separator":1530},[2907,11308,11309],{}," ",[1562,11311,11312],{},"38",[2907,11314,2909],{},[1562,11316,11317],{},"000",[1685,11319,1795],{"separator":1530},[2907,11321,11309],{},[1562,11323,11324],{},"37",[2907,11326,2909],{},[1562,11328,11329],{},"800",[1685,11331,1795],{"separator":1530},[2907,11333,11309],{},[1562,11335,9351],{},[2907,11337,2909],{},[1562,11339,11317],{},[1685,11341,1795],{"separator":1530},[2907,11343,11309],{},[1562,11345,3556],{},[2907,11347,2909],{},[1562,11349,11350],{},"200",[1685,11352,1884],{"stretchy":1872},[1319,11354,11355],{"encoding":1321},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1105,11357,11358,11359,1323,11362,1370,11365,11368],{},"Podle počtu sledovaných znaků rozlišujeme ",[1108,11360,11361],{},"jednorozměrné",[1108,11363,11364],{},"dvourozměrné",[1108,11366,11367],{},"vícerozměrné"," datové soubory.",[1148,11370,11371],{},[4382,11372],{"alt":11373,"className":11374,"src":11375},"mask-ilu-zakladni-soubor-vyber",[1245,4386],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1148,11377,11378,11379,11382,11383,11386],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1108,11380,11381],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1108,11384,11385],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1143,11388,11390],{"id":11389},"empirické-charakteristiky","Empirické charakteristiky",[1148,11392,11393,11394,11397,11398,11401,11402,11415,11416,11419,11420,11433],{},"Zpracováním datového souboru získáme ",[1108,11395,11396],{},"empirické charakteristiky"," a odhad ",[1108,11399,11400],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1296,11403,11405],{"className":11404},[1299],[1301,11406,11407],{"xmlns":1303},[1305,11408,11409,11413],{},[1308,11410,11411],{},[1314,11412,6728],{},[1319,11414,6728],{"encoding":1321},". Jde o ",[1108,11417,11418],{},"bodové odhady"," charakteristik ",[1296,11421,11423],{"className":11422},[1299],[1301,11424,11425],{"xmlns":1303},[1305,11426,11427,11431],{},[1308,11428,11429],{},[1314,11430,6728],{},[1319,11432,6728],{"encoding":1321},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1148,11435,11436],{},[1108,11437,11438],{},"Míry polohy",[1296,11440,11442],{"className":11441},[1299],[1301,11443,11444],{"xmlns":1303,"display":1962},[1305,11445,11446,11538],{},[1308,11447,11448,11455,11457,11463,11477,11483,11485],{},[2722,11449,11450,11452],{"accent":1530},[1314,11451,6716],{},[1685,11453,11454],{},"ˉ",[1685,11456,1980],{},[2738,11458,11459,11461],{},[1562,11460,1792],{},[1314,11462,1683],{},[1982,11464,11465,11467,11475],{},[1685,11466,1986],{},[1308,11468,11469,11471,11473],{},[1314,11470,1876],{},[1685,11472,1980],{},[1562,11474,1792],{},[1314,11476,1683],{},[1311,11478,11479,11481],{},[1314,11480,6716],{},[1314,11482,1876],{},[2010,11484],{"width":2012},[1308,11486,11487,11490,11497,11500,11507,11510,11516,11519,11527,11529,11535],{},[2907,11488,11489],{},"(v",[2722,11491,11492,11494],{"accent":1530},[2907,11493,7126],{},[1685,11495,11496],{},"ˊ",[2907,11498,11499],{},"b",[2722,11501,11502,11504],{"accent":1530},[2907,11503,8587],{},[1685,11505,11506],{},"ˇ",[2907,11508,11509],{},"rov",[2722,11511,11512,11514],{"accent":1530},[2907,11513,7126],{},[1685,11515,11496],{},[2907,11517,11518],{}," pr",[2722,11520,11521,11524],{"accent":1530},[2907,11522,11523],{},"u",[1685,11525,11526],{},"˚",[2907,11528,1366],{},[2722,11530,11531,11533],{"accent":1530},[2907,11532,8587],{},[1685,11534,11506],{},[2907,11536,11537],{},"r)",[1319,11539,11540],{"encoding":1321},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1148,11542,11543,11544,1370,11547,11550],{},"Dalšími mírami polohy jsou ",[1108,11545,11546],{},"medián",[1108,11548,11549],{},"modus"," (nejčetnější hodnota výběru).",[1148,11552,11553],{},[1108,11554,11555],{},"Míry variability",[1296,11557,11559],{"className":11558},[1299],[1301,11560,11561],{"xmlns":1303,"display":1962},[1305,11562,11563,11692],{},[1308,11564,11565,11571,11573,11585,11627,11629,11631,11633,11635,11643,11645],{},[1579,11566,11567,11569],{},[1314,11568,1852],{},[1562,11570,1586],{},[1685,11572,1980],{},[2738,11574,11575,11577],{},[1562,11576,1792],{},[1308,11578,11579,11581,11583],{},[1314,11580,1683],{},[1685,11582,3062],{},[1562,11584,1792],{},[1308,11586,11587,11589,11603,11611,11613,11615,11625],{},[1685,11588,1873],{"fence":1530},[1982,11590,11591,11593,11601],{},[1685,11592,1986],{},[1308,11594,11595,11597,11599],{},[1314,11596,1876],{},[1685,11598,1980],{},[1562,11600,1792],{},[1314,11602,1683],{},[3351,11604,11605,11607,11609],{},[1314,11606,6716],{},[1314,11608,1876],{},[1562,11610,1586],{},[1685,11612,3062],{},[1314,11614,1683],{},[1579,11616,11617,11623],{},[2722,11618,11619,11621],{"accent":1530},[1314,11620,6716],{},[1685,11622,11454],{},[1562,11624,1586],{},[1685,11626,1884],{"fence":1530},[1685,11628,1795],{"separator":1530},[2010,11630],{"width":2012},[1314,11632,1852],{},[1685,11634,1980],{},[4452,11636,11637],{},[1579,11638,11639,11641],{},[1314,11640,1852],{},[1562,11642,1586],{},[2010,11644],{"width":2012},[1308,11646,11647,11649,11655,11657,11663,11665,11671,11674,11680,11683,11689],{},[2907,11648,11489],{},[2722,11650,11651,11653],{"accent":1530},[2907,11652,7126],{},[1685,11654,11496],{},[2907,11656,11499],{},[2722,11658,11659,11661],{"accent":1530},[2907,11660,8587],{},[1685,11662,11506],{},[2907,11664,11509],{},[2722,11666,11667,11669],{"accent":1530},[2907,11668,7126],{},[1685,11670,11496],{},[2907,11672,11673],{}," rozptyl, sm",[2722,11675,11676,11678],{"accent":1530},[2907,11677,8587],{},[1685,11679,11506],{},[2907,11681,11682],{},"rodatn",[2722,11684,11685,11687],{"accent":1530},[2907,11686,1242],{},[1685,11688,11496],{},[2907,11690,11691],{}," odchylka)",[1319,11693,11694],{"encoding":1321},"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)}",[1296,11696,11698],{"className":11697},[1299],[1301,11699,11700],{"xmlns":1303,"display":1962},[1305,11701,11702,11768],{},[1308,11703,11704,11706,11708,11717,11719,11727,11729],{},[1314,11705,10218],{},[1685,11707,1980],{},[1311,11709,11710,11712,11715],{},[1314,11711,6716],{},[1314,11713,11714],{},"max",[1685,11716,4489],{},[1685,11718,3062],{},[1311,11720,11721,11723,11725],{},[1314,11722,6716],{},[1314,11724,4486],{},[1685,11726,4489],{},[2010,11728],{"width":2012},[1308,11730,11731,11734,11740,11742,11749,11752,11758,11760,11766],{},[2907,11732,11733],{},"(varia",[2722,11735,11736,11738],{"accent":1530},[2907,11737,3718],{},[1685,11739,11506],{},[2907,11741,1683],{},[2722,11743,11744,11747],{"accent":1530},[2907,11745,11746],{},"ı",[1685,11748,11496],{},[2907,11750,11751],{}," rozp",[2722,11753,11754,11756],{"accent":1530},[2907,11755,8587],{},[1685,11757,11506],{},[2907,11759,7140],{},[2722,11761,11762,11764],{"accent":1530},[2907,11763,11746],{},[1685,11765,11496],{},[2907,11767,1884],{},[1319,11769,11770],{"encoding":1321},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1148,11772,11773],{},[1108,11774,8298],{},[1148,11776,11777,11778,11801,11802,11824,11825,11846,11847,11875],{},"Kvantil ",[1296,11779,11781],{"className":11780},[1299],[1301,11782,11783],{"xmlns":1303},[1305,11784,11785,11798],{},[1308,11786,11787],{},[1311,11788,11789,11796],{},[2722,11790,11791,11793],{"accent":1530},[1314,11792,6716],{},[1685,11794,11795],{},"~",[1314,11797,1148],{},[1319,11799,11800],{"encoding":1321},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1296,11803,11805],{"className":11804},[1299],[1301,11806,11807],{"xmlns":1303},[1305,11808,11809,11821],{},[1308,11810,11811,11814,11816,11818],{},[1562,11812,11813],{},"100",[1314,11815,1148],{},[2907,11817,2909],{},[1314,11819,11820],{"mathvariant":2119},"%",[1319,11822,11823],{"encoding":1321},"100p\\,\\%"," hodnot je menších nebo rovných ",[1296,11826,11828],{"className":11827},[1299],[1301,11829,11830],{"xmlns":1303},[1305,11831,11832,11844],{},[1308,11833,11834],{},[1311,11835,11836,11842],{},[2722,11837,11838,11840],{"accent":1530},[1314,11839,6716],{},[1685,11841,11795],{},[1314,11843,1148],{},[1319,11845,11800],{"encoding":1321},", zbylých ",[1296,11848,11850],{"className":11849},[1299],[1301,11851,11852],{"xmlns":1303},[1305,11853,11854,11872],{},[1308,11855,11856,11858,11860,11862,11864,11866,11868,11870],{},[1562,11857,11813],{},[1685,11859,1873],{"stretchy":1872},[1562,11861,1792],{},[1685,11863,3062],{},[1314,11865,1148],{},[1685,11867,1884],{"stretchy":1872},[2907,11869,2909],{},[1314,11871,11820],{"mathvariant":2119},[1319,11873,11874],{"encoding":1321},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1102,11877,11878,11905],{},[1105,11879,11880,1651,11882,11904],{},[1108,11881,11546],{},[1296,11883,11885],{"className":11884},[1299],[1301,11886,11887],{"xmlns":1303},[1305,11888,11889,11901],{},[1308,11890,11891],{},[1311,11892,11893,11899],{},[2722,11894,11895,11897],{"accent":1530},[1314,11896,6716],{},[1685,11898,11795],{},[1562,11900,8452],{},[1319,11902,11903],{"encoding":1321},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1105,11906,11907,1651,11910,1370,11932,1651,11935,1395],{},[1108,11908,11909],{},"dolní kvartil",[1296,11911,11913],{"className":11912},[1299],[1301,11914,11915],{"xmlns":1303},[1305,11916,11917,11929],{},[1308,11918,11919],{},[1311,11920,11921,11927],{},[2722,11922,11923,11925],{"accent":1530},[1314,11924,6716],{},[1685,11926,11795],{},[1562,11928,8472],{},[1319,11930,11931],{"encoding":1321},"\\tilde{x}_{0{,}25}",[1108,11933,11934],{},"horní kvartil",[1296,11936,11938],{"className":11937},[1299],[1301,11939,11940],{"xmlns":1303},[1305,11941,11942,11954],{},[1308,11943,11944],{},[1311,11945,11946,11952],{},[2722,11947,11948,11950],{"accent":1530},[1314,11949,6716],{},[1685,11951,11795],{},[1562,11953,8492],{},[1319,11955,11956],{"encoding":1321},"\\tilde{x}_{0{,}75}",[1148,11958,11959,11960,11963],{},"Datový soubor se do R zadává buď přímo (",[3468,11961,11962],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3692,11965,11967],{"className":3694,"code":11966,"language":71,"meta":1452,"style":1452},"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",[3468,11968,11969,12030],{"__ignoreMap":1452},[1296,11970,11971,11973,11975,11977,11979,11982,11984,11987,11989,11992,11994,11997,11999,12001,12003,12005,12007,12010,12012,12015,12017,12019,12021,12023,12026],{"class":3700,"line":10},[1296,11972,6716],{"class":3703},[1296,11974,3708],{"class":3707},[1296,11976,3834],{"class":3711},[1296,11978,1873],{"class":3715},[1296,11980,11981],{"class":3723},"4.1",[1296,11983,1795],{"class":3707},[1296,11985,11986],{"class":3723}," 4.0",[1296,11988,1795],{"class":3707},[1296,11990,11991],{"class":3723}," 3.8",[1296,11993,1795],{"class":3707},[1296,11995,11996],{"class":3723}," 3.9",[1296,11998,1795],{"class":3707},[1296,12000,11991],{"class":3723},[1296,12002,1795],{"class":3707},[1296,12004,11991],{"class":3723},[1296,12006,1795],{"class":3707},[1296,12008,12009],{"class":3723}," 3.5",[1296,12011,1795],{"class":3707},[1296,12013,12014],{"class":3723}," 3.7",[1296,12016,1795],{"class":3707},[1296,12018,11986],{"class":3723},[1296,12020,1795],{"class":3707},[1296,12022,11986],{"class":3723},[1296,12024,12025],{"class":3715},")   ",[1296,12027,12029],{"class":12028},"sCsY4","# přímé zadání hodnot\n",[1296,12031,12032],{"class":3700,"line":27},[1296,12033,12034],{"class":12028},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1148,12036,12037,12038,12041,12042,12045,12046,12049,12050,12053],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3468,12039,12040],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3468,12043,12044],{},"read.table()"," vrací datovou tabulku (",[3468,12047,12048],{},"data.frame","), proto ",[3468,12051,12052],{},"[, 1]"," vybere její první sloupec jako vektor.",[1148,12055,9049],{},[3692,12057,12059],{"className":3694,"code":12058,"language":71,"meta":1452,"style":1452},"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",[3468,12060,12061,12118,12129,12140,12151,12162,12200,12226,12249],{"__ignoreMap":1452},[1296,12062,12063,12065,12067,12069,12071,12074,12076,12079,12081,12084,12086,12089,12091,12093,12095,12098,12100,12102,12104,12107,12109,12112,12114,12116],{"class":3700,"line":10},[1296,12064,6716],{"class":3703},[1296,12066,3708],{"class":3707},[1296,12068,3834],{"class":3711},[1296,12070,1873],{"class":3715},[1296,12072,12073],{"class":3723},"11.1",[1296,12075,1795],{"class":3707},[1296,12077,12078],{"class":3723}," 12.7",[1296,12080,1795],{"class":3707},[1296,12082,12083],{"class":3723}," 10.8",[1296,12085,1795],{"class":3707},[1296,12087,12088],{"class":3723}," 13.2",[1296,12090,1795],{"class":3707},[1296,12092,12078],{"class":3723},[1296,12094,1795],{"class":3707},[1296,12096,12097],{"class":3723}," 13.4",[1296,12099,1795],{"class":3707},[1296,12101,12078],{"class":3723},[1296,12103,1795],{"class":3707},[1296,12105,12106],{"class":3723}," 14.4",[1296,12108,1795],{"class":3707},[1296,12110,12111],{"class":3723}," 14.7",[1296,12113,1795],{"class":3707},[1296,12115,12106],{"class":3723},[1296,12117,3900],{"class":3715},[1296,12119,12120,12123,12125,12127],{"class":3700,"line":27},[1296,12121,12122],{"class":3711},"length",[1296,12124,1873],{"class":3715},[1296,12126,6716],{"class":3703},[1296,12128,3900],{"class":3715},[1296,12130,12131,12134,12136,12138],{"class":3700,"line":148},[1296,12132,12133],{"class":3711},"mean",[1296,12135,1873],{"class":3715},[1296,12137,6716],{"class":3703},[1296,12139,3900],{"class":3715},[1296,12141,12142,12145,12147,12149],{"class":3700,"line":111},[1296,12143,12144],{"class":3711},"var",[1296,12146,1873],{"class":3715},[1296,12148,6716],{"class":3703},[1296,12150,3900],{"class":3715},[1296,12152,12153,12156,12158,12160],{"class":3700,"line":96},[1296,12154,12155],{"class":3711},"sd",[1296,12157,1873],{"class":3715},[1296,12159,6716],{"class":3703},[1296,12161,3900],{"class":3715},[1296,12163,12164,12166,12168,12170,12173,12175,12177,12179,12181,12183,12185,12187,12189,12191,12194,12196,12198],{"class":3700,"line":89},[1296,12165,4486],{"class":3711},[1296,12167,1873],{"class":3715},[1296,12169,6716],{"class":3703},[1296,12171,12172],{"class":3715},"); ",[1296,12174,11714],{"class":3711},[1296,12176,1873],{"class":3715},[1296,12178,6716],{"class":3703},[1296,12180,12172],{"class":3715},[1296,12182,11714],{"class":3711},[1296,12184,1873],{"class":3715},[1296,12186,6716],{"class":3703},[1296,12188,4599],{"class":3715},[1296,12190,4635],{"class":3707},[1296,12192,12193],{"class":3711}," min",[1296,12195,1873],{"class":3715},[1296,12197,6716],{"class":3703},[1296,12199,3900],{"class":3715},[1296,12201,12202,12205,12207,12209,12211,12214,12216,12219,12221,12224],{"class":3700,"line":82},[1296,12203,12204],{"class":3711},"quantile",[1296,12206,1873],{"class":3715},[1296,12208,6716],{"class":3703},[1296,12210,1795],{"class":3707},[1296,12212,12213],{"class":3723}," 0.5",[1296,12215,1795],{"class":3707},[1296,12217,12218],{"class":3703}," type",[1296,12220,3796],{"class":3707},[1296,12222,12223],{"class":3723}," 6",[1296,12225,3900],{"class":3715},[1296,12227,12228,12230,12232,12234,12236,12239,12241,12243,12245,12247],{"class":3700,"line":75},[1296,12229,12204],{"class":3711},[1296,12231,1873],{"class":3715},[1296,12233,6716],{"class":3703},[1296,12235,1795],{"class":3707},[1296,12237,12238],{"class":3723}," 0.25",[1296,12240,1795],{"class":3707},[1296,12242,12218],{"class":3703},[1296,12244,3796],{"class":3707},[1296,12246,12223],{"class":3723},[1296,12248,3900],{"class":3715},[1296,12250,12251,12253,12255,12257,12259,12262,12264,12266,12268,12270],{"class":3700,"line":3890},[1296,12252,12204],{"class":3711},[1296,12254,1873],{"class":3715},[1296,12256,6716],{"class":3703},[1296,12258,1795],{"class":3707},[1296,12260,12261],{"class":3723}," 0.75",[1296,12263,1795],{"class":3707},[1296,12265,12218],{"class":3703},[1296,12267,3796],{"class":3707},[1296,12269,12223],{"class":3723},[1296,12271,3900],{"class":3715},[3692,12273,12276],{"className":12274,"code":12275,"language":3922,"meta":1452},[3920],"[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",[3468,12277,12275],{"__ignoreMap":1452},[1148,12279,12280,12283,12284,12287],{},[3468,12281,12282],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3468,12285,12286],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1148,12289,12290],{},[4382,12291],{"alt":12292,"className":12293,"src":12294},"mask-ps-kvantily",[1245,4386],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1148,12296,12297],{},"Seřazení souboru a krabicový graf:",[3692,12299,12301],{"className":3694,"code":12300,"language":71,"meta":1452,"style":1452},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3468,12302,12303,12318,12341],{"__ignoreMap":1452},[1296,12304,12305,12308,12310,12312,12315],{"class":3700,"line":10},[1296,12306,12307],{"class":3711},"sort",[1296,12309,1873],{"class":3715},[1296,12311,6716],{"class":3703},[1296,12313,12314],{"class":3715},")                     ",[1296,12316,12317],{"class":12028},"# vzestupně\n",[1296,12319,12320,12322,12324,12326,12328,12331,12333,12335,12338],{"class":3700,"line":27},[1296,12321,12307],{"class":3711},[1296,12323,1873],{"class":3715},[1296,12325,6716],{"class":3703},[1296,12327,1795],{"class":3707},[1296,12329,12330],{"class":3703}," decreasing",[1296,12332,3796],{"class":3707},[1296,12334,3809],{"class":3723},[1296,12336,12337],{"class":3715},")  ",[1296,12339,12340],{"class":12028},"# sestupně\n",[1296,12342,12343,12346,12348,12350],{"class":3700,"line":148},[1296,12344,12345],{"class":3711},"boxplot",[1296,12347,1873],{"class":3715},[1296,12349,6716],{"class":3703},[1296,12351,3900],{"class":3715},[3692,12353,12356],{"className":12354,"code":12355,"language":3922,"meta":1452},[3920]," [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",[3468,12357,12355],{"__ignoreMap":1452},[1148,12359,12360,12363,12364,12367],{},[3468,12361,12362],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3468,12365,12366],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1514,12369,12371,12378],{"className":12370,"dataCallout":3475},[1517,3474],[1148,12372,12374,12377],{"className":12373},[1523],[1296,12375],{"className":12376,"ariaHidden":1530},[1527,3482,1529],"Příklad: Empirické charakteristiky",[1148,12379,12380],{},"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.",[1148,12382,12383,12384,1323,12407,1323,12430,1323,12449,12468,12469,8456,12496,12511,12512,1395],{},"Výstup R kódu výše dává ",[1296,12385,12387],{"className":12386},[1299],[1301,12388,12389],{"xmlns":1303},[1305,12390,12391,12404],{},[1308,12392,12393,12399,12401],{},[2722,12394,12395,12397],{"accent":1530},[1314,12396,6716],{},[1685,12398,11454],{},[1685,12400,1980],{},[1562,12402,12403],{},"13,01",[1319,12405,12406],{"encoding":1321},"\\bar{x}=13{,}01",[1296,12408,12410],{"className":12409},[1299],[1301,12411,12412],{"xmlns":1303},[1305,12413,12414,12427],{},[1308,12415,12416,12422,12424],{},[1579,12417,12418,12420],{},[1314,12419,1852],{},[1562,12421,1586],{},[1685,12423,1980],{},[1562,12425,12426],{},"1,75",[1319,12428,12429],{"encoding":1321},"s^2=1{,}75",[1296,12431,12433],{"className":12432},[1299],[1301,12434,12435],{"xmlns":1303},[1305,12436,12437,12446],{},[1308,12438,12439,12441,12443],{},[1314,12440,1852],{},[1685,12442,1980],{},[1562,12444,12445],{},"1,32",[1319,12447,12448],{"encoding":1321},"s=1{,}32",[1296,12450,12452],{"className":12451},[1299],[1301,12453,12454],{"xmlns":1303},[1305,12455,12456,12465],{},[1308,12457,12458,12460,12462],{},[1314,12459,10218],{},[1685,12461,1980],{},[1562,12463,12464],{},"3,9",[1319,12466,12467],{"encoding":1321},"R=3{,}9",", medián ",[1296,12470,12472],{"className":12471},[1299],[1301,12473,12474],{"xmlns":1303},[1305,12475,12476,12493],{},[1308,12477,12478,12488,12490],{},[1311,12479,12480,12486],{},[2722,12481,12482,12484],{"accent":1530},[1314,12483,6716],{},[1685,12485,11795],{},[1562,12487,8452],{},[1685,12489,1980],{},[1562,12491,12492],{},"12,95",[1319,12494,12495],{"encoding":1321},"\\tilde{x}_{0{,}5}=12{,}95",[1296,12497,12499],{"className":12498},[1299],[1301,12500,12501],{"xmlns":1303},[1305,12502,12503,12508],{},[1308,12504,12505],{},[1562,12506,12507],{},"12,3",[1319,12509,12510],{"encoding":1321},"12{,}3",", horní kvartil ",[1296,12513,12515],{"className":12514},[1299],[1301,12516,12517],{"xmlns":1303},[1305,12518,12519,12524],{},[1308,12520,12521],{},[1562,12522,12523],{},"14,4",[1319,12525,12526],{"encoding":1321},"14{,}4",[1148,12528,12529],{},"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.",[1514,12531,12533,12540],{"className":12532,"dataCallout":3475},[1517,3474],[1148,12534,12536,12539],{"className":12535},[1523],[1296,12537],{"className":12538,"ariaHidden":1530},[1527,3482,1529],"Příklad: Doba oprav televizorů",[1148,12541,12542],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3692,12544,12546],{"className":3694,"code":12545,"language":71,"meta":1452,"style":1452},"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",[3468,12547,12548,12608,12659,12706,12753,12801,12811,12821,12831,12851],{"__ignoreMap":1452},[1296,12549,12550,12553,12555,12557,12559,12561,12563,12566,12568,12571,12573,12576,12578,12581,12583,12586,12588,12591,12593,12596,12598,12601,12603,12606],{"class":3700,"line":10},[1296,12551,12552],{"class":3703},"x6",[1296,12554,3708],{"class":3707},[1296,12556,3834],{"class":3711},[1296,12558,1873],{"class":3715},[1296,12560,3573],{"class":3723},[1296,12562,1795],{"class":3707},[1296,12564,12565],{"class":3723}," 40.2",[1296,12567,1795],{"class":3707},[1296,12569,12570],{"class":3723}," 41.9",[1296,12572,1795],{"class":3707},[1296,12574,12575],{"class":3723}," 43.4",[1296,12577,1795],{"class":3707},[1296,12579,12580],{"class":3723}," 42.8",[1296,12582,1795],{"class":3707},[1296,12584,12585],{"class":3723}," 42.3",[1296,12587,1795],{"class":3707},[1296,12589,12590],{"class":3723}," 43.2",[1296,12592,1795],{"class":3707},[1296,12594,12595],{"class":3723}," 45",[1296,12597,1795],{"class":3707},[1296,12599,12600],{"class":3723}," 41.5",[1296,12602,1795],{"class":3707},[1296,12604,12605],{"class":3723}," 42.7",[1296,12607,3736],{"class":3707},[1296,12609,12610,12613,12615,12618,12620,12623,12625,12628,12630,12633,12635,12638,12640,12643,12645,12648,12650,12652,12654,12657],{"class":3700,"line":27},[1296,12611,12612],{"class":3723},"        43.9",[1296,12614,1795],{"class":3707},[1296,12616,12617],{"class":3723}," 40.1",[1296,12619,1795],{"class":3707},[1296,12621,12622],{"class":3723}," 43.3",[1296,12624,1795],{"class":3707},[1296,12626,12627],{"class":3723}," 41.1",[1296,12629,1795],{"class":3707},[1296,12631,12632],{"class":3723}," 42.5",[1296,12634,1795],{"class":3707},[1296,12636,12637],{"class":3723}," 42.4",[1296,12639,1795],{"class":3707},[1296,12641,12642],{"class":3723}," 41.4",[1296,12644,1795],{"class":3707},[1296,12646,12647],{"class":3723}," 40.8",[1296,12649,1795],{"class":3707},[1296,12651,9330],{"class":3723},[1296,12653,1795],{"class":3707},[1296,12655,12656],{"class":3723}," 44.7",[1296,12658,3736],{"class":3707},[1296,12660,12661,12664,12666,12668,12670,12672,12674,12677,12679,12682,12684,12687,12689,12691,12693,12696,12698,12700,12702,12704],{"class":3700,"line":148},[1296,12662,12663],{"class":3723},"        41.2",[1296,12665,1795],{"class":3707},[1296,12667,12570],{"class":3723},[1296,12669,1795],{"class":3707},[1296,12671,12637],{"class":3723},[1296,12673,1795],{"class":3707},[1296,12675,12676],{"class":3723}," 44.4",[1296,12678,1795],{"class":3707},[1296,12680,12681],{"class":3723}," 40.5",[1296,12683,1795],{"class":3707},[1296,12685,12686],{"class":3723}," 39.7",[1296,12688,1795],{"class":3707},[1296,12690,12627],{"class":3723},[1296,12692,1795],{"class":3707},[1296,12694,12695],{"class":3723}," 41",[1296,12697,1795],{"class":3707},[1296,12699,12570],{"class":3723},[1296,12701,1795],{"class":3707},[1296,12703,12647],{"class":3723},[1296,12705,3736],{"class":3707},[1296,12707,12708,12711,12713,12715,12717,12720,12722,12724,12726,12728,12730,12733,12735,12738,12740,12742,12744,12747,12749,12751],{"class":3700,"line":111},[1296,12709,12710],{"class":3723},"        43",[1296,12712,1795],{"class":3707},[1296,12714,12580],{"class":3723},[1296,12716,1795],{"class":3707},[1296,12718,12719],{"class":3723}," 42.9",[1296,12721,1795],{"class":3707},[1296,12723,12605],{"class":3723},[1296,12725,1795],{"class":3707},[1296,12727,12622],{"class":3723},[1296,12729,1795],{"class":3707},[1296,12731,12732],{"class":3723}," 42.2",[1296,12734,1795],{"class":3707},[1296,12736,12737],{"class":3723}," 39.2",[1296,12739,1795],{"class":3707},[1296,12741,12600],{"class":3723},[1296,12743,1795],{"class":3707},[1296,12745,12746],{"class":3723}," 41.6",[1296,12748,1795],{"class":3707},[1296,12750,12605],{"class":3723},[1296,12752,3736],{"class":3707},[1296,12754,12755,12758,12760,12762,12764,12767,12769,12771,12773,12776,12778,12781,12783,12786,12788,12790,12792,12795,12797,12799],{"class":3700,"line":96},[1296,12756,12757],{"class":3723},"        45",[1296,12759,1795],{"class":3707},[1296,12761,12585],{"class":3723},[1296,12763,1795],{"class":3707},[1296,12765,12766],{"class":3723}," 43.6",[1296,12768,1795],{"class":3707},[1296,12770,12590],{"class":3723},[1296,12772,1795],{"class":3707},[1296,12774,12775],{"class":3723}," 38.8",[1296,12777,1795],{"class":3707},[1296,12779,12780],{"class":3723}," 43",[1296,12782,1795],{"class":3707},[1296,12784,12785],{"class":3723}," 44.2",[1296,12787,1795],{"class":3707},[1296,12789,12780],{"class":3723},[1296,12791,1795],{"class":3707},[1296,12793,12794],{"class":3723}," 40",[1296,12796,1795],{"class":3707},[1296,12798,12676],{"class":3723},[1296,12800,3900],{"class":3715},[1296,12802,12803,12805,12807,12809],{"class":3700,"line":89},[1296,12804,12122],{"class":3711},[1296,12806,1873],{"class":3715},[1296,12808,12552],{"class":3703},[1296,12810,3900],{"class":3715},[1296,12812,12813,12815,12817,12819],{"class":3700,"line":82},[1296,12814,12133],{"class":3711},[1296,12816,1873],{"class":3715},[1296,12818,12552],{"class":3703},[1296,12820,3900],{"class":3715},[1296,12822,12823,12825,12827,12829],{"class":3700,"line":75},[1296,12824,12155],{"class":3711},[1296,12826,1873],{"class":3715},[1296,12828,12552],{"class":3703},[1296,12830,3900],{"class":3715},[1296,12832,12833,12835,12837,12839,12841,12843,12845,12847,12849],{"class":3700,"line":3890},[1296,12834,11714],{"class":3711},[1296,12836,1873],{"class":3715},[1296,12838,12552],{"class":3703},[1296,12840,4599],{"class":3715},[1296,12842,4635],{"class":3707},[1296,12844,12193],{"class":3711},[1296,12846,1873],{"class":3715},[1296,12848,12552],{"class":3703},[1296,12850,3900],{"class":3715},[1296,12852,12853,12856,12858,12860],{"class":3700,"line":72},[1296,12854,12855],{"class":3711},"median",[1296,12857,1873],{"class":3715},[1296,12859,12552],{"class":3703},[1296,12861,3900],{"class":3715},[3692,12863,12866],{"className":12864,"code":12865,"language":3922,"meta":1452},[3920],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3468,12867,12865],{"__ignoreMap":1452},[1148,12869,12870],{},"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.",[1143,12872,12874],{"id":12873},"empirická-distribuční-funkce","Empirická distribuční funkce",[1148,12876,12877,12878,12891,12892,1651,12895,12918,12919,12953],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1296,12879,12881],{"className":12880},[1299],[1301,12882,12883],{"xmlns":1303},[1305,12884,12885,12889],{},[1308,12886,12887],{},[1314,12888,6728],{},[1319,12890,6728],{"encoding":1321},", lze sestrojit ",[1108,12893,12894],{},"empirickou distribuční funkci",[1296,12896,12898],{"className":12897},[1299],[1301,12899,12900],{"xmlns":1303},[1305,12901,12902,12916],{},[1308,12903,12904,12910,12912,12914],{},[1311,12905,12906,12908],{},[1314,12907,1225],{},[1314,12909,1683],{},[1685,12911,1873],{"stretchy":1872},[1314,12913,6716],{},[1685,12915,1884],{"stretchy":1872},[1319,12917,11178],{"encoding":1321},". Pro datový soubor ",[1296,12920,12922],{"className":12921},[1299],[1301,12923,12924],{"xmlns":1303},[1305,12925,12926,12950],{},[1308,12927,12928,12930,12936,12938,12940,12942,12948],{},[1685,12929,1873],{"stretchy":1872},[1311,12931,12932,12934],{},[1314,12933,6716],{},[1562,12935,1792],{},[1685,12937,1795],{"separator":1530},[1685,12939,1798],{},[1685,12941,1795],{"separator":1530},[1311,12943,12944,12946],{},[1314,12945,6716],{},[1314,12947,1683],{},[1685,12949,1884],{"stretchy":1872},[1319,12951,12952],{"encoding":1321},"(x_1,\\dots,x_n)"," je",[1296,12955,12957],{"className":12956},[1299],[1301,12958,12959],{"xmlns":1303,"display":1962},[1305,12960,12961,12985],{},[1308,12962,12963,12969,12971,12973,12975,12977,12983],{},[1311,12964,12965,12967],{},[1314,12966,1225],{},[1314,12968,1683],{},[1685,12970,1873],{"stretchy":1872},[1314,12972,6716],{},[1685,12974,1884],{"stretchy":1872},[1685,12976,1980],{},[2738,12978,12979,12981],{},[1314,12980,1343],{},[1314,12982,1683],{},[1685,12984,1795],{"separator":1530},[1319,12986,12987],{"encoding":1321},"F_n(x) = \\frac{k}{n},",[1148,12989,4505,12990,13003,13004,1395],{},[1296,12991,12993],{"className":12992},[1299],[1301,12994,12995],{"xmlns":1303},[1305,12996,12997,13001],{},[1308,12998,12999],{},[1314,13000,1343],{},[1319,13002,1343],{"encoding":1321}," je počet prvků datového souboru menších nebo rovných číslu ",[1296,13005,13007],{"className":13006},[1299],[1301,13008,13009],{"xmlns":1303},[1305,13010,13011,13015],{},[1308,13012,13013],{},[1314,13014,6716],{},[1319,13016,6716],{"encoding":1321},[1148,13018,9049],{},[3692,13020,13022],{"className":3694,"code":13021,"language":71,"meta":1452,"style":1452},"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",[3468,13023,13024,13039,13054,13072,13086],{"__ignoreMap":1452},[1296,13025,13026,13028,13030,13033,13035,13037],{"class":3700,"line":10},[1296,13027,6767],{"class":3703},[1296,13029,3708],{"class":3707},[1296,13031,13032],{"class":3711}," ecdf",[1296,13034,1873],{"class":3715},[1296,13036,6716],{"class":3703},[1296,13038,3900],{"class":3715},[1296,13040,13041,13044,13046,13048,13051],{"class":3700,"line":27},[1296,13042,13043],{"class":3711},"knots",[1296,13045,1873],{"class":3715},[1296,13047,6767],{"class":3703},[1296,13049,13050],{"class":3715},")        ",[1296,13052,13053],{"class":12028},"# vzestupně seřazené různé hodnoty datového souboru\n",[1296,13055,13056,13058,13060,13062,13064,13066,13069],{"class":3700,"line":148},[1296,13057,6767],{"class":3711},[1296,13059,1873],{"class":3715},[1296,13061,13043],{"class":3711},[1296,13063,1873],{"class":3715},[1296,13065,6767],{"class":3703},[1296,13067,13068],{"class":3715},"))      ",[1296,13070,13071],{"class":12028},"# hodnoty Fn(x) v těchto bodech\n",[1296,13073,13074,13076,13078,13080,13083],{"class":3700,"line":111},[1296,13075,6767],{"class":3711},[1296,13077,1873],{"class":3715},[1296,13079,3543],{"class":3723},[1296,13081,13082],{"class":3715},")            ",[1296,13084,13085],{"class":12028},"# Fn v libovolném bodě\n",[1296,13087,13088,13091,13093,13095],{"class":3700,"line":96},[1296,13089,13090],{"class":3711},"plot",[1296,13092,1873],{"class":3715},[1296,13094,6767],{"class":3703},[1296,13096,3900],{"class":3715},[3692,13098,13101],{"className":13099,"code":13100,"language":3922,"meta":1452},[3920],"[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",[3468,13102,13100],{"__ignoreMap":1452},[1148,13104,13105,13108,13109,13127,13128,13131,13132,13145,13146,1395],{},[3468,13106,13107],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1296,13110,13112],{"className":13111},[1299],[1301,13113,13114],{"xmlns":1303},[1305,13115,13116,13124],{},[1308,13117,13118],{},[1311,13119,13120,13122],{},[1314,13121,1225],{},[1314,13123,1683],{},[1319,13125,13126],{"encoding":1321},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3468,13129,13130],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1296,13133,13135],{"className":13134},[1299],[1301,13136,13137],{"xmlns":1303},[1305,13138,13139,13143],{},[1308,13140,13141],{},[1314,13142,1343],{},[1319,13144,1343],{"encoding":1321},"-násobek ",[1296,13147,13149],{"className":13148},[1299],[1301,13150,13151],{"xmlns":1303},[1305,13152,13153,13161],{},[1308,13154,13155,13157,13159],{},[1562,13156,1792],{},[1314,13158,1502],{"mathvariant":2119},[1314,13160,1683],{},[1319,13162,13163],{"encoding":1321},"1\u002Fn",[1148,13165,13166],{},[4382,13167],{"alt":13168,"className":13169,"src":13170},"mask-ps-ecdf",[1245,4386],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1514,13172,13174,13181],{"className":13173,"dataCallout":3475},[1517,3474],[1148,13175,13177,13180],{"className":13176},[1523],[1296,13178],{"className":13179,"ariaHidden":1530},[1527,3482,1529],"Příklad: Empirická distribuční funkce",[1148,13182,13183],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1148,13185,13186,13187,1395],{},"Uspořádaný soubor je ",[1296,13188,13190],{"className":13189},[1299],[1301,13191,13192],{"xmlns":1303},[1305,13193,13194,13258],{},[1308,13195,13196,13199,13201,13203,13206,13208,13210,13213,13215,13217,13219,13221,13223,13225,13227,13229,13232,13234,13236,13239,13241,13243,13245,13247,13249,13251,13253,13255],{},[1562,13197,13198],{},"10,8",[1685,13200,6890],{"separator":1530},[2907,13202,11309],{},[1562,13204,13205],{},"11,1",[1685,13207,6890],{"separator":1530},[2907,13209,11309],{},[1562,13211,13212],{},"12,7",[1685,13214,6890],{"separator":1530},[2907,13216,11309],{},[1562,13218,13212],{},[1685,13220,6890],{"separator":1530},[2907,13222,11309],{},[1562,13224,13212],{},[1685,13226,6890],{"separator":1530},[2907,13228,11309],{},[1562,13230,13231],{},"13,2",[1685,13233,6890],{"separator":1530},[2907,13235,11309],{},[1562,13237,13238],{},"13,4",[1685,13240,6890],{"separator":1530},[2907,13242,11309],{},[1562,13244,12523],{},[1685,13246,6890],{"separator":1530},[2907,13248,11309],{},[1562,13250,12523],{},[1685,13252,6890],{"separator":1530},[2907,13254,11309],{},[1562,13256,13257],{},"14,7",[1319,13259,13260],{"encoding":1321},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1162,13262,13263,13296],{},[1165,13264,13265],{},[1168,13266,13267,13282,13284,13286,13288,13290,13292,13294],{},[1171,13268,13269],{},[1296,13270,13272],{"className":13271},[1299],[1301,13273,13274],{"xmlns":1303},[1305,13275,13276,13280],{},[1308,13277,13278],{},[1314,13279,6716],{},[1319,13281,6716],{"encoding":1321},[1171,13283,13198],{},[1171,13285,13205],{},[1171,13287,13212],{},[1171,13289,13231],{},[1171,13291,13238],{},[1171,13293,12523],{},[1171,13295,13257],{},[1178,13297,13298,13330],{},[1168,13299,13300,13315,13317,13319,13321,13323,13326,13328],{},[1183,13301,13302],{},[1296,13303,13305],{"className":13304},[1299],[1301,13306,13307],{"xmlns":1303},[1305,13308,13309,13313],{},[1308,13310,13311],{},[1314,13312,1343],{},[1319,13314,1343],{"encoding":1321},[1183,13316,1792],{},[1183,13318,1586],{},[1183,13320,9921],{},[1183,13322,3963],{},[1183,13324,13325],{},"7",[1183,13327,3593],{},[1183,13329,9028],{},[1168,13331,13332,13357,13360,13363,13365,13368,13371,13374],{},[1183,13333,13334],{},[1296,13335,13337],{"className":13336},[1299],[1301,13338,13339],{"xmlns":1303},[1305,13340,13341,13355],{},[1308,13342,13343,13349,13351,13353],{},[1311,13344,13345,13347],{},[1314,13346,1225],{},[1314,13348,1683],{},[1685,13350,1873],{"stretchy":1872},[1314,13352,6716],{},[1685,13354,1884],{"stretchy":1872},[1319,13356,11178],{"encoding":1321},[1183,13358,13359],{},"0,1",[1183,13361,13362],{},"0,2",[1183,13364,8452],{},[1183,13366,13367],{},"0,6",[1183,13369,13370],{},"0,7",[1183,13372,13373],{},"0,9",[1183,13375,13376],{},"1,0",[1148,13378,13379,13380,13402,13403,13426],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1296,13381,13383],{"className":13382},[1299],[1301,13384,13385],{"xmlns":1303},[1305,13386,13387,13399],{},[1308,13388,13389,13391,13393,13395,13397],{},[1562,13390,1792],{},[1314,13392,1502],{"mathvariant":2119},[1314,13394,1683],{},[1685,13396,1980],{},[1562,13398,13359],{},[1319,13400,13401],{"encoding":1321},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1296,13404,13406],{"className":13405},[1299],[1301,13407,13408],{"xmlns":1303},[1305,13409,13410,13423],{},[1308,13411,13412,13414,13416,13418,13420],{},[1562,13413,3590],{},[1314,13415,1502],{"mathvariant":2119},[1314,13417,1683],{},[1685,13419,1980],{},[1562,13421,13422],{},"0,3",[1319,13424,13425],{"encoding":1321},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1514,13428,13430,13437],{"className":13429,"dataCallout":3475},[1517,3474],[1148,13431,13433,13436],{"className":13432},[1523],[1296,13434],{"className":13435,"ariaHidden":1530},[1527,3482,1529],"Příklad: Odpad materiálu",[1148,13438,13439],{},"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.",[3692,13441,13443],{"className":3694,"code":13442,"language":71,"meta":1452,"style":1452},"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",[3468,13444,13445,13496,13506,13516,13526,13546,13556,13571,13581],{"__ignoreMap":1452},[1296,13446,13447,13450,13452,13454,13456,13458,13460,13462,13464,13466,13468,13470,13472,13474,13476,13478,13480,13482,13484,13486,13488,13490,13492,13494],{"class":3700,"line":10},[1296,13448,13449],{"class":3703},"x4",[1296,13451,3708],{"class":3707},[1296,13453,3834],{"class":3711},[1296,13455,1873],{"class":3715},[1296,13457,11981],{"class":3723},[1296,13459,1795],{"class":3707},[1296,13461,11986],{"class":3723},[1296,13463,1795],{"class":3707},[1296,13465,11991],{"class":3723},[1296,13467,1795],{"class":3707},[1296,13469,11996],{"class":3723},[1296,13471,1795],{"class":3707},[1296,13473,11991],{"class":3723},[1296,13475,1795],{"class":3707},[1296,13477,11991],{"class":3723},[1296,13479,1795],{"class":3707},[1296,13481,12009],{"class":3723},[1296,13483,1795],{"class":3707},[1296,13485,12014],{"class":3723},[1296,13487,1795],{"class":3707},[1296,13489,11986],{"class":3723},[1296,13491,1795],{"class":3707},[1296,13493,11986],{"class":3723},[1296,13495,3900],{"class":3715},[1296,13497,13498,13500,13502,13504],{"class":3700,"line":27},[1296,13499,12122],{"class":3711},[1296,13501,1873],{"class":3715},[1296,13503,13449],{"class":3703},[1296,13505,3900],{"class":3715},[1296,13507,13508,13510,13512,13514],{"class":3700,"line":148},[1296,13509,12133],{"class":3711},[1296,13511,1873],{"class":3715},[1296,13513,13449],{"class":3703},[1296,13515,3900],{"class":3715},[1296,13517,13518,13520,13522,13524],{"class":3700,"line":111},[1296,13519,12155],{"class":3711},[1296,13521,1873],{"class":3715},[1296,13523,13449],{"class":3703},[1296,13525,3900],{"class":3715},[1296,13527,13528,13530,13532,13534,13536,13538,13540,13542,13544],{"class":3700,"line":96},[1296,13529,11714],{"class":3711},[1296,13531,1873],{"class":3715},[1296,13533,13449],{"class":3703},[1296,13535,4599],{"class":3715},[1296,13537,4635],{"class":3707},[1296,13539,12193],{"class":3711},[1296,13541,1873],{"class":3715},[1296,13543,13449],{"class":3703},[1296,13545,3900],{"class":3715},[1296,13547,13548,13550,13552,13554],{"class":3700,"line":89},[1296,13549,12855],{"class":3711},[1296,13551,1873],{"class":3715},[1296,13553,13449],{"class":3703},[1296,13555,3900],{"class":3715},[1296,13557,13558,13561,13563,13565,13567,13569],{"class":3700,"line":82},[1296,13559,13560],{"class":3703},"f4",[1296,13562,3708],{"class":3707},[1296,13564,13032],{"class":3711},[1296,13566,1873],{"class":3715},[1296,13568,13449],{"class":3703},[1296,13570,3900],{"class":3715},[1296,13572,13573,13575,13577,13579],{"class":3700,"line":75},[1296,13574,13043],{"class":3711},[1296,13576,1873],{"class":3715},[1296,13578,13560],{"class":3703},[1296,13580,3900],{"class":3715},[1296,13582,13583,13585,13587,13589,13591,13593],{"class":3700,"line":3890},[1296,13584,13560],{"class":3711},[1296,13586,1873],{"class":3715},[1296,13588,13043],{"class":3711},[1296,13590,1873],{"class":3715},[1296,13592,13560],{"class":3703},[1296,13594,9488],{"class":3715},[3692,13596,13599],{"className":13597,"code":13598,"language":3922,"meta":1452},[3920],"[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",[3468,13600,13598],{"__ignoreMap":1452},[1148,13602,13603,13604,13627],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1296,13605,13607],{"className":13606},[1299],[1301,13608,13609],{"xmlns":1303},[1305,13610,13611,13625],{},[1308,13612,13613,13619,13621,13623],{},[1311,13614,13615,13617],{},[1314,13616,1225],{},[1314,13618,1683],{},[1685,13620,1873],{"stretchy":1872},[1314,13622,6716],{},[1685,13624,1884],{"stretchy":1872},[1319,13626,11178],{"encoding":1321},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1143,13629,13631],{"id":13630},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1148,13633,13634,13635,13638,13639,13652,13653,13656],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1108,13636,13637],{},"roztřídí",": variační rozpětí ",[1296,13640,13642],{"className":13641},[1299],[1301,13643,13644],{"xmlns":1303},[1305,13645,13646,13650],{},[1308,13647,13648],{},[1314,13649,10218],{},[1319,13651,10218],{"encoding":1321}," se rozdělí na určitý počet ",[1108,13654,13655],{},"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.",[1148,13658,13659],{},"Výsledkem je tabulka četností se sloupci:",[1102,13661,13662,13742,13763,13784],{},[1105,13663,13664,13682,13683,13696,13697,13741],{},[1296,13665,13667],{"className":13666},[1299],[1301,13668,13669],{"xmlns":1303},[1305,13670,13671,13679],{},[1308,13672,13673],{},[1311,13674,13675,13677],{},[1314,13676,11195],{},[1314,13678,1881],{},[1319,13680,13681],{"encoding":1321},"I_j"," — ",[1296,13684,13686],{"className":13685},[1299],[1301,13687,13688],{"xmlns":1303},[1305,13689,13690,13694],{},[1308,13691,13692],{},[1314,13693,1881],{},[1319,13695,1881],{"encoding":1321},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1296,13698,13700],{"className":13699},[1299],[1301,13701,13702],{"xmlns":1303},[1305,13703,13704,13738],{},[1308,13705,13706,13712,13714,13716,13722,13724,13736],{},[1311,13707,13708,13710],{},[1314,13709,11195],{},[1314,13711,1881],{},[1685,13713,1980],{},[1685,13715,8420],{"stretchy":1872},[1311,13717,13718,13720],{},[1314,13719,3718],{},[1314,13721,1881],{},[1685,13723,6890],{"separator":1530},[1311,13725,13726,13728],{},[1314,13727,3718],{},[1308,13729,13730,13732,13734],{},[1314,13731,1881],{},[1685,13733,5474],{},[1562,13735,1792],{},[1685,13737,1884],{"stretchy":1872},[1319,13739,13740],{"encoding":1321},"I_j = \\langle c_j; c_{j+1})","),",[1105,13743,13744,13762],{},[1296,13745,13747],{"className":13746},[1299],[1301,13748,13749],{"xmlns":1303},[1305,13750,13751,13759],{},[1308,13752,13753],{},[1311,13754,13755,13757],{},[1314,13756,8920],{},[1314,13758,1881],{},[1319,13760,13761],{"encoding":1321},"Z_j"," — střed (reprezentant) intervalu,",[1105,13764,13765,13783],{},[1296,13766,13768],{"className":13767},[1299],[1301,13769,13770],{"xmlns":1303},[1305,13771,13772,13780],{},[1308,13773,13774],{},[1311,13775,13776,13778],{},[1314,13777,6767],{},[1314,13779,1881],{},[1319,13781,13782],{"encoding":1321},"f_j"," — četnost, počet hodnot v intervalu,",[1105,13785,13786,13816,13817,1370,13845,1395],{},[1296,13787,13789],{"className":13788},[1299],[1301,13790,13791],{"xmlns":1303},[1305,13792,13793,13813],{},[1308,13794,13795,13801,13803,13809,13811],{},[1311,13796,13797,13799],{},[1314,13798,1148],{},[1314,13800,1881],{},[1685,13802,1980],{},[1311,13804,13805,13807],{},[1314,13806,6767],{},[1314,13808,1881],{},[1314,13810,1502],{"mathvariant":2119},[1314,13812,1683],{},[1319,13814,13815],{"encoding":1321},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1296,13818,13820],{"className":13819},[1299],[1301,13821,13822],{"xmlns":1303},[1305,13823,13824,13842],{},[1308,13825,13826,13832,13838,13840],{},[1311,13827,13828,13830],{},[1685,13829,1986],{},[1314,13831,1881],{},[1311,13833,13834,13836],{},[1314,13835,6767],{},[1314,13837,1881],{},[1685,13839,1980],{},[1314,13841,1683],{},[1319,13843,13844],{"encoding":1321},"\\sum_j f_j = n",[1296,13846,13848],{"className":13847},[1299],[1301,13849,13850],{"xmlns":1303},[1305,13851,13852,13870],{},[1308,13853,13854,13860,13866,13868],{},[1311,13855,13856,13858],{},[1685,13857,1986],{},[1314,13859,1881],{},[1311,13861,13862,13864],{},[1314,13863,1148],{},[1314,13865,1881],{},[1685,13867,1980],{},[1562,13869,1792],{},[1319,13871,13872],{"encoding":1321},"\\sum_j p_j = 1",[1148,13874,13875,13876,13879,13880,13883,13884,13887,13888,13891,13892,4604,13895,13912,13913,13916,13917,4604,13920,1810,13937,13940],{},"V R se třídění provádí příkazem ",[3468,13877,13878],{},"hist()"," — buď necháme R zvolit třídy samo (",[3468,13881,13882],{},"hist(x)","), nebo zadáme hranice přímo (",[3468,13885,13886],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3468,13889,13890],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3468,13893,13894],{},"y$counts",[1296,13896,13898],{"className":13897},[1299],[1301,13899,13900],{"xmlns":1303},[1305,13901,13902,13910],{},[1308,13903,13904],{},[1311,13905,13906,13908],{},[1314,13907,6767],{},[1314,13909,1881],{},[1319,13911,13782],{"encoding":1321},"), ",[3468,13914,13915],{},"y$breaks"," (hranice tříd), ",[3468,13918,13919],{},"y$mids",[1296,13921,13923],{"className":13922},[1299],[1301,13924,13925],{"xmlns":1303},[1305,13926,13927,13935],{},[1308,13928,13929],{},[1311,13930,13931,13933],{},[1314,13932,8920],{},[1314,13934,1881],{},[1319,13936,13761],{"encoding":1321},[3468,13938,13939],{},"y$density"," (relativní četnosti na škále hustoty).",[1148,13942,13943,13944,13961,13962,13964,13965,14001,14002,14005,14006,1395],{},"Interval ",[1296,13945,13947],{"className":13946},[1299],[1301,13948,13949],{"xmlns":1303},[1305,13950,13951,13959],{},[1308,13952,13953],{},[1311,13954,13955,13957],{},[1314,13956,11195],{},[1314,13958,1881],{},[1319,13960,13681],{"encoding":1321}," je ve výchozím nastavení ",[3468,13963,13878],{}," zleva otevřený a zprava uzavřený, ",[1296,13966,13968],{"className":13967},[1299],[1301,13969,13970],{"xmlns":1303},[1305,13971,13972,13998],{},[1308,13973,13974,13976,13982,13984,13996],{},[1685,13975,1873],{"stretchy":1872},[1311,13977,13978,13980],{},[1314,13979,3718],{},[1314,13981,1881],{},[1685,13983,6890],{"separator":1530},[1311,13985,13986,13988],{},[1314,13987,3718],{},[1308,13989,13990,13992,13994],{},[1314,13991,1881],{},[1685,13993,5474],{},[1562,13995,1792],{},[1685,13997,7439],{"stretchy":1872},[1319,13999,14000],{"encoding":1321},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3468,14003,14004],{},"right = FALSE"," třídy obrátí na ",[1296,14007,14009],{"className":14008},[1299],[1301,14010,14011],{"xmlns":1303},[1305,14012,14013,14039],{},[1308,14014,14015,14017,14023,14025,14037],{},[1685,14016,8420],{"stretchy":1872},[1311,14018,14019,14021],{},[1314,14020,3718],{},[1314,14022,1881],{},[1685,14024,6890],{"separator":1530},[1311,14026,14027,14029],{},[1314,14028,3718],{},[1308,14030,14031,14033,14035],{},[1314,14032,1881],{},[1685,14034,5474],{},[1562,14036,1792],{},[1685,14038,1884],{"stretchy":1872},[1319,14040,14041],{"encoding":1321},"\\langle c_j; c_{j+1})",[1148,14043,14044],{},[4382,14045],{"alt":14046,"className":14047,"src":14048},"mask-ps-histogram-trideni",[1245,4386],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1514,14050,14052,14059],{"className":14051,"dataCallout":3475},[1517,3474],[1148,14053,14055,14058],{"className":14054},[1523],[1296,14056],{"className":14057,"ariaHidden":1530},[1527,3482,1529],"Příklad: Třídění datového souboru",[1148,14060,14061],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3692,14063,14065],{"className":3694,"code":14064,"language":71,"meta":1452,"style":1452},"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",[3468,14066,14067,14124,14175,14225,14276,14326,14374,14414,14424,14444,14508,14517,14547],{"__ignoreMap":1452},[1296,14068,14069,14072,14074,14076,14078,14081,14083,14086,14088,14091,14093,14096,14098,14100,14102,14104,14106,14108,14110,14113,14115,14117,14119,14122],{"class":3700,"line":10},[1296,14070,14071],{"class":3703},"x9",[1296,14073,3708],{"class":3707},[1296,14075,3834],{"class":3711},[1296,14077,1873],{"class":3715},[1296,14079,14080],{"class":3723},"101",[1296,14082,1795],{"class":3707},[1296,14084,14085],{"class":3723}," 338",[1296,14087,1795],{"class":3707},[1296,14089,14090],{"class":3723}," 150",[1296,14092,1795],{"class":3707},[1296,14094,14095],{"class":3723}," 47",[1296,14097,1795],{"class":3707},[1296,14099,9472],{"class":3723},[1296,14101,1795],{"class":3707},[1296,14103,4179],{"class":3723},[1296,14105,1795],{"class":3707},[1296,14107,3733],{"class":3723},[1296,14109,1795],{"class":3707},[1296,14111,14112],{"class":3723}," 392",[1296,14114,1795],{"class":3707},[1296,14116,9989],{"class":3723},[1296,14118,1795],{"class":3707},[1296,14120,14121],{"class":3723}," 73",[1296,14123,3736],{"class":3707},[1296,14125,14126,14129,14131,14134,14136,14139,14141,14144,14146,14148,14150,14153,14155,14158,14160,14163,14165,14168,14170,14173],{"class":3700,"line":27},[1296,14127,14128],{"class":3723},"        367",[1296,14130,1795],{"class":3707},[1296,14132,14133],{"class":3723}," 54",[1296,14135,1795],{"class":3707},[1296,14137,14138],{"class":3723}," 114",[1296,14140,1795],{"class":3707},[1296,14142,14143],{"class":3723}," 213",[1296,14145,1795],{"class":3707},[1296,14147,3751],{"class":3723},[1296,14149,1795],{"class":3707},[1296,14151,14152],{"class":3723}," 341",[1296,14154,1795],{"class":3707},[1296,14156,14157],{"class":3723}," 313",[1296,14159,1795],{"class":3707},[1296,14161,14162],{"class":3723}," 112",[1296,14164,1795],{"class":3707},[1296,14166,14167],{"class":3723}," 343",[1296,14169,1795],{"class":3707},[1296,14171,14172],{"class":3723}," 151",[1296,14174,3736],{"class":3707},[1296,14176,14177,14180,14182,14185,14187,14190,14192,14195,14197,14200,14202,14204,14206,14209,14211,14213,14215,14218,14220,14223],{"class":3700,"line":148},[1296,14178,14179],{"class":3723},"        9",[1296,14181,1795],{"class":3707},[1296,14183,14184],{"class":3723}," 160",[1296,14186,1795],{"class":3707},[1296,14188,14189],{"class":3723}," 18",[1296,14191,1795],{"class":3707},[1296,14193,14194],{"class":3723}," 113",[1296,14196,1795],{"class":3707},[1296,14198,14199],{"class":3723}," 77",[1296,14201,1795],{"class":3707},[1296,14203,3751],{"class":3723},[1296,14205,1795],{"class":3707},[1296,14207,14208],{"class":3723}," 159",[1296,14210,1795],{"class":3707},[1296,14212,3733],{"class":3723},[1296,14214,1795],{"class":3707},[1296,14216,14217],{"class":3723}," 119",[1296,14219,1795],{"class":3707},[1296,14221,14222],{"class":3723}," 130",[1296,14224,3736],{"class":3707},[1296,14226,14227,14230,14232,14235,14237,14240,14242,14244,14246,14249,14251,14254,14256,14259,14261,14264,14266,14269,14271,14274],{"class":3700,"line":111},[1296,14228,14229],{"class":3723},"        140",[1296,14231,1795],{"class":3707},[1296,14233,14234],{"class":3723}," 161",[1296,14236,1795],{"class":3707},[1296,14238,14239],{"class":3723}," 379",[1296,14241,1795],{"class":3707},[1296,14243,14133],{"class":3723},[1296,14245,1795],{"class":3707},[1296,14247,14248],{"class":3723}," 373",[1296,14250,1795],{"class":3707},[1296,14252,14253],{"class":3723}," 168",[1296,14255,1795],{"class":3707},[1296,14257,14258],{"class":3723}," 365",[1296,14260,1795],{"class":3707},[1296,14262,14263],{"class":3723}," 110",[1296,14265,1795],{"class":3707},[1296,14267,14268],{"class":3723}," 145",[1296,14270,1795],{"class":3707},[1296,14272,14273],{"class":3723}," 88",[1296,14275,3736],{"class":3707},[1296,14277,14278,14281,14283,14286,14288,14291,14293,14296,14298,14301,14303,14305,14307,14310,14312,14314,14316,14319,14321,14324],{"class":3700,"line":96},[1296,14279,14280],{"class":3723},"        74",[1296,14282,1795],{"class":3707},[1296,14284,14285],{"class":3723}," 46",[1296,14287,1795],{"class":3707},[1296,14289,14290],{"class":3723}," 246",[1296,14292,1795],{"class":3707},[1296,14294,14295],{"class":3723}," 259",[1296,14297,1795],{"class":3707},[1296,14299,14300],{"class":3723}," 19",[1296,14302,1795],{"class":3707},[1296,14304,14217],{"class":3723},[1296,14306,1795],{"class":3707},[1296,14308,14309],{"class":3723}," 48",[1296,14311,1795],{"class":3707},[1296,14313,10850],{"class":3723},[1296,14315,1795],{"class":3707},[1296,14317,14318],{"class":3723}," 163",[1296,14320,1795],{"class":3707},[1296,14322,14323],{"class":3723}," 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91",[1296,14413,3900],{"class":3715},[1296,14415,14416,14418,14420,14422],{"class":3700,"line":75},[1296,14417,12122],{"class":3711},[1296,14419,1873],{"class":3715},[1296,14421,14071],{"class":3703},[1296,14423,3900],{"class":3715},[1296,14425,14426,14428,14430,14432,14434,14436,14438,14440,14442],{"class":3700,"line":3890},[1296,14427,11714],{"class":3711},[1296,14429,1873],{"class":3715},[1296,14431,14071],{"class":3703},[1296,14433,4599],{"class":3715},[1296,14435,4635],{"class":3707},[1296,14437,12193],{"class":3711},[1296,14439,1873],{"class":3715},[1296,14441,14071],{"class":3703},[1296,14443,3900],{"class":3715},[1296,14445,14446,14449,14451,14454,14456,14458,14460,14463,14465,14468,14470,14472,14474,14477,14479,14482,14484,14486,14488,14490,14493,14495,14497,14499,14502,14504,14506],{"class":3700,"line":72},[1296,14447,14448],{"class":3703},"y9",[1296,14450,3708],{"class":3707},[1296,14452,14453],{"class":3711}," hist",[1296,14455,1873],{"class":3715},[1296,14457,14071],{"class":3703},[1296,14459,1795],{"class":3707},[1296,14461,14462],{"class":3703}," br",[1296,14464,3796],{"class":3707},[1296,14466,14467],{"class":3711}," seq",[1296,14469,1873],{"class":3715},[1296,14471,1564],{"class":3723},[1296,14473,1795],{"class":3707},[1296,14475,14476],{"class":3723}," 550",[1296,14478,1795],{"class":3707},[1296,14480,14481],{"class":3703}," by",[1296,14483,3796],{"class":3707},[1296,14485,6241],{"class":3723},[1296,14487,1884],{"class":3715},[1296,14489,1795],{"class":3707},[1296,14491,14492],{"class":3703}," right",[1296,14494,3796],{"class":3707},[1296,14496,6334],{"class":3723},[1296,14498,1795],{"class":3707},[1296,14500,14501],{"class":3703}," plot",[1296,14503,3796],{"class":3707},[1296,14505,6334],{"class":3723},[1296,14507,3900],{"class":3715},[1296,14509,14510,14512,14514],{"class":3700,"line":25},[1296,14511,14448],{"class":3703},[1296,14513,3913],{"class":3707},[1296,14515,14516],{"class":3703},"counts\n",[1296,14518,14519,14521,14523,14525,14527,14530,14532,14535,14537,14539,14541,14543,14545],{"class":3700,"line":65},[1296,14520,9975],{"class":3711},[1296,14522,1873],{"class":3715},[1296,14524,14448],{"class":3703},[1296,14526,3913],{"class":3707},[1296,14528,14529],{"class":3703},"counts",[1296,14531,10070],{"class":3707},[1296,14533,14534],{"class":3711}," length",[1296,14536,1873],{"class":3715},[1296,14538,14071],{"class":3703},[1296,14540,1884],{"class":3715},[1296,14542,1795],{"class":3707},[1296,14544,10850],{"class":3723},[1296,14546,3900],{"class":3715},[1296,14548,14549,14551,14553,14555,14557,14559,14561,14563],{"class":3700,"line":63},[1296,14550,12133],{"class":3711},[1296,14552,1873],{"class":3715},[1296,14554,14071],{"class":3703},[1296,14556,12172],{"class":3715},[1296,14558,12155],{"class":3711},[1296,14560,1873],{"class":3715},[1296,14562,14071],{"class":3703},[1296,14564,3900],{"class":3715},[3692,14566,14569],{"className":14567,"code":14568,"language":3922,"meta":1452},[3920],"[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",[3468,14570,14568],{"__ignoreMap":1452},[1148,14572,14573,14574,14602],{},"Variační rozpětí je ",[1296,14575,14577],{"className":14576},[1299],[1301,14578,14579],{"xmlns":1303},[1305,14580,14581,14599],{},[1308,14582,14583,14585,14587,14590,14592,14594,14596],{},[1314,14584,10218],{},[1685,14586,1980],{},[1562,14588,14589],{},"501",[1685,14591,3062],{},[1562,14593,1586],{},[1685,14595,1980],{},[1562,14597,14598],{},"499",[1319,14600,14601],{"encoding":1321},"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:",[1162,14604,14605,14701],{},[1165,14606,14607],{},[1168,14608,14609,14624,14643,14662,14681],{},[1171,14610,14611],{},[1296,14612,14614],{"className":14613},[1299],[1301,14615,14616],{"xmlns":1303},[1305,14617,14618,14622],{},[1308,14619,14620],{},[1314,14621,1881],{},[1319,14623,1881],{"encoding":1321},[1171,14625,14626],{},[1296,14627,14629],{"className":14628},[1299],[1301,14630,14631],{"xmlns":1303},[1305,14632,14633,14641],{},[1308,14634,14635],{},[1311,14636,14637,14639],{},[1314,14638,11195],{},[1314,14640,1881],{},[1319,14642,13681],{"encoding":1321},[1171,14644,14645],{},[1296,14646,14648],{"className":14647},[1299],[1301,14649,14650],{"xmlns":1303},[1305,14651,14652,14660],{},[1308,14653,14654],{},[1311,14655,14656,14658],{},[1314,14657,8920],{},[1314,14659,1881],{},[1319,14661,13761],{"encoding":1321},[1171,14663,14664],{},[1296,14665,14667],{"className":14666},[1299],[1301,14668,14669],{"xmlns":1303},[1305,14670,14671,14679],{},[1308,14672,14673],{},[1311,14674,14675,14677],{},[1314,14676,6767],{},[1314,14678,1881],{},[1319,14680,13782],{"encoding":1321},[1171,14682,14683],{},[1296,14684,14686],{"className":14685},[1299],[1301,14687,14688],{"xmlns":1303},[1305,14689,14690,14698],{},[1308,14691,14692],{},[1311,14693,14694,14696],{},[1314,14695,1148],{},[1314,14697,1881],{},[1319,14699,14700],{"encoding":1321},"p_j",[1178,14702,14703,14718,14733,14748,14761,14776,14791,14805,14820,14834,14849],{},[1168,14704,14705,14707,14710,14712,14715],{},[1183,14706,1792],{},[1183,14708,14709],{},"⟨0; 50)",[1183,14711,4057],{},[1183,14713,14714],{},"19",[1183,14716,14717],{},"0,279",[1168,14719,14720,14722,14725,14728,14730],{},[1183,14721,1586],{},[1183,14723,14724],{},"⟨50; 100)",[1183,14726,14727],{},"75",[1183,14729,2253],{},[1183,14731,14732],{},"0,162",[1168,14734,14735,14737,14740,14743,14745],{},[1183,14736,3590],{},[1183,14738,14739],{},"⟨100; 150)",[1183,14741,14742],{},"125",[1183,14744,9028],{},[1183,14746,14747],{},"0,147",[1168,14749,14750,14752,14755,14757,14759],{},[1183,14751,3540],{},[1183,14753,14754],{},"⟨150; 200)",[1183,14756,7475],{},[1183,14758,9028],{},[1183,14760,14747],{},[1168,14762,14763,14765,14768,14771,14773],{},[1183,14764,9921],{},[1183,14766,14767],{},"⟨200; 250)",[1183,14769,14770],{},"225",[1183,14772,9921],{},[1183,14774,14775],{},"0,074",[1168,14777,14778,14780,14783,14786,14788],{},[1183,14779,3963],{},[1183,14781,14782],{},"⟨250; 300)",[1183,14784,14785],{},"275",[1183,14787,1792],{},[1183,14789,14790],{},"0,015",[1168,14792,14793,14795,14798,14801,14803],{},[1183,14794,13325],{},[1183,14796,14797],{},"⟨300; 350)",[1183,14799,14800],{},"325",[1183,14802,9921],{},[1183,14804,14775],{},[1168,14806,14807,14810,14813,14816,14818],{},[1183,14808,14809],{},"8",[1183,14811,14812],{},"⟨350; 400)",[1183,14814,14815],{},"375",[1183,14817,9921],{},[1183,14819,14775],{},[1168,14821,14822,14824,14827,14830,14832],{},[1183,14823,3593],{},[1183,14825,14826],{},"⟨400; 450)",[1183,14828,14829],{},"425",[1183,14831,1792],{},[1183,14833,14790],{},[1168,14835,14836,14838,14841,14844,14846],{},[1183,14837,9028],{},[1183,14839,14840],{},"⟨450; 500)",[1183,14842,14843],{},"475",[1183,14845,1564],{},[1183,14847,14848],{},"0,000",[1168,14850,14851,14853,14856,14859,14861],{},[1183,14852,2253],{},[1183,14854,14855],{},"⟨500; ∞)",[1183,14857,14858],{},"525",[1183,14860,1792],{},[1183,14862,14790],{},[1148,14864,14865,14866,14883,14884,14901,14902,1323,14925,1323,14953,14972,14973,1323,14996,15015],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1296,14867,14869],{"className":14868},[1299],[1301,14870,14871],{"xmlns":1303},[1305,14872,14873,14881],{},[1308,14874,14875],{},[1311,14876,14877,14879],{},[1314,14878,8920],{},[1314,14880,1881],{},[1319,14882,13761],{"encoding":1321}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1296,14885,14887],{"className":14886},[1299],[1301,14888,14889],{"xmlns":1303},[1305,14890,14891,14899],{},[1308,14892,14893],{},[1311,14894,14895,14897],{},[1314,14896,8920],{},[1314,14898,1881],{},[1319,14900,13761],{"encoding":1321},") vycházejí ",[1296,14903,14905],{"className":14904},[1299],[1301,14906,14907],{"xmlns":1303},[1305,14908,14909,14922],{},[1308,14910,14911,14917,14919],{},[2722,14912,14913,14915],{"accent":1530},[1314,14914,6716],{},[1685,14916,11454],{},[1685,14918,9435],{},[1562,14920,14921],{},"149,26",[1319,14923,14924],{"encoding":1321},"\\bar{x} \\approx 149{,}26",[1296,14926,14928],{"className":14927},[1299],[1301,14929,14930],{"xmlns":1303},[1305,14931,14932,14950],{},[1308,14933,14934,14940,14942,14945,14947],{},[1579,14935,14936,14938],{},[1314,14937,1852],{},[1562,14939,1586],{},[1685,14941,9435],{},[1562,14943,14944],{},"15",[2907,14946,2909],{},[1562,14948,14949],{},"484,5",[1319,14951,14952],{"encoding":1321},"s^2 \\approx 15\\,484{,}5",[1296,14954,14956],{"className":14955},[1299],[1301,14957,14958],{"xmlns":1303},[1305,14959,14960,14969],{},[1308,14961,14962,14964,14966],{},[1314,14963,1852],{},[1685,14965,9435],{},[1562,14967,14968],{},"124,44",[1319,14970,14971],{"encoding":1321},"s \\approx 124{,}44"," — blízko hodnotám ",[1296,14974,14976],{"className":14975},[1299],[1301,14977,14978],{"xmlns":1303},[1305,14979,14980,14993],{},[1308,14981,14982,14988,14990],{},[2722,14983,14984,14986],{"accent":1530},[1314,14985,6716],{},[1685,14987,11454],{},[1685,14989,1980],{},[1562,14991,14992],{},"145,44",[1319,14994,14995],{"encoding":1321},"\\bar{x}=145{,}44",[1296,14997,14999],{"className":14998},[1299],[1301,15000,15001],{"xmlns":1303},[1305,15002,15003,15012],{},[1308,15004,15005,15007,15009],{},[1314,15006,1852],{},[1685,15008,1980],{},[1562,15010,15011],{},"126,13",[1319,15013,15014],{"encoding":1321},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1148,15017,15018,15019,15022,15023,15059,15060,15078,15079,15093,15094,15120,15121,15123,15124,4863],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1108,15020,15021],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1296,15024,15026],{"className":15025},[1299],[1301,15027,15028],{"xmlns":1303},[1305,15029,15030,15056],{},[1308,15031,15032,15034,15036,15038,15040,15042,15044],{},[1314,15033,6767],{},[1685,15035,1873],{"stretchy":1872},[1314,15037,6716],{},[1685,15039,1884],{"stretchy":1872},[1685,15041,1980],{},[1314,15043,9707],{},[1579,15045,15046,15048],{},[1314,15047,8587],{},[1308,15049,15050,15052,15054],{},[1685,15051,3062],{},[1314,15053,9707],{},[1314,15055,6716],{},[1319,15057,15058],{"encoding":1321},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1296,15061,15063],{"className":15062},[1299],[1301,15064,15065],{"xmlns":1303},[1305,15066,15067,15075],{},[1308,15068,15069,15071,15073],{},[1314,15070,6716],{},[1685,15072,3349],{},[1562,15074,1564],{},[1319,15076,15077],{"encoding":1321},"x \\ge 0",", s parametrem ",[1296,15080,15082],{"className":15081},[1299],[1301,15083,15084],{"xmlns":1303},[1305,15085,15086,15090],{},[1308,15087,15088],{},[1314,15089,9707],{},[1319,15091,15092],{"encoding":1321},"\\lambda"," odhadnutým jako ",[1296,15095,15097],{"className":15096},[1299],[1301,15098,15099],{"xmlns":1303},[1305,15100,15101,15117],{},[1308,15102,15103,15105,15107,15109,15111],{},[1314,15104,9707],{},[1685,15106,1980],{},[1562,15108,1792],{},[1314,15110,1502],{"mathvariant":2119},[2722,15112,15113,15115],{"accent":1530},[1314,15114,6716],{},[1685,15116,11454],{},[1319,15118,15119],{"encoding":1321},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3468,15122,9874],{}," parametrem ",[3468,15125,15126],{},"dexp()",[3692,15128,15130],{"className":3694,"code":15129,"language":71,"meta":1452,"style":1452},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3468,15131,15132,15151],{"__ignoreMap":1452},[1296,15133,15134,15137,15139,15141,15143,15145,15147,15149],{"class":3700,"line":10},[1296,15135,15136],{"class":3703},"rate9",[1296,15138,3708],{"class":3707},[1296,15140,4638],{"class":3723},[1296,15142,10070],{"class":3707},[1296,15144,9226],{"class":3711},[1296,15146,1873],{"class":3715},[1296,15148,14071],{"class":3703},[1296,15150,3900],{"class":3715},[1296,15152,15153],{"class":3700,"line":27},[1296,15154,15155],{"class":3703},"rate9\n",[3692,15157,15160],{"className":15158,"code":15159,"language":3922,"meta":1452},[3920],"[1] 0.006875632\n",[3468,15161,15159],{"__ignoreMap":1452},[1148,15163,15164],{},[4382,15165],{"alt":15166,"className":15167,"src":15168},"mask-ps-hustota-fit",[1245,4386],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1148,15170,15171,15172,1395],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1242,15173,1266],{"className":15174,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1514,15176,15178,15185],{"className":15177,"dataCallout":3475},[1517,3474],[1148,15179,15181,15184],{"className":15180},[1523],[1296,15182],{"className":15183,"ariaHidden":1530},[1527,3482,1529],"Příklad: Doba života výrobku",[1148,15186,15187],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3692,15189,15191],{"className":3694,"code":15190,"language":71,"meta":1452,"style":1452},"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",[3468,15192,15193,15254,15305,15356,15407,15459,15469,15495,15515,15573,15582,15590],{"__ignoreMap":1452},[1296,15194,15195,15198,15200,15202,15204,15207,15209,15212,15214,15217,15219,15222,15224,15227,15229,15232,15234,15237,15239,15242,15244,15247,15249,15252],{"class":3700,"line":10},[1296,15196,15197],{"class":3703},"x5",[1296,15199,3708],{"class":3707},[1296,15201,3834],{"class":3711},[1296,15203,1873],{"class":3715},[1296,15205,15206],{"class":3723},"63",[1296,15208,1795],{"class":3707},[1296,15210,15211],{"class":3723}," 156",[1296,15213,1795],{"class":3707},[1296,15215,15216],{"class":3723}," 184",[1296,15218,1795],{"class":3707},[1296,15220,15221],{"class":3723}," 786",[1296,15223,1795],{"class":3707},[1296,15225,15226],{"class":3723}," 822",[1296,15228,1795],{"class":3707},[1296,15230,15231],{"class":3723}," 278",[1296,15233,1795],{"class":3707},[1296,15235,15236],{"class":3723}," 15",[1296,15238,1795],{"class":3707},[1296,15240,15241],{"class":3723}," 561",[1296,15243,1795],{"class":3707},[1296,15245,15246],{"class":3723}," 229",[1296,15248,1795],{"class":3707},[1296,15250,15251],{"class":3723}," 8",[1296,15253,3736],{"class":3707},[1296,15255,15256,15259,15261,15264,15266,15268,15270,15273,15275,15278,15280,15283,15285,15288,15290,15293,15295,15298,15300,15303],{"class":3700,"line":27},[1296,15257,15258],{"class":3723},"        4",[1296,15260,1795],{"class":3707},[1296,15262,15263],{"class":3723}," 35",[1296,15265,1795],{"class":3707},[1296,15267,14121],{"class":3723},[1296,15269,1795],{"class":3707},[1296,15271,15272],{"class":3723}," 203",[1296,15274,1795],{"class":3707},[1296,15276,15277],{"class":3723}," 178",[1296,15279,1795],{"class":3707},[1296,15281,15282],{"class":3723}," 323",[1296,15284,1795],{"class":3707},[1296,15286,15287],{"class":3723}," 275",[1296,15289,1795],{"class":3707},[1296,15291,15292],{"class":3723}," 176",[1296,15294,1795],{"class":3707},[1296,15296,15297],{"class":3723}," 427",[1296,15299,1795],{"class":3707},[1296,15301,15302],{"class":3723}," 196",[1296,15304,3736],{"class":3707},[1296,15306,15307,15310,15312,15315,15317,15320,15322,15325,15327,15330,15332,15335,15337,15340,15342,15344,15346,15349,15351,15354],{"class":3700,"line":148},[1296,15308,15309],{"class":3723},"        415",[1296,15311,1795],{"class":3707},[1296,15313,15314],{"class":3723}," 140",[1296,15316,1795],{"class":3707},[1296,15318,15319],{"class":3723}," 17",[1296,15321,1795],{"class":3707},[1296,15323,15324],{"class":3723}," 293",[1296,15326,1795],{"class":3707},[1296,15328,15329],{"class":3723}," 991",[1296,15331,1795],{"class":3707},[1296,15333,15334],{"class":3723}," 100",[1296,15336,1795],{"class":3707},[1296,15338,15339],{"class":3723}," 189",[1296,15341,1795],{"class":3707},[1296,15343,15292],{"class":3723},[1296,15345,1795],{"class":3707},[1296,15347,15348],{"class":3723}," 672",[1296,15350,1795],{"class":3707},[1296,15352,15353],{"class":3723}," 134",[1296,15355,3736],{"class":3707},[1296,15357,15358,15361,15363,15366,15368,15371,15373,15376,15378,15380,15382,15385,15387,15390,15392,15395,15397,15400,15402,15405],{"class":3700,"line":111},[1296,15359,15360],{"class":3723},"        529",[1296,15362,1795],{"class":3707},[1296,15364,15365],{"class":3723}," 310",[1296,15367,1795],{"class":3707},[1296,15369,15370],{"class":3723}," 22",[1296,15372,1795],{"class":3707},[1296,15374,15375],{"class":3723}," 69",[1296,15377,1795],{"class":3707},[1296,15379,14222],{"class":3723},[1296,15381,1795],{"class":3707},[1296,15383,15384],{"class":3723}," 272",[1296,15386,1795],{"class":3707},[1296,15388,15389],{"class":3723}," 117",[1296,15391,1795],{"class":3707},[1296,15393,15394],{"class":3723}," 169",[1296,15396,1795],{"class":3707},[1296,15398,15399],{"class":3723}," 466",[1296,15401,1795],{"class":3707},[1296,15403,15404],{"class":3723}," 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1050",[1296,15546,1795],{"class":3707},[1296,15548,14481],{"class":3703},[1296,15550,3796],{"class":3707},[1296,15552,14090],{"class":3723},[1296,15554,1884],{"class":3715},[1296,15556,1795],{"class":3707},[1296,15558,14492],{"class":3703},[1296,15560,3796],{"class":3707},[1296,15562,6334],{"class":3723},[1296,15564,1795],{"class":3707},[1296,15566,14501],{"class":3703},[1296,15568,3796],{"class":3707},[1296,15570,6334],{"class":3723},[1296,15572,3900],{"class":3715},[1296,15574,15575,15577,15579],{"class":3700,"line":72},[1296,15576,15519],{"class":3703},[1296,15578,3913],{"class":3707},[1296,15580,15581],{"class":3703},"mids\n",[1296,15583,15584,15586,15588],{"class":3700,"line":25},[1296,15585,15519],{"class":3703},[1296,15587,3913],{"class":3707},[1296,15589,14516],{"class":3703},[1296,15591,15592,15594,15596,15598,15600,15602,15604,15606,15608,15610,15612,15614,15616],{"class":3700,"line":65},[1296,15593,9975],{"class":3711},[1296,15595,1873],{"class":3715},[1296,15597,15519],{"class":3703},[1296,15599,3913],{"class":3707},[1296,15601,14529],{"class":3703},[1296,15603,10070],{"class":3707},[1296,15605,14534],{"class":3711},[1296,15607,1873],{"class":3715},[1296,15609,15197],{"class":3703},[1296,15611,1884],{"class":3715},[1296,15613,1795],{"class":3707},[1296,15615,10850],{"class":3723},[1296,15617,3900],{"class":3715},[3692,15619,15622],{"className":15620,"code":15621,"language":3922,"meta":1452},[3920],"[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",[3468,15623,15621],{"__ignoreMap":1452},[1148,15625,15626],{},"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.",[1143,15628,6404],{"id":6403},[1102,15630,15631,15649,15750,15818],{},[1105,15632,15633,1651,15636,15639,15640,15643,15644,15646,15647,1395],{},[1108,15634,15635],{},"Výchozí typ kvantilu v R.",[3468,15637,15638],{},"quantile()"," bez argumentu ",[3468,15641,15642],{},"type"," používá jiný výpočetní vzorec (",[3468,15645,12286],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3468,15648,12282],{},[1105,15650,15651,15656,15657,15659,15660,15695,15696,15731,15732,15749],{},[1108,15652,15653,15654,1395],{},"Výchozí ohraničení tříd v ",[3468,15655,13878],{}," Bez ",[3468,15658,14004],{}," jsou třídy zprava uzavřené, ",[1296,15661,15663],{"className":15662},[1299],[1301,15664,15665],{"xmlns":1303},[1305,15666,15667,15693],{},[1308,15668,15669,15671,15677,15679,15691],{},[1685,15670,1873],{"stretchy":1872},[1311,15672,15673,15675],{},[1314,15674,3718],{},[1314,15676,1881],{},[1685,15678,6890],{"separator":1530},[1311,15680,15681,15683],{},[1314,15682,3718],{},[1308,15684,15685,15687,15689],{},[1314,15686,1881],{},[1685,15688,5474],{},[1562,15690,1792],{},[1685,15692,7439],{"stretchy":1872},[1319,15694,14000],{"encoding":1321}," — opačně než konvence ",[1296,15697,15699],{"className":15698},[1299],[1301,15700,15701],{"xmlns":1303},[1305,15702,15703,15729],{},[1308,15704,15705,15707,15713,15715,15727],{},[1685,15706,8420],{"stretchy":1872},[1311,15708,15709,15711],{},[1314,15710,3718],{},[1314,15712,1881],{},[1685,15714,6890],{"separator":1530},[1311,15716,15717,15719],{},[1314,15718,3718],{},[1308,15720,15721,15723,15725],{},[1314,15722,1881],{},[1685,15724,5474],{},[1562,15726,1792],{},[1685,15728,1884],{"stretchy":1872},[1319,15730,14041],{"encoding":1321}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1296,15733,15735],{"className":15734},[1299],[1301,15736,15737],{"xmlns":1303},[1305,15738,15739,15747],{},[1308,15740,15741],{},[1311,15742,15743,15745],{},[1314,15744,6767],{},[1314,15746,1881],{},[1319,15748,13782],{"encoding":1321}," vyjdou jinak.",[1105,15751,15752,1651,15755,15773,15774,15787,15788,9043,15801,1395],{},[1108,15753,15754],{},"Rozptyl vs. směrodatná odchylka.",[1296,15756,15758],{"className":15757},[1299],[1301,15759,15760],{"xmlns":1303},[1305,15761,15762,15770],{},[1308,15763,15764],{},[1579,15765,15766,15768],{},[1314,15767,1852],{},[1562,15769,1586],{},[1319,15771,15772],{"encoding":1321},"s^2"," se udává v jednotkách znaku na druhou, ",[1296,15775,15777],{"className":15776},[1299],[1301,15778,15779],{"xmlns":1303},[1305,15780,15781,15785],{},[1308,15782,15783],{},[1314,15784,1852],{},[1319,15786,1852],{"encoding":1321}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1296,15789,15791],{"className":15790},[1299],[1301,15792,15793],{"xmlns":1303},[1305,15794,15795,15799],{},[1308,15796,15797],{},[1314,15798,1852],{},[1319,15800,1852],{"encoding":1321},[1296,15802,15804],{"className":15803},[1299],[1301,15805,15806],{"xmlns":1303},[1305,15807,15808,15816],{},[1308,15809,15810],{},[1579,15811,15812,15814],{},[1314,15813,1852],{},[1562,15815,1586],{},[1319,15817,15772],{"encoding":1321},[1105,15819,15820,15823],{},[1108,15821,15822],{},"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.",[1143,15825,6592],{"id":6591},[1102,15827,15828,15833,15838,15843,15848,15853,15858],{},[1105,15829,15830],{},[1242,15831,1717],{"className":15832,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,15834,15835],{},[1242,15836,1248],{"className":15837,"dataFsResolvedFilePath":1246,"href":1247},[1245],[1105,15839,15840],{},[1242,15841,1266],{"className":15842,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1105,15844,15845],{},[1242,15846,1275],{"className":15847,"dataFsResolvedFilePath":1273,"href":1274},[1245],[1105,15849,15850],{},[1242,15851,1284],{"className":15852,"dataFsResolvedFilePath":1282,"href":1283},[1245],[1105,15854,15855],{},[1242,15856,1293],{"className":15857,"dataFsResolvedFilePath":1291,"href":1292},[1245],[1105,15859,15860],{},[1242,15861,6630],{"className":15862,"dataFsResolvedFilePath":1447,"href":1448},[1245],[1143,15864,6633],{"id":934},[1148,15866,6636,15867,6641],{},[6638,15868,6640],{},[6643,15870,15871],{},"html pre.shiki code .sP4rz, html 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analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1296,15919,15921],{"className":15920},[1299],[1301,15922,15923],{"xmlns":1303},[1305,15924,15925,15929],{},[1308,15926,15927],{},[1314,15928,7126],{},[1319,15930,7126],{"encoding":1321}," na vysvětlujících proměnných ",[1296,15933,15935],{"className":15934},[1299],[1301,15936,15937],{"xmlns":1303},[1305,15938,15939,15943],{},[1308,15940,15941],{},[1314,15942,6716],{},[1319,15944,6716],{"encoding":1321}," (příčina → následek); ",[1108,15947,15948],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1105,15951,15952,15953,15956,15957,1395],{},"Parametry regresní funkce se odhadují ",[1108,15954,15955],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1296,15958,15960],{"className":15959},[1299],[1301,15961,15962],{"xmlns":1303},[1305,15963,15964,15994],{},[1308,15965,15966,15968,15970,15976,15978,15988],{},[1685,15967,1986],{},[1685,15969,1873],{"stretchy":1872},[1311,15971,15972,15974],{},[1314,15973,7126],{},[1314,15975,1876],{},[1685,15977,3062],{},[1311,15979,15980,15986],{},[2722,15981,15982,15984],{"accent":1530},[1314,15983,7126],{},[1685,15985,2728],{},[1314,15987,1876],{},[1579,15989,15990,15992],{},[1685,15991,1884],{"stretchy":1872},[1562,15993,1586],{},[1319,15995,15996],{"encoding":1321},"\\sum(y_i-\\hat y_i)^2",[1105,15998,15999,16000,1651,16003,16021,16022,1651,16025,16049,16050,1651,16053,1395],{},"Kvalitu fitu měří ",[1108,16001,16002],{},"index determinace",[1296,16004,16006],{"className":16005},[1299],[1301,16007,16008],{"xmlns":1303},[1305,16009,16010,16018],{},[1308,16011,16012],{},[1579,16013,16014,16016],{},[1314,16015,10218],{},[1562,16017,1586],{},[1319,16019,16020],{"encoding":1321},"R^2","; obecnou těsnost závislosti ",[1108,16023,16024],{},"index korelace",[1296,16026,16028],{"className":16027},[1299],[1301,16029,16030],{"xmlns":1303},[1305,16031,16032,16046],{},[1308,16033,16034,16036,16038],{},[1314,16035,11195],{},[1685,16037,1980],{},[4452,16039,16040],{},[1579,16041,16042,16044],{},[1314,16043,10218],{},[1562,16045,1586],{},[1319,16047,16048],{"encoding":1321},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1108,16051,16052],{},"koeficientu korelace",[1296,16054,16056],{"className":16055},[1299],[1301,16057,16058],{"xmlns":1303},[1305,16059,16060,16072],{},[1308,16061,16062],{},[1311,16063,16064,16066],{},[1314,16065,71],{},[1308,16067,16068,16070],{},[1314,16069,6716],{},[1314,16071,7126],{},[1319,16073,16074],{"encoding":1321},"r_{xy}",[1105,16076,16077,16078,16081,16082,16085,16086,16089],{},"Když přímka nestačí, volí se ",[1108,16079,16080],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1108,16083,16084],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3468,16087,16088],{},"nls2",").",[1105,16091,16092,16095],{},[1108,16093,16094],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1105,16097,16098,16099,1323,16102,1323,16105,1323,16108,1323,16111,1323,16114,1323,16117,1323,16120,1323,16123,1323,16126,1395],{},"V R: ",[3468,16100,16101],{},"lm()",[3468,16103,16104],{},"nls2()",[3468,16106,16107],{},"summary()",[3468,16109,16110],{},"confint()",[3468,16112,16113],{},"predict()",[3468,16115,16116],{},"step()",[3468,16118,16119],{},"car::vif()",[3468,16121,16122],{},"lmtest::dwtest()",[3468,16124,16125],{},"whitestrap::white_test()",[3468,16127,16128],{},"shapiro.test()",[1143,16130,11232],{"id":11231},[1148,16132,16133,16136,16137,1370,16150,16163,16164,16166,16167,16180,16181,16194,16195,16198],{},[1242,16134,1717],{"className":16135,"dataFsResolvedFilePath":1715,"href":1716},[1245]," pracuje se dvěma znaky ",[1296,16138,16140],{"className":16139},[1299],[1301,16141,16142],{"xmlns":1303},[1305,16143,16144,16148],{},[1308,16145,16146],{},[1314,16147,6716],{},[1319,16149,6716],{"encoding":1321},[1296,16151,16153],{"className":16152},[1299],[1301,16154,16155],{"xmlns":1303},[1305,16156,16157,16161],{},[1308,16158,16159],{},[1314,16160,7126],{},[1319,16162,7126],{"encoding":1321}," zjištěnými na stejných jednotkách. ",[1108,16165,15916],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1296,16168,16170],{"className":16169},[1299],[1301,16171,16172],{"xmlns":1303},[1305,16173,16174,16178],{},[1308,16175,16176],{},[1314,16177,6716],{},[1319,16179,6716],{"encoding":1321}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1296,16182,16184],{"className":16183},[1299],[1301,16185,16186],{"xmlns":1303},[1305,16187,16188,16192],{},[1308,16189,16190],{},[1314,16191,7126],{},[1319,16193,7126],{"encoding":1321}," v úloze následku. ",[1108,16196,16197],{},"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.",[1148,16200,16201,16202,16089],{},"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 (",[1108,16203,16204],{},"regresní funkce",[1148,16206,16207],{},"Druh regresní analýzy určuje struktura datového souboru:",[1102,16209,16210,16247],{},[1105,16211,16212,16215,16216,16229,16230,16243,16244,1795],{},[1108,16213,16214],{},"dvourozměrný datový soubor"," (jedna ",[1296,16217,16219],{"className":16218},[1299],[1301,16220,16221],{"xmlns":1303},[1305,16222,16223,16227],{},[1308,16224,16225],{},[1314,16226,6716],{},[1319,16228,6716],{"encoding":1321},", jedna ",[1296,16231,16233],{"className":16232},[1299],[1301,16234,16235],{"xmlns":1303},[1305,16236,16237,16241],{},[1308,16238,16239],{},[1314,16240,7126],{},[1319,16242,7126],{"encoding":1321},") → ",[1108,16245,16246],{},"regresní analýza dvou proměnných",[1105,16248,16249,16252,16253,16243,16283,1395],{},[1108,16250,16251],{},"vícerozměrný datový soubor"," (více ",[1296,16254,16256],{"className":16255},[1299],[1301,16257,16258],{"xmlns":1303},[1305,16259,16260,16280],{},[1308,16261,16262,16268,16270,16272,16274],{},[1311,16263,16264,16266],{},[1314,16265,6716],{},[1562,16267,1792],{},[1685,16269,1795],{"separator":1530},[1685,16271,1798],{},[1685,16273,1795],{"separator":1530},[1311,16275,16276,16278],{},[1314,16277,6716],{},[1314,16279,1148],{},[1319,16281,16282],{"encoding":1321},"x_1,\\dots,x_p",[1108,16284,16285],{},"vícenásobná regresní analýza",[1148,16287,16288,16289,16292,16293,16296],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1108,16290,16291],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1108,16294,16295],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1143,16298,16300],{"id":16299},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1148,16302,16303,16304,1651,16307,16361,16362,16380,16381,1651,16384,16440,16441,16459,16460,16477,16478,16516,16517,1395],{},"Rozlišují se ",[1108,16305,16306],{},"teoretická regresní funkce",[1296,16308,16310],{"className":16309},[1299],[1301,16311,16312],{"xmlns":1303},[1305,16313,16314,16358],{},[1308,16315,16316,16319,16321,16323,16325,16327,16329,16336,16338,16344,16346,16348,16350,16356],{},[1314,16317,16318],{},"η",[1685,16320,1980],{},[1314,16322,6767],{},[1685,16324,1873],{"stretchy":1872},[1314,16326,6716],{},[1685,16328,6890],{"separator":1530},[1311,16330,16331,16334],{},[1314,16332,16333],{},"β",[1562,16335,1564],{},[1685,16337,1795],{"separator":1530},[1311,16339,16340,16342],{},[1314,16341,16333],{},[1562,16343,1792],{},[1685,16345,1795],{"separator":1530},[1685,16347,1798],{},[1685,16349,1795],{"separator":1530},[1311,16351,16352,16354],{},[1314,16353,16333],{},[1314,16355,1148],{},[1685,16357,1884],{"stretchy":1872},[1319,16359,16360],{"encoding":1321},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1296,16363,16365],{"className":16364},[1299],[1301,16366,16367],{"xmlns":1303},[1305,16368,16369,16377],{},[1308,16370,16371],{},[1311,16372,16373,16375],{},[1314,16374,16333],{},[1314,16376,1876],{},[1319,16378,16379],{"encoding":1321},"\\beta_i"," — a ",[1108,16382,16383],{},"empirická regresní funkce",[1296,16385,16387],{"className":16386},[1299],[1301,16388,16389],{"xmlns":1303},[1305,16390,16391,16437],{},[1308,16392,16393,16399,16401,16403,16405,16407,16409,16415,16417,16423,16425,16427,16429,16435],{},[2722,16394,16395,16397],{"accent":1530},[1314,16396,7126],{},[1685,16398,2728],{},[1685,16400,1980],{},[1314,16402,6767],{},[1685,16404,1873],{"stretchy":1872},[1314,16406,6716],{},[1685,16408,6890],{"separator":1530},[1311,16410,16411,16413],{},[1314,16412,11499],{},[1562,16414,1564],{},[1685,16416,1795],{"separator":1530},[1311,16418,16419,16421],{},[1314,16420,11499],{},[1562,16422,1792],{},[1685,16424,1795],{"separator":1530},[1685,16426,1798],{},[1685,16428,1795],{"separator":1530},[1311,16430,16431,16433],{},[1314,16432,11499],{},[1314,16434,1148],{},[1685,16436,1884],{"stretchy":1872},[1319,16438,16439],{"encoding":1321},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1296,16442,16444],{"className":16443},[1299],[1301,16445,16446],{"xmlns":1303},[1305,16447,16448,16456],{},[1308,16449,16450],{},[1311,16451,16452,16454],{},[1314,16453,11499],{},[1314,16455,1876],{},[1319,16457,16458],{"encoding":1321},"b_i"," jsou odhadem ",[1296,16461,16463],{"className":16462},[1299],[1301,16464,16465],{"xmlns":1303},[1305,16466,16467,16475],{},[1308,16468,16469],{},[1311,16470,16471,16473],{},[1314,16472,16333],{},[1314,16474,1876],{},[1319,16476,16379],{"encoding":1321}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1296,16479,16481],{"className":16480},[1299],[1301,16482,16483],{"xmlns":1303},[1305,16484,16485,16513],{},[1308,16486,16487,16493,16495,16501,16503],{},[1311,16488,16489,16491],{},[1314,16490,8587],{},[1314,16492,1876],{},[1685,16494,1980],{},[1311,16496,16497,16499],{},[1314,16498,7126],{},[1314,16500,1876],{},[1685,16502,3062],{},[1311,16504,16505,16511],{},[2722,16506,16507,16509],{"accent":1530},[1314,16508,7126],{},[1685,16510,2728],{},[1314,16512,1876],{},[1319,16514,16515],{"encoding":1321},"e_i=y_i-\\hat y_i",", se nazývají ",[1108,16518,16519],{},"rezidua",[1148,16521,16522,16523,16526],{},"Nejpoužívanější metodou odhadu parametrů je ",[1108,16524,16525],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1296,16528,16530],{"className":16529},[1299],[1301,16531,16532],{"xmlns":1303,"display":1962},[1305,16533,16534,16584],{},[1308,16535,16536,16550,16552,16558,16560,16570,16576,16578,16580,16582],{},[1982,16537,16538,16540,16548],{},[1685,16539,1986],{},[1308,16541,16542,16544,16546],{},[1314,16543,1876],{},[1685,16545,1980],{},[1562,16547,1792],{},[1314,16549,1683],{},[1685,16551,1873],{"stretchy":1872},[1311,16553,16554,16556],{},[1314,16555,7126],{},[1314,16557,1876],{},[1685,16559,3062],{},[1311,16561,16562,16568],{},[2722,16563,16564,16566],{"accent":1530},[1314,16565,7126],{},[1685,16567,2728],{},[1314,16569,1876],{},[1579,16571,16572,16574],{},[1685,16573,1884],{"stretchy":1872},[1562,16575,1586],{},[1685,16577,7603],{},[1314,16579,4486],{},[1685,16581,4489],{},[1314,16583,1395],{"mathvariant":2119},[1319,16585,16586],{"encoding":1321},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1148,16588,16589],{},"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.",[1148,16591,16592],{},[4382,16593],{"alt":16594,"className":16595,"src":16596},"mask-ra-primka-rezidua",[1245,4386],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1148,16598,16599,16600,16618],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1296,16601,16603],{"className":16602},[1299],[1301,16604,16605],{"xmlns":1303},[1305,16606,16607,16615],{},[1308,16608,16609],{},[1311,16610,16611,16613],{},[1314,16612,8587],{},[1314,16614,1876],{},[1319,16616,16617],{"encoding":1321},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1143,16620,16622],{"id":16621},"regresní-přímka","Regresní přímka",[1148,16624,16625,16626,1956],{},"Nejjednodušší regresní funkcí je ",[1108,16627,16628],{},"regresní přímka",[1296,16630,16632],{"className":16631},[1299],[1301,16633,16634],{"xmlns":1303,"display":1962},[1305,16635,16636,16688],{},[1308,16637,16638,16640,16642,16648,16650,16656,16658,16660,16662,16668,16670,16676,16678,16684,16686],{},[1314,16639,16318],{},[1685,16641,1980],{},[1311,16643,16644,16646],{},[1314,16645,16333],{},[1562,16647,1564],{},[1685,16649,5474],{},[1311,16651,16652,16654],{},[1314,16653,16333],{},[1562,16655,1792],{},[1314,16657,6716],{},[1685,16659,1795],{"separator":1530},[2010,16661],{"width":2012},[2722,16663,16664,16666],{"accent":1530},[1314,16665,7126],{},[1685,16667,2728],{},[1685,16669,1980],{},[1311,16671,16672,16674],{},[1314,16673,11499],{},[1562,16675,1564],{},[1685,16677,5474],{},[1311,16679,16680,16682],{},[1314,16681,11499],{},[1562,16683,1792],{},[1314,16685,6716],{},[1314,16687,1395],{"mathvariant":2119},[1319,16689,16690],{"encoding":1321},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1148,16692,16693,16694,16712,16713,16726,16727,16740],{},"Koeficient ",[1296,16695,16697],{"className":16696},[1299],[1301,16698,16699],{"xmlns":1303},[1305,16700,16701,16709],{},[1308,16702,16703],{},[1311,16704,16705,16707],{},[1314,16706,11499],{},[1562,16708,1792],{},[1319,16710,16711],{"encoding":1321},"b_1"," udává změnu průměru ",[1296,16714,16716],{"className":16715},[1299],[1301,16717,16718],{"xmlns":1303},[1305,16719,16720,16724],{},[1308,16721,16722],{},[1314,16723,7126],{},[1319,16725,7126],{"encoding":1321}," při jednotkové změně ",[1296,16728,16730],{"className":16729},[1299],[1301,16731,16732],{"xmlns":1303},[1305,16733,16734,16738],{},[1308,16735,16736],{},[1314,16737,6716],{},[1319,16739,6716],{"encoding":1321},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[16742,16743,16745],"h3",{"id":16744},"v-r","V R",[1148,16747,16748,16749,16752,16753,16756],{},"Vstupní data se nahrají buď ze souboru (",[3468,16750,16751],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3468,16754,16755],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3692,16758,16760],{"className":3694,"code":16759,"language":71,"meta":1452,"style":1452},"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",[3468,16761,16762,16797,16838,16859],{"__ignoreMap":1452},[1296,16763,16764,16767,16769,16771,16773,16775,16777,16779,16781,16783,16785,16787,16789,16791,16793,16795],{"class":3700,"line":10},[1296,16765,16766],{"class":3703},"pocet_clenu",[1296,16768,3708],{"class":3707},[1296,16770,3834],{"class":3711},[1296,16772,1873],{"class":3715},[1296,16774,1792],{"class":3723},[1296,16776,1795],{"class":3707},[1296,16778,4179],{"class":3723},[1296,16780,1795],{"class":3707},[1296,16782,10850],{"class":3723},[1296,16784,1795],{"class":3707},[1296,16786,3799],{"class":3723},[1296,16788,1795],{"class":3707},[1296,16790,9989],{"class":3723},[1296,16792,1795],{"class":3707},[1296,16794,12223],{"class":3723},[1296,16796,3900],{"class":3715},[1296,16798,16799,16802,16804,16806,16808,16811,16813,16816,16818,16821,16823,16826,16828,16831,16833,16836],{"class":3700,"line":27},[1296,16800,16801],{"class":3703},"tydenni_vydaje",[1296,16803,3708],{"class":3707},[1296,16805,3834],{"class":3711},[1296,16807,1873],{"class":3715},[1296,16809,16810],{"class":3723},"490",[1296,16812,1795],{"class":3707},[1296,16814,16815],{"class":3723}," 820",[1296,16817,1795],{"class":3707},[1296,16819,16820],{"class":3723}," 1230",[1296,16822,1795],{"class":3707},[1296,16824,16825],{"class":3723}," 1570",[1296,16827,1795],{"class":3707},[1296,16829,16830],{"class":3723}," 1950",[1296,16832,1795],{"class":3707},[1296,16834,16835],{"class":3723}," 2320",[1296,16837,3900],{"class":3715},[1296,16839,16840,16842,16844,16847,16849,16851,16854,16857],{"class":3700,"line":148},[1296,16841,786],{"class":3703},[1296,16843,3708],{"class":3707},[1296,16845,16846],{"class":3711}," lm",[1296,16848,1873],{"class":3715},[1296,16850,16801],{"class":3703},[1296,16852,16853],{"class":3707}," ~",[1296,16855,16856],{"class":3703}," pocet_clenu",[1296,16858,3900],{"class":3715},[1296,16860,16861,16864,16866,16868],{"class":3700,"line":111},[1296,16862,16863],{"class":3711},"summary",[1296,16865,1873],{"class":3715},[1296,16867,786],{"class":3703},[1296,16869,3900],{"class":3715},[3692,16871,16874],{"className":16872,"code":16873,"language":3922,"meta":1452},[3920],"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",[3468,16875,16873],{"__ignoreMap":1452},[1148,16877,16878,16879,16911,16912,16915,16916,16946,16947,16977,16978,16981,16982,17005],{},"Odhadnutý model je ",[1296,16880,16882],{"className":16881},[1299],[1301,16883,16884],{"xmlns":1303},[1305,16885,16886,16908],{},[1308,16887,16888,16894,16896,16899,16901,16904,16906],{},[2722,16889,16890,16892],{"accent":1530},[1314,16891,7126],{},[1685,16893,2728],{},[1685,16895,1980],{},[1562,16897,16898],{},"108,7",[1685,16900,5474],{},[1562,16902,16903],{},"368,0",[2907,16905,2909],{},[1314,16907,6716],{},[1319,16909,16910],{"encoding":1321},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3468,16913,16914],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1296,16917,16919],{"className":16918},[1299],[1301,16920,16921],{"xmlns":1303},[1305,16922,16923,16943],{},[1308,16924,16925,16931,16933,16939,16941],{},[1311,16926,16927,16929],{},[1314,16928,1560],{},[1562,16930,1564],{},[1685,16932,1956],{},[1311,16934,16935,16937],{},[1314,16936,16333],{},[1314,16938,1876],{},[1685,16940,1980],{},[1562,16942,1564],{},[1319,16944,16945],{"encoding":1321},"H_0:\\beta_i=0"," proti ",[1296,16948,16950],{"className":16949},[1299],[1301,16951,16952],{"xmlns":1303},[1305,16953,16954,16974],{},[1308,16955,16956,16962,16964,16970,16972],{},[1311,16957,16958,16960],{},[1314,16959,1560],{},[1562,16961,1792],{},[1685,16963,1956],{},[1311,16965,16966,16968],{},[1314,16967,16333],{},[1314,16969,1876],{},[1685,16971,10951],{"mathvariant":2119},[1562,16973,1564],{},[1319,16975,16976],{"encoding":1321},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3468,16979,16980],{},"Multiple R-squared"," je index determinace ",[1296,16983,16985],{"className":16984},[1299],[1301,16986,16987],{"xmlns":1303},[1305,16988,16989,17002],{},[1308,16990,16991,16997,16999],{},[1579,16992,16993,16995],{},[1314,16994,10218],{},[1562,16996,1586],{},[1685,16998,1980],{},[1562,17000,17001],{},"0,9995",[1319,17003,17004],{"encoding":1321},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1148,17007,17008],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3692,17010,17012],{"className":3694,"code":17011,"language":71,"meta":1452,"style":1452},"coef(model)\nfitted(model)\nresiduals(model)\n",[3468,17013,17014,17025,17036],{"__ignoreMap":1452},[1296,17015,17016,17019,17021,17023],{"class":3700,"line":10},[1296,17017,17018],{"class":3711},"coef",[1296,17020,1873],{"class":3715},[1296,17022,786],{"class":3703},[1296,17024,3900],{"class":3715},[1296,17026,17027,17030,17032,17034],{"class":3700,"line":27},[1296,17028,17029],{"class":3711},"fitted",[1296,17031,1873],{"class":3715},[1296,17033,786],{"class":3703},[1296,17035,3900],{"class":3715},[1296,17037,17038,17041,17043,17045],{"class":3700,"line":148},[1296,17039,17040],{"class":3711},"residuals",[1296,17042,1873],{"class":3715},[1296,17044,786],{"class":3703},[1296,17046,3900],{"class":3715},[3692,17048,17051],{"className":17049,"code":17050,"language":3922,"meta":1452},[3920],"(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",[3468,17052,17050],{"__ignoreMap":1452},[1148,17054,17055,17058,17059,1323,17085,17088,17089,17111,17112,1323,17130,17133,17134,17171],{},[3468,17056,17057],{},"coef()"," vrací odhadnuté parametry ",[1296,17060,17062],{"className":17061},[1299],[1301,17063,17064],{"xmlns":1303},[1305,17065,17066,17082],{},[1308,17067,17068,17074,17076],{},[1311,17069,17070,17072],{},[1314,17071,11499],{},[1562,17073,1564],{},[1685,17075,1795],{"separator":1530},[1311,17077,17078,17080],{},[1314,17079,11499],{},[1562,17081,1792],{},[1319,17083,17084],{"encoding":1321},"b_0,b_1",[3468,17086,17087],{},"fitted()"," predikce ",[1296,17090,17092],{"className":17091},[1299],[1301,17093,17094],{"xmlns":1303},[1305,17095,17096,17108],{},[1308,17097,17098],{},[1311,17099,17100,17106],{},[2722,17101,17102,17104],{"accent":1530},[1314,17103,7126],{},[1685,17105,2728],{},[1314,17107,1876],{},[1319,17109,17110],{"encoding":1321},"\\hat y_i"," pro pozorované ",[1296,17113,17115],{"className":17114},[1299],[1301,17116,17117],{"xmlns":1303},[1305,17118,17119,17127],{},[1308,17120,17121],{},[1311,17122,17123,17125],{},[1314,17124,6716],{},[1314,17126,1876],{},[1319,17128,17129],{"encoding":1321},"x_i",[3468,17131,17132],{},"residuals()"," rezidua ",[1296,17135,17137],{"className":17136},[1299],[1301,17138,17139],{"xmlns":1303},[1305,17140,17141,17169],{},[1308,17142,17143,17149,17151,17157,17159],{},[1311,17144,17145,17147],{},[1314,17146,8587],{},[1314,17148,1876],{},[1685,17150,1980],{},[1311,17152,17153,17155],{},[1314,17154,7126],{},[1314,17156,1876],{},[1685,17158,3062],{},[1311,17160,17161,17167],{},[2722,17162,17163,17165],{"accent":1530},[1314,17164,7126],{},[1685,17166,2728],{},[1314,17168,1876],{},[1319,17170,16515],{"encoding":1321}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1148,17173,17174,17175,17188],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1296,17176,17178],{"className":17177},[1299],[1301,17179,17180],{"xmlns":1303},[1305,17181,17182,17186],{},[1308,17183,17184],{},[1314,17185,6716],{},[1319,17187,6716],{"encoding":1321}," (zde 7 a 8 členů domácnosti):",[3692,17190,17192],{"className":3694,"code":17191,"language":71,"meta":1452,"style":1452},"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",[3468,17193,17194,17214,17242,17281],{"__ignoreMap":1452},[1296,17195,17196,17199,17201,17203,17205,17208,17210,17212],{"class":3700,"line":10},[1296,17197,17198],{"class":3711},"confint",[1296,17200,1873],{"class":3715},[1296,17202,786],{"class":3703},[1296,17204,1795],{"class":3707},[1296,17206,17207],{"class":3703}," level",[1296,17209,3796],{"class":3707},[1296,17211,9994],{"class":3723},[1296,17213,3900],{"class":3715},[1296,17215,17216,17219,17221,17224,17226,17228,17230,17232,17234,17236,17238,17240],{"class":3700,"line":27},[1296,17217,17218],{"class":3703},"nove",[1296,17220,3708],{"class":3707},[1296,17222,17223],{"class":3711}," data.frame",[1296,17225,1873],{"class":3715},[1296,17227,16766],{"class":3703},[1296,17229,3796],{"class":3707},[1296,17231,3834],{"class":3711},[1296,17233,1873],{"class":3715},[1296,17235,13325],{"class":3723},[1296,17237,1795],{"class":3707},[1296,17239,15251],{"class":3723},[1296,17241,9488],{"class":3715},[1296,17243,17244,17247,17249,17251,17253,17256,17258,17261,17263,17266,17268,17271,17273,17275,17277,17279],{"class":3700,"line":148},[1296,17245,17246],{"class":3711},"predict",[1296,17248,1873],{"class":3715},[1296,17250,786],{"class":3703},[1296,17252,1795],{"class":3707},[1296,17254,17255],{"class":3703}," newdata",[1296,17257,3796],{"class":3707},[1296,17259,17260],{"class":3703}," nove",[1296,17262,1795],{"class":3707},[1296,17264,17265],{"class":3703}," interval",[1296,17267,3796],{"class":3707},[1296,17269,17270],{"class":3839}," \"confidence\"",[1296,17272,1795],{"class":3707},[1296,17274,17207],{"class":3703},[1296,17276,3796],{"class":3707},[1296,17278,9994],{"class":3723},[1296,17280,3900],{"class":3715},[1296,17282,17283,17285,17287,17289,17291,17293,17295,17297,17299,17301,17303,17306,17308,17310,17312,17314],{"class":3700,"line":111},[1296,17284,17246],{"class":3711},[1296,17286,1873],{"class":3715},[1296,17288,786],{"class":3703},[1296,17290,1795],{"class":3707},[1296,17292,17255],{"class":3703},[1296,17294,3796],{"class":3707},[1296,17296,17260],{"class":3703},[1296,17298,1795],{"class":3707},[1296,17300,17265],{"class":3703},[1296,17302,3796],{"class":3707},[1296,17304,17305],{"class":3839}," \"prediction\"",[1296,17307,1795],{"class":3707},[1296,17309,17207],{"class":3703},[1296,17311,3796],{"class":3707},[1296,17313,9994],{"class":3723},[1296,17315,3900],{"class":3715},[3692,17317,17320],{"className":17318,"code":17319,"language":3922,"meta":1452},[3920],"                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",[3468,17321,17319],{"__ignoreMap":1452},[1148,17323,17324,17327,17328,1651,17331,17344,17345,1323,17358,17361,17362,17365],{},[3468,17325,17326],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1108,17329,17330],{},"střední hodnotu",[1296,17332,17334],{"className":17333},[1299],[1301,17335,17336],{"xmlns":1303},[1305,17337,17338,17342],{},[1308,17339,17340],{},[1314,17341,7126],{},[1319,17343,7126],{"encoding":1321}," při daném ",[1296,17346,17348],{"className":17347},[1299],[1301,17349,17350],{"xmlns":1303},[1305,17351,17352,17356],{},[1308,17353,17354],{},[1314,17355,6716],{},[1319,17357,6716],{"encoding":1321},[3468,17359,17360],{},"interval = \"prediction\""," širší interval pro ",[1108,17363,17364],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[16742,17367,17369],{"id":17368},"diagnostika-modelu","Diagnostika modelu",[1148,17371,17372,17373,1323,17376,1370,17379,17382],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1108,17374,17375],{},"absenci autokorelace",[1108,17377,17378],{},"stálosti rozptylu (homoskedasticitě)",[1108,17380,17381],{},"normalitě",". V R se ověřují takto:",[3692,17384,17386],{"className":3694,"code":17385,"language":71,"meta":1452,"style":1452},"library(lmtest)\ndwtest(model)\n",[3468,17387,17388,17400],{"__ignoreMap":1452},[1296,17389,17390,17393,17395,17398],{"class":3700,"line":10},[1296,17391,17392],{"class":3707},"library",[1296,17394,1873],{"class":3715},[1296,17396,17397],{"class":3703},"lmtest",[1296,17399,3900],{"class":3715},[1296,17401,17402,17405,17407,17409],{"class":3700,"line":27},[1296,17403,17404],{"class":3711},"dwtest",[1296,17406,1873],{"class":3715},[1296,17408,786],{"class":3703},[1296,17410,3900],{"class":3715},[3692,17412,17415],{"className":17413,"code":17414,"language":3922,"meta":1452},[3920],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3468,17416,17414],{"__ignoreMap":1452},[1148,17418,17419,17420,17437,17438,17455,17456,17473],{},"Durbinův–Watsonův test má ",[1296,17421,17423],{"className":17422},[1299],[1301,17424,17425],{"xmlns":1303},[1305,17426,17427,17435],{},[1308,17428,17429],{},[1311,17430,17431,17433],{},[1314,17432,1560],{},[1562,17434,1564],{},[1319,17436,1567],{"encoding":1321},": v modelu není problém s autokorelací, proti ",[1296,17439,17441],{"className":17440},[1299],[1301,17442,17443],{"xmlns":1303},[1305,17444,17445,17453],{},[1308,17446,17447],{},[1311,17448,17449,17451],{},[1314,17450,1560],{},[1562,17452,1792],{},[1319,17454,2994],{"encoding":1321},": 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, ",[1296,17457,17459],{"className":17458},[1299],[1301,17460,17461],{"xmlns":1303},[1305,17462,17463,17471],{},[1308,17464,17465],{},[1311,17466,17467,17469],{},[1314,17468,1560],{},[1562,17470,1564],{},[1319,17472,1567],{"encoding":1321}," se nezamítá.",[3692,17475,17477],{"className":3694,"code":17476,"language":71,"meta":1452,"style":1452},"library(whitestrap)\nwhite_test(model)\n",[3468,17478,17479,17490],{"__ignoreMap":1452},[1296,17480,17481,17483,17485,17488],{"class":3700,"line":10},[1296,17482,17392],{"class":3707},[1296,17484,1873],{"class":3715},[1296,17486,17487],{"class":3703},"whitestrap",[1296,17489,3900],{"class":3715},[1296,17491,17492,17495,17497,17499],{"class":3700,"line":27},[1296,17493,17494],{"class":3711},"white_test",[1296,17496,1873],{"class":3715},[1296,17498,786],{"class":3703},[1296,17500,3900],{"class":3715},[3692,17502,17505],{"className":17503,"code":17504,"language":3922,"meta":1452},[3920],"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",[3468,17506,17504],{"__ignoreMap":1452},[1148,17508,17509,17510,17527,17528,17545,17546,17473],{},"Whiteův test má ",[1296,17511,17513],{"className":17512},[1299],[1301,17514,17515],{"xmlns":1303},[1305,17516,17517,17525],{},[1308,17518,17519],{},[1311,17520,17521,17523],{},[1314,17522,1560],{},[1562,17524,1564],{},[1319,17526,1567],{"encoding":1321},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1296,17529,17531],{"className":17530},[1299],[1301,17532,17533],{"xmlns":1303},[1305,17534,17535,17543],{},[1308,17536,17537],{},[1311,17538,17539,17541],{},[1314,17540,1560],{},[1562,17542,1792],{},[1319,17544,2994],{"encoding":1321},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1296,17547,17549],{"className":17548},[1299],[1301,17550,17551],{"xmlns":1303},[1305,17552,17553,17561],{},[1308,17554,17555],{},[1311,17556,17557,17559],{},[1314,17558,1560],{},[1562,17560,1564],{},[1319,17562,1567],{"encoding":1321},[3692,17564,17566],{"className":3694,"code":17565,"language":71,"meta":1452,"style":1452},"shapiro.test(residuals(model))\n",[3468,17567,17568],{"__ignoreMap":1452},[1296,17569,17570,17573,17575,17577,17579,17581],{"class":3700,"line":10},[1296,17571,17572],{"class":3711},"shapiro.test",[1296,17574,1873],{"class":3715},[1296,17576,17040],{"class":3711},[1296,17578,1873],{"class":3715},[1296,17580,786],{"class":3703},[1296,17582,9488],{"class":3715},[3692,17584,17587],{"className":17585,"code":17586,"language":3922,"meta":1452},[3920],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3468,17588,17586],{"__ignoreMap":1452},[1148,17590,17591,17592,17609],{},"Shapiro–Wilkův test má ",[1296,17593,17595],{"className":17594},[1299],[1301,17596,17597],{"xmlns":1303},[1305,17598,17599,17607],{},[1308,17600,17601],{},[1311,17602,17603,17605],{},[1314,17604,1560],{},[1562,17606,1564],{},[1319,17608,1567],{"encoding":1321},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1148,17611,17612],{},[4382,17613],{"alt":17614,"className":17615,"src":17616},"mask-ra-diagnostika-rezidui",[1245,4386],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1148,17618,17619],{},"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.",[1514,17621,17623,17630,17661,17696,17761],{"className":17622,"dataCallout":3475},[1517,3474],[1148,17624,17626,17629],{"className":17625},[1523],[1296,17627],{"className":17628,"ariaHidden":1530},[1527,3482,1529],"Příklad: Regresní přímka",[1148,17631,17632,17633,17646,17647,17660],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1296,17634,17636],{"className":17635},[1299],[1301,17637,17638],{"xmlns":1303},[1305,17639,17640,17644],{},[1308,17641,17642],{},[1314,17643,7126],{},[1319,17645,7126],{"encoding":1321},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1296,17648,17650],{"className":17649},[1299],[1301,17651,17652],{"xmlns":1303},[1305,17653,17654,17658],{},[1308,17655,17656],{},[1314,17657,6716],{},[1319,17659,6716],{"encoding":1321},") 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.",[1148,17662,17663,17664,1395],{},"Výsledek: ",[1296,17665,17667],{"className":17666},[1299],[1301,17668,17669],{"xmlns":1303},[1305,17670,17671,17693],{},[1308,17672,17673,17679,17681,17684,17686,17689,17691],{},[2722,17674,17675,17677],{"accent":1530},[1314,17676,7126],{},[1685,17678,2728],{},[1685,17680,1980],{},[1562,17682,17683],{},"32,74",[1685,17685,5474],{},[1562,17687,17688],{},"2,15",[2907,17690,2909],{},[1314,17692,6716],{},[1319,17694,17695],{"encoding":1321},"\\hat y = 32{,}74 + 2{,}15\\,x",[1148,17697,16693,17698,17720,17721,17760],{},[1296,17699,17701],{"className":17700},[1299],[1301,17702,17703],{"xmlns":1303},[1305,17704,17705,17717],{},[1308,17706,17707,17713,17715],{},[1311,17708,17709,17711],{},[1314,17710,11499],{},[1562,17712,1792],{},[1685,17714,1980],{},[1562,17716,17688],{},[1319,17718,17719],{"encoding":1321},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1296,17722,17724],{"className":17723},[1299],[1301,17725,17726],{"xmlns":1303},[1305,17727,17728,17757],{},[1308,17729,17730,17732,17734,17736,17738,17740,17742,17744,17746,17748,17750,17753,17755],{},[1562,17731,17688],{},[1685,17733,8106],{},[1562,17735,1792],{},[2907,17737,2909],{},[1562,17739,11317],{},[2907,17741,2909],{},[1562,17743,11317],{},[1685,17745,1980],{},[1562,17747,1586],{},[2907,17749,2909],{},[1562,17751,17752],{},"150",[2907,17754,2909],{},[1562,17756,11317],{},[1319,17758,17759],{"encoding":1321},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1148,17762,17763,17764,3987,17783,17831,17832,16089],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1296,17765,17767],{"className":17766},[1299],[1301,17768,17769],{"xmlns":1303},[1305,17770,17771,17780],{},[1308,17772,17773,17775,17777],{},[1314,17774,6716],{},[1685,17776,1980],{},[1562,17778,17779],{},"34",[1319,17781,17782],{"encoding":1321},"x=34",[1296,17784,17786],{"className":17785},[1299],[1301,17787,17788],{"xmlns":1303},[1305,17789,17790,17828],{},[1308,17791,17792,17802,17804,17810,17812,17818,17820,17822,17825],{},[1311,17793,17794,17800],{},[2722,17795,17796,17798],{"accent":1530},[1314,17797,7126],{},[1685,17799,2728],{},[1562,17801,3543],{},[1685,17803,1980],{},[1311,17805,17806,17808],{},[1314,17807,11499],{},[1562,17809,1564],{},[1685,17811,5474],{},[1311,17813,17814,17816],{},[1314,17815,11499],{},[1562,17817,1792],{},[1685,17819,8106],{},[1562,17821,17779],{},[1685,17823,17824],{},"≐",[1562,17826,17827],{},"105,81",[1319,17829,17830],{"encoding":1321},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1296,17833,17835],{"className":17834},[1299],[1301,17836,17837],{"xmlns":1303},[1305,17838,17839,17856],{},[1308,17840,17841,17843,17845,17847,17849,17851,17853],{},[1562,17842,17683],{},[1685,17844,5474],{},[1562,17846,17688],{},[1685,17848,8106],{},[1562,17850,17779],{},[1685,17852,17824],{},[1562,17854,17855],{},"105,8",[1319,17857,17858],{"encoding":1321},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1143,17860,17862],{"id":17861},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1148,17864,17865,17866,17869,17870,17937,17938,17956,17957,17974],{},"Když přímka závislost nevystihuje, nabízí se další ",[1108,17867,17868],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1296,17871,17873],{"className":17872},[1299],[1301,17874,17875],{"xmlns":1303},[1305,17876,17877,17934],{},[1308,17878,17879,17881,17883,17889,17891,17897,17903,17905,17907,17909,17911,17914,17916,17922,17928,17930,17932],{},[1314,17880,16318],{},[1685,17882,1980],{},[1311,17884,17885,17887],{},[1314,17886,16333],{},[1562,17888,1564],{},[1685,17890,5474],{},[1311,17892,17893,17895],{},[1314,17894,16333],{},[1562,17896,1792],{},[1311,17898,17899,17901],{},[1314,17900,6767],{},[1562,17902,1792],{},[1685,17904,1873],{"stretchy":1872},[1314,17906,6716],{},[1685,17908,1884],{"stretchy":1872},[1685,17910,5474],{},[1685,17912,17913],{},"⋯",[1685,17915,5474],{},[1311,17917,17918,17920],{},[1314,17919,16333],{},[1314,17921,1148],{},[1311,17923,17924,17926],{},[1314,17925,6767],{},[1314,17927,1148],{},[1685,17929,1873],{"stretchy":1872},[1314,17931,6716],{},[1685,17933,1884],{"stretchy":1872},[1319,17935,17936],{"encoding":1321},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1296,17939,17941],{"className":17940},[1299],[1301,17942,17943],{"xmlns":1303},[1305,17944,17945,17953],{},[1308,17946,17947],{},[1311,17948,17949,17951],{},[1314,17950,6767],{},[1314,17952,1876],{},[1319,17954,17955],{"encoding":1321},"f_i"," a neznámými parametry ",[1296,17958,17960],{"className":17959},[1299],[1301,17961,17962],{"xmlns":1303},[1305,17963,17964,17972],{},[1308,17965,17966],{},[1311,17967,17968,17970],{},[1314,17969,16333],{},[1314,17971,1876],{},[1319,17973,16379],{"encoding":1321},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1296,17976,17978],{"className":17977},[1299],[1301,17979,17980],{"xmlns":1303,"display":1962},[1305,17981,17982,18292],{},[17983,17984,17987,18060,18173,18232],"mtable",{"rowspacing":17985,"columnalign":17986,"columnspacing":6755},"0.25em","right left",[17988,17989,17990,18014],"mtr",{},[17991,17992,17993],"mtd",{},[3239,17994,17995],{"scriptlevel":1564,"displaystyle":1530},[1308,17996,17997,18011],{},[1308,17998,17999,18002,18008],{},[2907,18000,18001],{},"parabolick",[2722,18003,18004,18006],{"accent":1530},[2907,18005,1242],{},[1685,18007,11496],{},[2907,18009,18010],{}," regrese: ",[2010,18012],{"width":18013},"1em",[17991,18015,18016],{},[3239,18017,18018],{"scriptlevel":1564,"displaystyle":1530},[1308,18019,18020,18022,18028,18030,18036,18038,18044,18046,18048,18054],{},[1308,18021],{},[2722,18023,18024,18026],{"accent":1530},[1314,18025,7126],{},[1685,18027,2728],{},[1685,18029,1980],{},[1311,18031,18032,18034],{},[1314,18033,11499],{},[1562,18035,1564],{},[1685,18037,5474],{},[1311,18039,18040,18042],{},[1314,18041,11499],{},[1562,18043,1792],{},[1314,18045,6716],{},[1685,18047,5474],{},[1311,18049,18050,18052],{},[1314,18051,11499],{},[1562,18053,1586],{},[1579,18055,18056,18058],{},[1314,18057,6716],{},[1562,18059,1586],{},[17988,18061,18062,18109],{},[17991,18063,18064],{},[3239,18065,18066],{"scriptlevel":1564,"displaystyle":1530},[1308,18067,18068,18107],{},[1308,18069,18070,18073,18079,18082,18086,18089,18095,18098,18104],{},[2907,18071,18072],{},"polynomick",[2722,18074,18075,18077],{"accent":1530},[2907,18076,1242],{},[1685,18078,11496],{},[2907,18080,18081],{}," regrese ",[3239,18083,18084],{"scriptlevel":1564,"displaystyle":1872},[1314,18085,1148],{},[2907,18087,18088],{},"-t",[2722,18090,18091,18093],{"accent":1530},[2907,18092,8587],{},[1685,18094,11496],{},[2907,18096,18097],{},"ho stupn",[2722,18099,18100,18102],{"accent":1530},[2907,18101,8587],{},[1685,18103,11506],{},[2907,18105,18106],{},": ",[2010,18108],{"width":18013},[17991,18110,18111],{},[3239,18112,18113],{"scriptlevel":1564,"displaystyle":1530},[1308,18114,18115,18117,18123,18125,18131,18133,18139,18141,18143,18149,18155,18157,18159,18161,18167],{},[1308,18116],{},[2722,18118,18119,18121],{"accent":1530},[1314,18120,7126],{},[1685,18122,2728],{},[1685,18124,1980],{},[1311,18126,18127,18129],{},[1314,18128,11499],{},[1562,18130,1564],{},[1685,18132,5474],{},[1311,18134,18135,18137],{},[1314,18136,11499],{},[1562,18138,1792],{},[1314,18140,6716],{},[1685,18142,5474],{},[1311,18144,18145,18147],{},[1314,18146,11499],{},[1562,18148,1586],{},[1579,18150,18151,18153],{},[1314,18152,6716],{},[1562,18154,1586],{},[1685,18156,5474],{},[1685,18158,17913],{},[1685,18160,5474],{},[1311,18162,18163,18165],{},[1314,18164,11499],{},[1314,18166,1148],{},[1579,18168,18169,18171],{},[1314,18170,6716],{},[1314,18172,1148],{},[17988,18174,18175,18196],{},[17991,18176,18177],{},[3239,18178,18179],{"scriptlevel":1564,"displaystyle":1530},[1308,18180,18181,18194],{},[1308,18182,18183,18186,18192],{},[2907,18184,18185],{},"hyperbolick",[2722,18187,18188,18190],{"accent":1530},[2907,18189,1242],{},[1685,18191,11496],{},[2907,18193,18010],{},[2010,18195],{"width":18013},[17991,18197,18198],{},[3239,18199,18200],{"scriptlevel":1564,"displaystyle":1530},[1308,18201,18202,18204,18210,18212,18218,18220,18226],{},[1308,18203],{},[2722,18205,18206,18208],{"accent":1530},[1314,18207,7126],{},[1685,18209,2728],{},[1685,18211,1980],{},[1311,18213,18214,18216],{},[1314,18215,11499],{},[1562,18217,1564],{},[1685,18219,5474],{},[1311,18221,18222,18224],{},[1314,18223,11499],{},[1562,18225,1792],{},[2738,18227,18228,18230],{},[1562,18229,1792],{},[1314,18231,6716],{},[17988,18233,18234,18255],{},[17991,18235,18236],{},[3239,18237,18238],{"scriptlevel":1564,"displaystyle":1530},[1308,18239,18240,18253],{},[1308,18241,18242,18245,18251],{},[2907,18243,18244],{},"logaritmick",[2722,18246,18247,18249],{"accent":1530},[2907,18248,1242],{},[1685,18250,11496],{},[2907,18252,18010],{},[2010,18254],{"width":18013},[17991,18256,18257],{},[3239,18258,18259],{"scriptlevel":1564,"displaystyle":1530},[1308,18260,18261,18263,18269,18271,18277,18279,18285,18288,18290],{},[1308,18262],{},[2722,18264,18265,18267],{"accent":1530},[1314,18266,7126],{},[1685,18268,2728],{},[1685,18270,1980],{},[1311,18272,18273,18275],{},[1314,18274,11499],{},[1562,18276,1564],{},[1685,18278,5474],{},[1311,18280,18281,18283],{},[1314,18282,11499],{},[1562,18284,1792],{},[1314,18286,18287],{},"ln",[1685,18289,4489],{},[1314,18291,6716],{},[1319,18293,18294],{"encoding":1321},"\\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}",[1148,18296,18297,18298,18301,18302,18348,18349,1956],{},"Naproti tomu ",[1108,18299,18300],{},"nelineární funkce"," nelze do tvaru ",[1296,18303,18305],{"className":18304},[1299],[1301,18306,18307],{"xmlns":1303},[1305,18308,18309,18345],{},[1308,18310,18311,18313,18315,18321,18323,18329,18335,18337,18339,18341,18343],{},[1314,18312,16318],{},[1685,18314,1980],{},[1311,18316,18317,18319],{},[1314,18318,16333],{},[1562,18320,1564],{},[1685,18322,5474],{},[1311,18324,18325,18327],{},[1314,18326,16333],{},[1562,18328,1792],{},[1311,18330,18331,18333],{},[1314,18332,6767],{},[1562,18334,1792],{},[1685,18336,1873],{"stretchy":1872},[1314,18338,6716],{},[1685,18340,1884],{"stretchy":1872},[1685,18342,5474],{},[1685,18344,1798],{},[1319,18346,18347],{"encoding":1321},"\\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 ",[1108,18350,18351],{},"exponenciální regrese",[1296,18353,18355],{"className":18354},[1299],[1301,18356,18357],{"xmlns":1303,"display":1962},[1305,18358,18359,18391],{},[1308,18360,18361,18367,18369,18375,18377,18389],{},[2722,18362,18363,18365],{"accent":1530},[1314,18364,7126],{},[1685,18366,2728],{},[1685,18368,1980],{},[1311,18370,18371,18373],{},[1314,18372,11499],{},[1562,18374,1564],{},[1685,18376,8106],{},[3351,18378,18379,18381,18383],{},[1314,18380,11499],{},[1562,18382,1792],{},[1308,18384,18385,18387],{},[2907,18386,2909],{},[1314,18388,6716],{},[1314,18390,1395],{"mathvariant":2119},[1319,18392,18393],{"encoding":1321},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1148,18395,18396],{},[4382,18397],{"alt":18398,"className":18399,"src":18400},"mask-ra-nelinearni-krivky",[1245,4386],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[16742,18402,18404],{"id":18403},"v-r-parabolická-regrese","V R — parabolická regrese",[1148,18406,18407,18408,1956],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3468,18409,18410],{},"I(x^2)",[3692,18412,18414],{"className":3694,"code":18413,"language":71,"meta":1452,"style":1452},"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",[3468,18415,18416,18451,18491,18525],{"__ignoreMap":1452},[1296,18417,18418,18421,18423,18425,18427,18429,18431,18433,18435,18437,18439,18441,18443,18445,18447,18449],{"class":3700,"line":10},[1296,18419,18420],{"class":3703},"rok",[1296,18422,3708],{"class":3707},[1296,18424,3834],{"class":3711},[1296,18426,1873],{"class":3715},[1296,18428,1792],{"class":3723},[1296,18430,1795],{"class":3707},[1296,18432,4179],{"class":3723},[1296,18434,1795],{"class":3707},[1296,18436,10850],{"class":3723},[1296,18438,1795],{"class":3707},[1296,18440,3799],{"class":3723},[1296,18442,1795],{"class":3707},[1296,18444,9989],{"class":3723},[1296,18446,1795],{"class":3707},[1296,18448,12223],{"class":3723},[1296,18450,3900],{"class":3715},[1296,18452,18453,18455,18457,18459,18461,18464,18466,18469,18471,18474,18476,18479,18481,18484,18486,18489],{"class":3700,"line":27},[1296,18454,1088],{"class":3703},[1296,18456,3708],{"class":3707},[1296,18458,3834],{"class":3711},[1296,18460,1873],{"class":3715},[1296,18462,18463],{"class":3723},"112",[1296,18465,1795],{"class":3707},[1296,18467,18468],{"class":3723}," 149",[1296,18470,1795],{"class":3707},[1296,18472,18473],{"class":3723}," 238",[1296,18475,1795],{"class":3707},[1296,18477,18478],{"class":3723}," 354",[1296,18480,1795],{"class":3707},[1296,18482,18483],{"class":3723}," 580",[1296,18485,1795],{"class":3707},[1296,18487,18488],{"class":3723}," 867",[1296,18490,3900],{"class":3715},[1296,18492,18493,18496,18498,18500,18502,18504,18506,18509,18512,18515,18517,18519,18521,18523],{"class":3700,"line":148},[1296,18494,18495],{"class":3703},"model_parabola",[1296,18497,3708],{"class":3707},[1296,18499,16846],{"class":3711},[1296,18501,1873],{"class":3715},[1296,18503,1088],{"class":3703},[1296,18505,16853],{"class":3707},[1296,18507,18508],{"class":3703}," rok",[1296,18510,18511],{"class":3707}," +",[1296,18513,18514],{"class":3711}," I",[1296,18516,1873],{"class":3715},[1296,18518,18420],{"class":3703},[1296,18520,2728],{"class":3707},[1296,18522,1586],{"class":3723},[1296,18524,9488],{"class":3715},[1296,18526,18527,18529,18531,18533],{"class":3700,"line":111},[1296,18528,16863],{"class":3711},[1296,18530,1873],{"class":3715},[1296,18532,18495],{"class":3703},[1296,18534,3900],{"class":3715},[3692,18536,18539],{"className":18537,"code":18538,"language":3922,"meta":1452},[3920],"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",[3468,18540,18538],{"__ignoreMap":1452},[1148,18542,18543,18544,18589],{},"Odhadnutá parabola ",[1296,18545,18547],{"className":18546},[1299],[1301,18548,18549],{"xmlns":1303},[1305,18550,18551,18586],{},[1308,18552,18553,18559,18561,18564,18566,18569,18571,18573,18575,18578,18580],{},[2722,18554,18555,18557],{"accent":1530},[1314,18556,7126],{},[1685,18558,2728],{},[1685,18560,1980],{},[1562,18562,18563],{},"164,6",[1685,18565,3062],{},[1562,18567,18568],{},"76,6",[2907,18570,2909],{},[1314,18572,6716],{},[1685,18574,5474],{},[1562,18576,18577],{},"32,1",[2907,18579,2909],{},[1579,18581,18582,18584],{},[1314,18583,6716],{},[1562,18585,1586],{},[1319,18587,18588],{"encoding":1321},"\\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.",[16742,18591,18593],{"id":18592},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1148,18595,18596,18597,18599],{},"Nelineární funkce se v R odhadují funkcí ",[3468,18598,16104],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3692,18601,18603],{"className":3694,"code":18602,"language":71,"meta":1452,"style":1452},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3468,18604,18605,18615,18651],{"__ignoreMap":1452},[1296,18606,18607,18609,18611,18613],{"class":3700,"line":10},[1296,18608,17392],{"class":3707},[1296,18610,1873],{"class":3715},[1296,18612,16088],{"class":3703},[1296,18614,3900],{"class":3715},[1296,18616,18617,18620,18622,18625,18627,18629,18631,18634,18637,18640,18642,18645,18647,18649],{"class":3700,"line":27},[1296,18618,18619],{"class":3703},"model_exp",[1296,18621,3708],{"class":3707},[1296,18623,18624],{"class":3711}," nls2",[1296,18626,1873],{"class":3715},[1296,18628,1088],{"class":3703},[1296,18630,16853],{"class":3707},[1296,18632,18633],{"class":3703}," b1",[1296,18635,18636],{"class":3707}," *",[1296,18638,18639],{"class":3711}," exp",[1296,18641,1873],{"class":3715},[1296,18643,18644],{"class":3703},"b2",[1296,18646,18636],{"class":3707},[1296,18648,18508],{"class":3703},[1296,18650,9488],{"class":3715},[1296,18652,18653,18655,18657,18659],{"class":3700,"line":148},[1296,18654,16863],{"class":3711},[1296,18656,1873],{"class":3715},[1296,18658,18619],{"class":3703},[1296,18660,3900],{"class":3715},[3692,18662,18665],{"className":18663,"code":18664,"language":3922,"meta":1452},[3920],"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",[3468,18666,18664],{"__ignoreMap":1452},[1148,18668,18669,18670,1956],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1296,18671,18673],{"className":18672},[1299],[1301,18674,18675],{"xmlns":1303},[1305,18676,18677,18703],{},[1308,18678,18679,18685,18687,18693,18695],{},[2722,18680,18681,18683],{"accent":1530},[1314,18682,7126],{},[1685,18684,2728],{},[1685,18686,1980],{},[1311,18688,18689,18691],{},[1314,18690,11499],{},[1562,18692,1792],{},[1685,18694,8106],{},[3351,18696,18697,18699,18701],{},[1314,18698,11499],{},[1562,18700,1586],{},[1314,18702,6716],{},[1319,18704,18705],{"encoding":1321},"\\hat y=b_1\\cdot b_2^{x}",[3692,18707,18709],{"className":3694,"code":18708,"language":71,"meta":1452,"style":1452},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3468,18710,18711,18740],{"__ignoreMap":1452},[1296,18712,18713,18716,18718,18720,18722,18724,18726,18728,18730,18732,18734,18736,18738],{"class":3700,"line":10},[1296,18714,18715],{"class":3703},"model_pow",[1296,18717,3708],{"class":3707},[1296,18719,18624],{"class":3711},[1296,18721,1873],{"class":3715},[1296,18723,1088],{"class":3703},[1296,18725,16853],{"class":3707},[1296,18727,18633],{"class":3703},[1296,18729,18636],{"class":3707},[1296,18731,4604],{"class":3715},[1296,18733,18644],{"class":3703},[1296,18735,2728],{"class":3707},[1296,18737,18420],{"class":3703},[1296,18739,9488],{"class":3715},[1296,18741,18742,18744,18746,18748],{"class":3700,"line":27},[1296,18743,16863],{"class":3711},[1296,18745,1873],{"class":3715},[1296,18747,18715],{"class":3703},[1296,18749,3900],{"class":3715},[3692,18751,18754],{"className":18752,"code":18753,"language":3922,"meta":1452},[3920],"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",[3468,18755,18753],{"__ignoreMap":1452},[1148,18757,18758,18759,18823,18824,18848],{},"Obě varianty popisují stejnou křivku (",[1296,18760,18762],{"className":18761},[1299],[1301,18763,18764],{"xmlns":1303},[1305,18765,18766,18820],{},[1308,18767,18768,18785,18787],{},[3351,18769,18770,18772,18774],{},[1314,18771,11499],{},[1562,18773,1586],{},[1308,18775,18776,18779],{},[2907,18777,18778],{},"mocninn",[2722,18780,18781,18783],{"accent":1530},[2907,18782,7126],{},[1685,18784,11496],{},[1685,18786,1980],{},[1579,18788,18789,18791],{},[1314,18790,8587],{},[1308,18792,18793,18795],{},[2907,18794,2909],{},[3351,18796,18797,18799,18801],{},[1314,18798,11499],{},[1562,18800,1586],{},[1308,18802,18803,18806,18812,18814],{},[2907,18804,18805],{},"exponenci",[2722,18807,18808,18810],{"accent":1530},[2907,18809,1242],{},[1685,18811,11496],{},[2907,18813,18287],{},[2722,18815,18816,18818],{"accent":1530},[2907,18817,11746],{},[1685,18819,11496],{},[1319,18821,18822],{"encoding":1321},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1296,18825,18827],{"className":18826},[1299],[1301,18828,18829],{"xmlns":1303},[1305,18830,18831,18845],{},[1308,18832,18833,18840,18842],{},[1579,18834,18835,18837],{},[1314,18836,8587],{},[1562,18838,18839],{},"0,4316",[1685,18841,9435],{},[1562,18843,18844],{},"1,540",[1319,18846,18847],{"encoding":1321},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[16742,18850,18852],{"id":18851},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1148,18854,18855,18856,1956],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3468,18857,18858],{},"I(1\u002Fx)",[3692,18860,18862],{"className":3694,"code":18861,"language":71,"meta":1452,"style":1452},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3468,18863,18864,18891],{"__ignoreMap":1452},[1296,18865,18866,18869,18871,18873,18875,18877,18879,18881,18883,18885,18887,18889],{"class":3700,"line":10},[1296,18867,18868],{"class":3703},"model_hyperbola",[1296,18870,3708],{"class":3707},[1296,18872,16846],{"class":3711},[1296,18874,1873],{"class":3715},[1296,18876,16801],{"class":3703},[1296,18878,16853],{"class":3707},[1296,18880,18514],{"class":3711},[1296,18882,1873],{"class":3715},[1296,18884,1792],{"class":3723},[1296,18886,10070],{"class":3707},[1296,18888,16856],{"class":3703},[1296,18890,9488],{"class":3715},[1296,18892,18893,18895,18897,18899],{"class":3700,"line":27},[1296,18894,16863],{"class":3711},[1296,18896,1873],{"class":3715},[1296,18898,18868],{"class":3703},[1296,18900,3900],{"class":3715},[3692,18902,18905],{"className":18903,"code":18904,"language":3922,"meta":1452},[3920],"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",[3468,18906,18904],{"__ignoreMap":1452},[1148,18908,18909,18910,18944,18945,18966],{},"Model ",[1296,18911,18913],{"className":18912},[1299],[1301,18914,18915],{"xmlns":1303},[1305,18916,18917,18941],{},[1308,18918,18919,18925,18927,18930,18932],{},[2722,18920,18921,18923],{"accent":1530},[1314,18922,7126],{},[1685,18924,2728],{},[1685,18926,1980],{},[1562,18928,18929],{},"2180,7",[1685,18931,3062],{},[3239,18933,18934],{"scriptlevel":1564,"displaystyle":1530},[2738,18935,18936,18939],{},[1562,18937,18938],{},"1920,0",[1314,18940,6716],{},[1319,18942,18943],{"encoding":1321},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1296,18946,18948],{"className":18947},[1299],[1301,18949,18950],{"xmlns":1303},[1305,18951,18952,18964],{},[1308,18953,18954,18960,18962],{},[1579,18955,18956,18958],{},[1314,18957,10218],{},[1562,18959,1586],{},[1685,18961,1980],{},[1562,18963,17001],{},[1319,18965,17004],{"encoding":1321},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1514,18968,18970,18977,19008,19056],{"className":18969,"dataCallout":3475},[1517,3474],[1148,18971,18973,18976],{"className":18972},[1523],[1296,18974],{"className":18975,"ariaHidden":1530},[1527,3482,1529],"Příklad: Parabolická regrese",[1148,18978,18979,18980,18993,18994,19007],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1296,18981,18983],{"className":18982},[1299],[1301,18984,18985],{"xmlns":1303},[1305,18986,18987,18991],{},[1308,18988,18989],{},[1314,18990,6716],{},[1319,18992,6716],{"encoding":1321},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1296,18995,18997],{"className":18996},[1299],[1301,18998,18999],{"xmlns":1303},[1305,19000,19001,19005],{},[1308,19002,19003],{},[1314,19004,7126],{},[1319,19006,7126],{"encoding":1321},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1148,19009,17663,19010,1395],{},[1296,19011,19013],{"className":19012},[1299],[1301,19014,19015],{"xmlns":1303},[1305,19016,19017,19053],{},[1308,19018,19019,19025,19027,19029,19032,19034,19037,19039,19041,19043,19045,19047],{},[2722,19020,19021,19023],{"accent":1530},[1314,19022,7126],{},[1685,19024,2728],{},[1685,19026,1980],{},[1685,19028,3062],{},[1562,19030,19031],{},"60,3",[1685,19033,5474],{},[1562,19035,19036],{},"4,55",[2907,19038,2909],{},[1314,19040,6716],{},[1685,19042,3062],{},[1562,19044,3983],{},[2907,19046,2909],{},[1579,19048,19049,19051],{},[1314,19050,6716],{},[1562,19052,1586],{},[1319,19054,19055],{"encoding":1321},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1148,19057,19058,19059,19077],{},"Záporný koeficient ",[1296,19060,19062],{"className":19061},[1299],[1301,19063,19064],{"xmlns":1303},[1305,19065,19066,19074],{},[1308,19067,19068],{},[1311,19069,19070,19072],{},[1314,19071,11499],{},[1562,19073,1586],{},[1319,19075,19076],{"encoding":1321},"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.",[1514,19079,19081,19088,19118,19163],{"className":19080,"dataCallout":3475},[1517,3474],[1148,19082,19084,19087],{"className":19083},[1523],[1296,19085],{"className":19086,"ariaHidden":1530},[1527,3482,1529],"Příklad: Hyperbolická regrese",[1148,19089,19090,19091,19104,19105,16089],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1296,19092,19094],{"className":19093},[1299],[1301,19095,19096],{"xmlns":1303},[1305,19097,19098,19102],{},[1308,19099,19100],{},[1314,19101,7126],{},[1319,19103,7126],{"encoding":1321},") na objemu produkce v tisících kusů (proměnná ",[1296,19106,19108],{"className":19107},[1299],[1301,19109,19110],{"xmlns":1303},[1305,19111,19112,19116],{},[1308,19113,19114],{},[1314,19115,6716],{},[1319,19117,6716],{"encoding":1321},[1148,19119,17663,19120,1395],{},[1296,19121,19123],{"className":19122},[1299],[1301,19124,19125],{"xmlns":1303},[1305,19126,19127,19160],{},[1308,19128,19129,19135,19137,19139,19142,19144],{},[2722,19130,19131,19133],{"accent":1530},[1314,19132,7126],{},[1685,19134,2728],{},[1685,19136,1980],{},[1685,19138,3062],{},[1562,19140,19141],{},"96,78",[1685,19143,5474],{},[3239,19145,19146],{"scriptlevel":1564,"displaystyle":1530},[2738,19147,19148,19158],{},[1308,19149,19150,19153,19155],{},[1562,19151,19152],{},"250",[2907,19154,2909],{},[1562,19156,19157],{},"528,88",[1314,19159,6716],{},[1319,19161,19162],{"encoding":1321},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1148,19164,19165,19166,19183],{},"Záporná hodnota ",[1296,19167,19169],{"className":19168},[1299],[1301,19170,19171],{"xmlns":1303},[1305,19172,19173,19181],{},[1308,19174,19175],{},[1311,19176,19177,19179],{},[1314,19178,11499],{},[1562,19180,1792],{},[1319,19182,16711],{"encoding":1321}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1143,19185,19187],{"id":19186},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1148,19189,19190,19191,1956],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1108,19192,16002],{},[1296,19194,19196],{"className":19195},[1299],[1301,19197,19198],{"xmlns":1303,"display":1962},[1305,19199,19200,19268],{},[1308,19201,19202,19208,19210,19232,19234,19236,19238,19266],{},[1579,19203,19204,19206],{},[1314,19205,10218],{},[1562,19207,1586],{},[1685,19209,1980],{},[2738,19211,19212,19224],{},[3351,19213,19214,19216,19222],{},[1314,19215,1852],{},[2722,19217,19218,19220],{"accent":1530},[1314,19219,7126],{},[1685,19221,2728],{},[1562,19223,1586],{},[3351,19225,19226,19228,19230],{},[1314,19227,1852],{},[1314,19229,7126],{},[1562,19231,1586],{},[1685,19233,1980],{},[1562,19235,1792],{},[1685,19237,3062],{},[2738,19239,19240,19258],{},[3351,19241,19242,19244,19256],{},[1314,19243,1852],{},[1308,19245,19246,19248,19250],{},[1314,19247,7126],{},[1685,19249,3062],{},[2722,19251,19252,19254],{"accent":1530},[1314,19253,7126],{},[1685,19255,2728],{},[1562,19257,1586],{},[3351,19259,19260,19262,19264],{},[1314,19261,1852],{},[1314,19263,7126],{},[1562,19265,1586],{},[1314,19267,1395],{"mathvariant":2119},[1319,19269,19270],{"encoding":1321},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1148,19272,19273,19274,19291,19292,19305],{},"Čím blíž je ",[1296,19275,19277],{"className":19276},[1299],[1301,19278,19279],{"xmlns":1303},[1305,19280,19281,19289],{},[1308,19282,19283],{},[1579,19284,19285,19287],{},[1314,19286,10218],{},[1562,19288,1586],{},[1319,19290,16020],{"encoding":1321}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1296,19293,19295],{"className":19294},[1299],[1301,19296,19297],{"xmlns":1303},[1305,19298,19299,19303],{},[1308,19300,19301],{},[1314,19302,7126],{},[1319,19304,7126],{"encoding":1321}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1148,19307,19308,19309,1651,19311,19334,19335,1956],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1108,19310,16024],{},[1296,19312,19314],{"className":19313},[1299],[1301,19315,19316],{"xmlns":1303},[1305,19317,19318,19332],{},[1308,19319,19320,19322,19324],{},[1314,19321,11195],{},[1685,19323,1980],{},[4452,19325,19326],{},[1579,19327,19328,19330],{},[1314,19329,10218],{},[1562,19331,1586],{},[1319,19333,16048],{"encoding":1321},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1108,19336,16052],{},[1296,19338,19340],{"className":19339},[1299],[1301,19341,19342],{"xmlns":1303,"display":1962},[1305,19343,19344,19394],{},[1308,19345,19346,19356,19358,19392],{},[1311,19347,19348,19350],{},[1314,19349,71],{},[1308,19351,19352,19354],{},[1314,19353,6716],{},[1314,19355,7126],{},[1685,19357,1980],{},[2738,19359,19360,19370],{},[1311,19361,19362,19364],{},[1314,19363,1852],{},[1308,19365,19366,19368],{},[1314,19367,6716],{},[1314,19369,7126],{},[4452,19371,19372],{},[1308,19373,19374,19382,19384],{},[3351,19375,19376,19378,19380],{},[1314,19377,1852],{},[1314,19379,6716],{},[1562,19381,1586],{},[1685,19383,8106],{},[3351,19385,19386,19388,19390],{},[1314,19387,1852],{},[1314,19389,7126],{},[1562,19391,1586],{},[1314,19393,1395],{"mathvariant":2119},[1319,19395,19396],{"encoding":1321},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1148,19398,19399,19400,19416,19417,19433],{},"Koeficient korelace nabývá hodnot od ",[1296,19401,19403],{"className":19402},[1299],[1301,19404,19405],{"xmlns":1303},[1305,19406,19407,19413],{},[1308,19408,19409,19411],{},[1685,19410,3062],{},[1562,19412,1792],{},[1319,19414,19415],{"encoding":1321},"-1"," do ",[1296,19418,19420],{"className":19419},[1299],[1301,19421,19422],{"xmlns":1303},[1305,19423,19424,19430],{},[1308,19425,19426,19428],{},[1685,19427,5474],{},[1562,19429,1792],{},[1319,19431,19432],{"encoding":1321},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1148,19435,19436],{},[4382,19437],{"alt":19438,"className":19439,"src":19440},"mask-ra-korelace-sila",[1245,4386],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1148,19442,19443,19444,19457,19458,19476,19477,1370,19490,19503],{},"S rostoucí absolutní hodnotou ",[1296,19445,19447],{"className":19446},[1299],[1301,19448,19449],{"xmlns":1303},[1305,19450,19451,19455],{},[1308,19452,19453],{},[1314,19454,71],{},[1319,19456,71],{"encoding":1321}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1296,19459,19461],{"className":19460},[1299],[1301,19462,19463],{"xmlns":1303},[1305,19464,19465,19473],{},[1308,19466,19467,19469,19471],{},[1314,19468,71],{},[1685,19470,9435],{},[1562,19472,1564],{},[1319,19474,19475],{"encoding":1321},"r\\approx 0"," je mezi ",[1296,19478,19480],{"className":19479},[1299],[1301,19481,19482],{"xmlns":1303},[1305,19483,19484,19488],{},[1308,19485,19486],{},[1314,19487,6716],{},[1319,19489,6716],{"encoding":1321},[1296,19491,19493],{"className":19492},[1299],[1301,19494,19495],{"xmlns":1303},[1305,19496,19497,19501],{},[1308,19498,19499],{},[1314,19500,7126],{},[1319,19502,7126],{"encoding":1321}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[16742,19505,16745],{"id":19506},"v-r-1",[3692,19508,19510],{"className":3694,"code":19509,"language":71,"meta":1452,"style":1452},"cor(pocet_clenu, tydenni_vydaje)\n",[3468,19511,19512],{"__ignoreMap":1452},[1296,19513,19514,19517,19519,19521,19523,19526],{"class":3700,"line":10},[1296,19515,19516],{"class":3711},"cor",[1296,19518,1873],{"class":3715},[1296,19520,16766],{"class":3703},[1296,19522,1795],{"class":3707},[1296,19524,19525],{"class":3703}," tydenni_vydaje",[1296,19527,3900],{"class":3715},[3692,19529,19532],{"className":19530,"code":19531,"language":3922,"meta":1452},[3920],"[1] 0.9997441\n",[3468,19533,19531],{"__ignoreMap":1452},[1148,19535,19536,19537,19563],{},"Hodnota 0,9997 odpovídá ",[1296,19538,19540],{"className":19539},[1299],[1301,19541,19542],{"xmlns":1303},[1305,19543,19544,19560],{},[1308,19545,19546,19554,19556],{},[4452,19547,19548],{},[1579,19549,19550,19552],{},[1314,19551,10218],{},[1562,19553,1586],{},[1685,19555,1980],{},[4452,19557,19558],{},[1562,19559,17001],{},[1319,19561,19562],{"encoding":1321},"\\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.",[1514,19565,19567,19574,19577],{"className":19566,"dataCallout":3475},[1517,3474],[1148,19568,19570,19573],{"className":19569},[1523],[1296,19571],{"className":19572,"ariaHidden":1530},[1527,3482,1529],"Příklad: Koeficient korelace",[1148,19575,19576],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1148,19578,17663,19579,19606],{},[1296,19580,19582],{"className":19581},[1299],[1301,19583,19584],{"xmlns":1303},[1305,19585,19586,19603],{},[1308,19587,19588,19598,19600],{},[1311,19589,19590,19592],{},[1314,19591,71],{},[1308,19593,19594,19596],{},[1314,19595,6716],{},[1314,19597,7126],{},[1685,19599,1980],{},[1562,19601,19602],{},"0,739",[1319,19604,19605],{"encoding":1321},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1143,19608,19610],{"id":19609},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1148,19612,19613,19614,19627],{},"Pokud na závisle proměnnou ",[1296,19615,19617],{"className":19616},[1299],[1301,19618,19619],{"xmlns":1303},[1305,19620,19621,19625],{},[1308,19622,19623],{},[1314,19624,7126],{},[1319,19626,7126],{"encoding":1321}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1296,19629,19631],{"className":19630},[1299],[1301,19632,19633],{"xmlns":1303,"display":1962},[1305,19634,19635,19745],{},[1308,19636,19637,19639,19641,19647,19649,19655,19661,19663,19669,19675,19677,19679,19681,19687,19693,19695,19697,19703,19705,19711,19713,19719,19725,19727,19729,19731,19737,19743],{},[1314,19638,16318],{},[1685,19640,1980],{},[1311,19642,19643,19645],{},[1314,19644,16333],{},[1562,19646,1564],{},[1685,19648,5474],{},[1311,19650,19651,19653],{},[1314,19652,16333],{},[1562,19654,1792],{},[1311,19656,19657,19659],{},[1314,19658,6716],{},[1562,19660,1792],{},[1685,19662,5474],{},[1311,19664,19665,19667],{},[1314,19666,16333],{},[1562,19668,1586],{},[1311,19670,19671,19673],{},[1314,19672,6716],{},[1562,19674,1586],{},[1685,19676,5474],{},[1685,19678,17913],{},[1685,19680,5474],{},[1311,19682,19683,19685],{},[1314,19684,16333],{},[1314,19686,1148],{},[1311,19688,19689,19691],{},[1314,19690,6716],{},[1314,19692,1148],{},[1685,19694,1795],{"separator":1530},[2010,19696],{"width":2012},[2722,19698,19699,19701],{"accent":1530},[1314,19700,7126],{},[1685,19702,2728],{},[1685,19704,1980],{},[1311,19706,19707,19709],{},[1314,19708,11499],{},[1562,19710,1564],{},[1685,19712,5474],{},[1311,19714,19715,19717],{},[1314,19716,11499],{},[1562,19718,1792],{},[1311,19720,19721,19723],{},[1314,19722,6716],{},[1562,19724,1792],{},[1685,19726,5474],{},[1685,19728,17913],{},[1685,19730,5474],{},[1311,19732,19733,19735],{},[1314,19734,11499],{},[1314,19736,1148],{},[1311,19738,19739,19741],{},[1314,19740,6716],{},[1314,19742,1148],{},[1314,19744,1395],{"mathvariant":2119},[1319,19746,19747],{"encoding":1321},"\\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.",[16742,19749,19751],{"id":19750},"výběr-proměnných","Výběr proměnných",[1102,19753,19754,19760],{},[1105,19755,19756,19759],{},[1108,19757,19758],{},"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.",[1105,19761,19762,19765,19766,19769,19770,19773],{},[1108,19763,19764],{},"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 ",[1108,19767,19768],{},"forward"," proměnné postupně přidává, varianta ",[1108,19771,19772],{},"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.",[16742,19775,19777],{"id":19776},"postup-odhadu","Postup odhadu",[1237,19779,19780,19783,19786],{},[1105,19781,19782],{},"ověření předpokladů regresního modelu,",[1105,19784,19785],{},"samotný odhad parametrů,",[1105,19787,19788],{},"reziduální analýza výsledného modelu.",[1148,19790,19791,19792,19809,19810,3987,19812,19841,19842,19871,19872,19889],{},"Důležitost každého parametru ",[1296,19793,19795],{"className":19794},[1299],[1301,19796,19797],{"xmlns":1303},[1305,19798,19799,19807],{},[1308,19800,19801],{},[1311,19802,19803,19805],{},[1314,19804,11499],{},[1314,19806,1876],{},[1319,19808,16458],{"encoding":1321}," v modelu ověřuje ",[1108,19811,992],{},[1296,19813,19815],{"className":19814},[1299],[1301,19816,19817],{"xmlns":1303},[1305,19818,19819,19839],{},[1308,19820,19821,19827,19829,19835,19837],{},[1311,19822,19823,19825],{},[1314,19824,1560],{},[1562,19826,1564],{},[1685,19828,1956],{},[1311,19830,19831,19833],{},[1314,19832,16333],{},[1314,19834,1876],{},[1685,19836,1980],{},[1562,19838,1564],{},[1319,19840,16945],{"encoding":1321}," (proměnná je v modelu nevýznamná) proti ",[1296,19843,19845],{"className":19844},[1299],[1301,19846,19847],{"xmlns":1303},[1305,19848,19849,19869],{},[1308,19850,19851,19857,19859,19865,19867],{},[1311,19852,19853,19855],{},[1314,19854,1560],{},[1562,19856,1792],{},[1685,19858,1956],{},[1311,19860,19861,19863],{},[1314,19862,16333],{},[1314,19864,1876],{},[1685,19866,10951],{"mathvariant":2119},[1562,19868,1564],{},[1319,19870,16976],{"encoding":1321}," (proměnná je významná). Při nezamítnutí ",[1296,19873,19875],{"className":19874},[1299],[1301,19876,19877],{"xmlns":1303},[1305,19878,19879,19887],{},[1308,19880,19881],{},[1311,19882,19883,19885],{},[1314,19884,1560],{},[1562,19886,1564],{},[1319,19888,1567],{"encoding":1321}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[16742,19891,19893],{"id":19892},"předpoklady-modelu","Předpoklady modelu",[1237,19895,19896,19913,19946,19952,19955,19958],{},[1105,19897,19898,19899,19912],{},"Závisle proměnná ",[1296,19900,19902],{"className":19901},[1299],[1301,19903,19904],{"xmlns":1303},[1305,19905,19906,19910],{},[1308,19907,19908],{},[1314,19909,7126],{},[1319,19911,7126],{"encoding":1321}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1105,19914,19915,19916,19945],{},"Nezávislé proměnné ",[1296,19917,19919],{"className":19918},[1299],[1301,19920,19921],{"xmlns":1303},[1305,19922,19923,19943],{},[1308,19924,19925,19931,19933,19935,19937],{},[1311,19926,19927,19929],{},[1314,19928,6716],{},[1562,19930,1792],{},[1685,19932,1795],{"separator":1530},[1685,19934,1798],{},[1685,19936,1795],{"separator":1530},[1311,19938,19939,19941],{},[1314,19940,6716],{},[1314,19942,1148],{},[1319,19944,16282],{"encoding":1321}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1105,19947,19948,19949,1395],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1108,19950,19951],{},"multikolinearita",[1105,19953,19954],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1105,19956,19957],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1105,19959,19960,19961,19965],{},"Proměnné mají mít ",[1242,19962,19964],{"className":19963,"dataFsResolvedFilePath":1246,"href":1247},[1245],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1148,19967,19968,19969,19972],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1242,19970,1722],{"className":19971,"dataFsResolvedFilePath":1264,"href":1265},[1245],") — 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.",[16742,19974,19975],{"id":19951},"Multikolinearita",[1148,19977,19978],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1102,19980,19981,19984,19987],{},[1105,19982,19983],{},"výsledky regrese jsou pak nespolehlivé,",[1105,19985,19986],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1105,19988,19989],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1148,19991,19992,19993,19996,19997,20020,20021,20039,20040,20056],{},"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 ",[1108,19994,19995],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1296,19998,20000],{"className":19999},[1299],[1301,20001,20002],{"xmlns":1303},[1305,20003,20004,20017],{},[1308,20005,20006,20008,20010,20013,20015],{},[1562,20007,1792],{},[1685,20009,4331],{},[2907,20011,20012],{},"VIF",[1685,20014,4331],{},[1562,20016,9921],{},[1319,20018,20019],{"encoding":1321},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1296,20022,20024],{"className":20023},[1299],[1301,20025,20026],{"xmlns":1303},[1305,20027,20028,20036],{},[1308,20029,20030,20032,20034],{},[2907,20031,20012],{},[1685,20033,1687],{},[1562,20035,9921],{},[1319,20037,20038],{"encoding":1321},"\\text{VIF}>5"," (přísněji ",[1296,20041,20043],{"className":20042},[1299],[1301,20044,20045],{"xmlns":1303},[1305,20046,20047,20053],{},[1308,20048,20049,20051],{},[1685,20050,1687],{},[1562,20052,9028],{},[1319,20054,20055],{"encoding":1321},">10",") značí vysokou multikolinearitu.",[1148,20058,20059],{},"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.",[16742,20061,20063],{"id":20062},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1102,20065,20066,20072,20078],{},[1105,20067,20068,20071],{},[1108,20069,20070],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1105,20073,20074,20077],{},[1108,20075,20076],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1105,20079,20080,20083,20084,20087],{},[1108,20081,20082],{},"AIC"," (Akaikeho informační kritérium) a ",[1108,20085,20086],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[16742,20089,16745],{"id":20090},"v-r-2",[1148,20092,20093],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3692,20095,20097],{"className":3694,"code":20096,"language":71,"meta":1452,"style":1452},"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",[3468,20098,20099,20125,20169,20195,20205,20209,20220,20231,20235,20245,20255,20259,20269,20279,20284],{"__ignoreMap":1452},[1296,20100,20101,20104,20106,20109,20111,20114,20116,20119,20121,20123],{"class":3700,"line":10},[1296,20102,20103],{"class":3703},"data",[1296,20105,3708],{"class":3707},[1296,20107,20108],{"class":3711}," read.table",[1296,20110,1873],{"class":3715},[1296,20112,20113],{"class":3839},"\"4_4.txt\"",[1296,20115,1795],{"class":3707},[1296,20117,20118],{"class":3703}," header",[1296,20120,3796],{"class":3707},[1296,20122,3809],{"class":3723},[1296,20124,3900],{"class":3715},[1296,20126,20127,20130,20132,20134,20136,20138,20140,20143,20145,20148,20150,20153,20155,20158,20160,20163,20165,20167],{"class":3700,"line":27},[1296,20128,20129],{"class":3703},"model_plny",[1296,20131,3708],{"class":3707},[1296,20133,16846],{"class":3711},[1296,20135,1873],{"class":3715},[1296,20137,7126],{"class":3703},[1296,20139,16853],{"class":3707},[1296,20141,20142],{"class":3703}," x1",[1296,20144,18511],{"class":3707},[1296,20146,20147],{"class":3703}," x2",[1296,20149,18511],{"class":3707},[1296,20151,20152],{"class":3703}," x3",[1296,20154,18511],{"class":3707},[1296,20156,20157],{"class":3703}," x4",[1296,20159,1795],{"class":3707},[1296,20161,20162],{"class":3703}," data",[1296,20164,3796],{"class":3707},[1296,20166,20162],{"class":3703},[1296,20168,3900],{"class":3715},[1296,20170,20171,20174,20176,20179,20181,20183,20185,20188,20190,20193],{"class":3700,"line":148},[1296,20172,20173],{"class":3703},"model_krok",[1296,20175,3708],{"class":3707},[1296,20177,20178],{"class":3711}," step",[1296,20180,1873],{"class":3715},[1296,20182,20129],{"class":3703},[1296,20184,1795],{"class":3707},[1296,20186,20187],{"class":3703}," direction",[1296,20189,3796],{"class":3707},[1296,20191,20192],{"class":3839}," \"both\"",[1296,20194,3900],{"class":3715},[1296,20196,20197,20199,20201,20203],{"class":3700,"line":111},[1296,20198,16863],{"class":3711},[1296,20200,1873],{"class":3715},[1296,20202,20173],{"class":3703},[1296,20204,3900],{"class":3715},[1296,20206,20207],{"class":3700,"line":96},[1296,20208,10036],{"emptyLinePlaceholder":1464},[1296,20210,20211,20213,20215,20218],{"class":3700,"line":89},[1296,20212,17392],{"class":3707},[1296,20214,1873],{"class":3715},[1296,20216,20217],{"class":3703},"car",[1296,20219,3900],{"class":3715},[1296,20221,20222,20225,20227,20229],{"class":3700,"line":82},[1296,20223,20224],{"class":3711},"vif",[1296,20226,1873],{"class":3715},[1296,20228,20173],{"class":3703},[1296,20230,3900],{"class":3715},[1296,20232,20233],{"class":3700,"line":75},[1296,20234,10036],{"emptyLinePlaceholder":1464},[1296,20236,20237,20239,20241,20243],{"class":3700,"line":3890},[1296,20238,17392],{"class":3707},[1296,20240,1873],{"class":3715},[1296,20242,17397],{"class":3703},[1296,20244,3900],{"class":3715},[1296,20246,20247,20249,20251,20253],{"class":3700,"line":72},[1296,20248,17404],{"class":3711},[1296,20250,1873],{"class":3715},[1296,20252,20173],{"class":3703},[1296,20254,3900],{"class":3715},[1296,20256,20257],{"class":3700,"line":25},[1296,20258,10036],{"emptyLinePlaceholder":1464},[1296,20260,20261,20263,20265,20267],{"class":3700,"line":65},[1296,20262,17392],{"class":3707},[1296,20264,1873],{"class":3715},[1296,20266,17487],{"class":3703},[1296,20268,3900],{"class":3715},[1296,20270,20271,20273,20275,20277],{"class":3700,"line":63},[1296,20272,17494],{"class":3711},[1296,20274,1873],{"class":3715},[1296,20276,20173],{"class":3703},[1296,20278,3900],{"class":3715},[1296,20280,20282],{"class":3700,"line":20281},14,[1296,20283,10036],{"emptyLinePlaceholder":1464},[1296,20285,20286,20288,20290,20292,20294,20296],{"class":3700,"line":60},[1296,20287,17572],{"class":3711},[1296,20289,1873],{"class":3715},[1296,20291,17040],{"class":3711},[1296,20293,1873],{"class":3715},[1296,20295,20173],{"class":3703},[1296,20297,9488],{"class":3715},[1148,20299,20300,20302,20303,20306],{},[3468,20301,16116],{}," provádí stepwise výběr podle AIC, ",[3468,20304,20305],{},"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.",[1514,20308,20310,20317,20320,20323],{"className":20309,"dataCallout":3475},[1517,3474],[1148,20311,20313,20316],{"className":20312},[1523],[1296,20314],{"className":20315,"ariaHidden":1530},[1527,3482,1529],"Příklad: Vícenásobná regrese",[1148,20318,20319],{},"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.",[1148,20321,20322],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1148,20324,20325,20326,20329,20330,20332,20333,20336],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1108,20327,20328],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1108,20331,19951],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1108,20334,20335],{},"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.",[1143,20338,6404],{"id":6403},[1514,20340,20342,20349],{"className":20341,"dataCallout":6409},[1517,6408],[1148,20343,20345,20348],{"className":20344},[1523],[1296,20346],{"className":20347,"ariaHidden":1530},[1527,6416,1529],"Koeficient korelace jen pro přímku",[1148,20350,20351,20352,20408,20409,20426,20427,20447,20448,1370,20461,1395],{},"Vzorec ",[1296,20353,20355],{"className":20354},[1299],[1301,20356,20357],{"xmlns":1303},[1305,20358,20359,20405],{},[1308,20360,20361,20371,20373,20383,20385],{},[1311,20362,20363,20365],{},[1314,20364,71],{},[1308,20366,20367,20369],{},[1314,20368,6716],{},[1314,20370,7126],{},[1685,20372,1980],{},[1311,20374,20375,20377],{},[1314,20376,1852],{},[1308,20378,20379,20381],{},[1314,20380,6716],{},[1314,20382,7126],{},[1314,20384,1502],{"mathvariant":2119},[4452,20386,20387],{},[1308,20388,20389,20397],{},[3351,20390,20391,20393,20395],{},[1314,20392,1852],{},[1314,20394,6716],{},[1562,20396,1586],{},[3351,20398,20399,20401,20403],{},[1314,20400,1852],{},[1314,20402,7126],{},[1562,20404,1586],{},[1319,20406,20407],{"encoding":1321},"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 ",[1296,20410,20412],{"className":20411},[1299],[1301,20413,20414],{"xmlns":1303},[1305,20415,20416,20424],{},[1308,20417,20418],{},[1579,20419,20420,20422],{},[1314,20421,10218],{},[1562,20423,1586],{},[1319,20425,16020],{"encoding":1321},", případně obecným indexem korelace ",[1296,20428,20430],{"className":20429},[1299],[1301,20431,20432],{"xmlns":1303},[1305,20433,20434,20444],{},[1308,20435,20436],{},[4452,20437,20438],{},[1579,20439,20440,20442],{},[1314,20441,10218],{},[1562,20443,1586],{},[1319,20445,20446],{"encoding":1321},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1296,20449,20451],{"className":20450},[1299],[1301,20452,20453],{"xmlns":1303},[1305,20454,20455,20459],{},[1308,20456,20457],{},[1314,20458,6716],{},[1319,20460,6716],{"encoding":1321},[1296,20462,20464],{"className":20463},[1299],[1301,20465,20466],{"xmlns":1303},[1305,20467,20468,20472],{},[1308,20469,20470],{},[1314,20471,7126],{},[1319,20473,7126],{"encoding":1321},[1514,20475,20477,20484],{"className":20476,"dataCallout":6409},[1517,6408],[1148,20478,20480,20483],{"className":20479},[1523],[1296,20481],{"className":20482,"ariaHidden":1530},[1527,6416,1529],"Významný F-test, nevýznamné t-testy",[1148,20485,20486],{},"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.",[1514,20488,20490,20497],{"className":20489,"dataCallout":6409},[1517,6408],[1148,20491,20493,20496],{"className":20492},[1523],[1296,20494],{"className":20495,"ariaHidden":1530},[1527,6416,1529],"Durbin-Watsonova statistika mimo okolí 2",[1148,20498,20499],{},"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.",[1514,20501,20503,20510],{"className":20502,"dataCallout":6409},[1517,6408],[1148,20504,20506,20509],{"className":20505},[1523],[1296,20507],{"className":20508,"ariaHidden":1530},[1527,6416,1529],"Nízký počet pozorování při stepwise výběru",[1148,20511,20512],{},"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.",[1143,20514,6592],{"id":6591},[1102,20516,20517,20522,20527,20532,20537,20542,20547],{},[1105,20518,20519],{},[1242,20520,1717],{"className":20521,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,20523,20524],{},[1242,20525,1248],{"className":20526,"dataFsResolvedFilePath":1246,"href":1247},[1245],[1105,20528,20529],{},[1242,20530,1257],{"className":20531,"dataFsResolvedFilePath":1255,"href":1256},[1245],[1105,20533,20534],{},[1242,20535,1266],{"className":20536,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1105,20538,20539],{},[1242,20540,1284],{"className":20541,"dataFsResolvedFilePath":1282,"href":1283},[1245],[1105,20543,20544],{},[1242,20545,1293],{"className":20546,"dataFsResolvedFilePath":1291,"href":1292},[1245],[1105,20548,20549],{},[1242,20550,6630],{"className":20551,"dataFsResolvedFilePath":1447,"href":1448},[1245],[1143,20553,6633],{"id":934},[1148,20555,6636,20556,6641],{},[6638,20557,6640],{},[6643,20559,20560],{},"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.",[1105,20619,20620,20621,1323,20647,1370,20673,1395],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1296,20622,20624],{"className":20623},[1299],[1301,20625,20626],{"xmlns":1303},[1305,20627,20628,20644],{},[1308,20629,20630,20632,20638,20640,20642],{},[1685,20631,1873],{"stretchy":1872},[2722,20633,20634,20636],{"accent":1530},[1314,20635,6716],{},[1685,20637,11454],{},[1685,20639,1795],{"separator":1530},[1314,20641,10218],{},[1685,20643,1884],{"stretchy":1872},[1319,20645,20646],{"encoding":1321},"(\\bar{x}, R)",[1296,20648,20650],{"className":20649},[1299],[1301,20651,20652],{"xmlns":1303},[1305,20653,20654,20670],{},[1308,20655,20656,20658,20664,20666,20668],{},[1685,20657,1873],{"stretchy":1872},[2722,20659,20660,20662],{"accent":1530},[1314,20661,6716],{},[1685,20663,11454],{},[1685,20665,1795],{"separator":1530},[1314,20667,1852],{},[1685,20669,1884],{"stretchy":1872},[1319,20671,20672],{"encoding":1321},"(\\bar{x}, s)",[1296,20674,20676],{"className":20675},[1299],[1301,20677,20678],{"xmlns":1303},[1305,20679,20680,20709],{},[1308,20681,20682,20684,20690,20692,20707],{},[1685,20683,1873],{"stretchy":1872},[1311,20685,20686,20688],{},[1314,20687,6716],{},[1314,20689,1876],{},[1685,20691,1795],{"separator":1530},[1311,20693,20694,20696],{},[1314,20695,10218],{},[1308,20697,20698,20700,20703,20705],{},[1314,20699,1343],{},[1314,20701,20702],{},"l",[1685,20704,1795],{"separator":1530},[1314,20706,1876],{},[1685,20708,1884],{"stretchy":1872},[1319,20710,20711],{"encoding":1321},"(x_i, R_{kl,i})",[1105,20713,20714,20715,20728,20729,20742,20743,20759,20760,20773],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1296,20716,20718],{"className":20717},[1299],[1301,20719,20720],{"xmlns":1303},[1305,20721,20722,20726],{},[1308,20723,20724],{},[1314,20725,3718],{},[1319,20727,3718],{"encoding":1321}," (konstantní rozsah) a ",[1296,20730,20732],{"className":20731},[1299],[1301,20733,20734],{"xmlns":1303},[1305,20735,20736,20740],{},[1308,20737,20738],{},[1314,20739,11523],{},[1319,20741,11523],{"encoding":1321}," (nekonstantní rozsah), počet neshodných produktů ",[1296,20744,20746],{"className":20745},[1299],[1301,20747,20748],{"xmlns":1303},[1305,20749,20750,20756],{},[1308,20751,20752,20754],{},[1314,20753,1683],{},[1314,20755,1148],{},[1319,20757,20758],{"encoding":1321},"np"," (konstantní rozsah) a jejich podíl ",[1296,20761,20763],{"className":20762},[1299],[1301,20764,20765],{"xmlns":1303},[1305,20766,20767,20771],{},[1308,20768,20769],{},[1314,20770,1148],{},[1319,20772,1148],{"encoding":1321}," (nekonstantní rozsah).",[1105,20775,20776],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1105,20778,20779,20780,1323,20797,1323,20818,1323,20839,20862,20863,20884],{},"Indexy způsobilosti ",[1296,20781,20783],{"className":20782},[1299],[1301,20784,20785],{"xmlns":1303},[1305,20786,20787,20795],{},[1308,20788,20789],{},[1311,20790,20791,20793],{},[1314,20792,1201],{},[1314,20794,1148],{},[1319,20796,1322],{"encoding":1321},[1296,20798,20800],{"className":20799},[1299],[1301,20801,20802],{"xmlns":1303},[1305,20803,20804,20816],{},[1308,20805,20806],{},[1311,20807,20808,20810],{},[1314,20809,1201],{},[1308,20811,20812,20814],{},[1314,20813,1148],{},[1314,20815,1343],{},[1319,20817,1346],{"encoding":1321},[1296,20819,20821],{"className":20820},[1299],[1301,20822,20823],{"xmlns":1303},[1305,20824,20825,20837],{},[1308,20826,20827],{},[1311,20828,20829,20831],{},[1314,20830,1201],{},[1308,20832,20833,20835],{},[1314,20834,1148],{},[1314,20836,1366],{},[1319,20838,1369],{"encoding":1321},[1296,20840,20842],{"className":20841},[1299],[1301,20843,20844],{"xmlns":1303},[1305,20845,20846,20860],{},[1308,20847,20848],{},[1311,20849,20850,20852],{},[1314,20851,1201],{},[1308,20853,20854,20856,20858],{},[1314,20855,1148],{},[1314,20857,1366],{},[1314,20859,1343],{},[1319,20861,1394],{"encoding":1321}," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1296,20864,20866],{"className":20865},[1299],[1301,20867,20868],{"xmlns":1303},[1305,20869,20870,20882],{},[1308,20871,20872],{},[1311,20873,20874,20876],{},[1314,20875,1201],{},[1308,20877,20878,20880],{},[1314,20879,1148],{},[1314,20881,1343],{},[1319,20883,1346],{"encoding":1321}," navíc zohledňuje vychýlení střední hodnoty.",[1105,20886,20887,20888,1395],{},"V R diagramy i indexy počítá balíček ",[3468,20889,360],{},[1143,20891,20893],{"id":20892},"statistická-regulace-procesu","Statistická regulace procesu",[1148,20895,20896,20897,20899,20900,1395],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1108,20898,20893],{}," 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 ",[1108,20901,20902],{},"statisticky zvládnutém stavu",[1148,20904,20905,20906,20909],{},"Teorie regulace vychází z ",[1108,20907,20908],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1162,20911,20912,20924],{},[1165,20913,20914],{},[1168,20915,20916,20918,20921],{},[1171,20917],{},[1171,20919,20920],{},"Náhodné příčiny",[1171,20922,20923],{},"Vymezitelné příčiny",[1178,20925,20926,20937,20948],{},[1168,20927,20928,20931,20934],{},[1183,20929,20930],{},"Povaha",[1183,20932,20933],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1183,20935,20936],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1168,20938,20939,20942,20945],{},[1183,20940,20941],{},"Stav procesu",[1183,20943,20944],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1183,20946,20947],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1168,20949,20950,20953,20956],{},[1183,20951,20952],{},"Příklady",[1183,20954,20955],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1183,20957,20958],{},"změna materiálu, nezaškolená obsluha",[1148,20960,20961,20962,20965,20966,20969],{},"Vymezitelné příčiny jsou ",[1108,20963,20964],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1108,20967,20968],{},"přetrvávající"," (trvají stále nebo se mění).",[1148,20971,20972],{},[4382,20973],{"alt":20974,"className":20975,"src":20976},"mask-ilu-pricin-variability",[1245,4386],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1148,20978,20979],{},"Regulace probíhá ve třech fázích:",[1237,20981,20982,20992,20998],{},[1105,20983,20984,20987,20988,20991],{},[1108,20985,20986],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1108,20989,20990],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1105,20993,20994,20997],{},[1108,20995,20996],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1105,20999,21000,21003],{},[1108,21001,21002],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1143,21005,21007],{"id":21006},"princip-regulačního-diagramu","Princip regulačního diagramu",[1148,21009,21010,21013],{},[1108,21011,21012],{},"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.",[1102,21015,21016,21022,21028],{},[1105,21017,21018,21021],{},[1108,21019,21020],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1105,21023,21024,21027],{},[1108,21025,21026],{},"UCL"," — horní akční regulační mez,",[1105,21029,21030,21033],{},[1108,21031,21032],{},"LCL"," — dolní akční regulační mez.",[1148,21035,21036],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1148,21038,21039],{},[4382,21040],{"alt":21041,"className":21042,"src":21043},"mask-rd-schema",[1245,4386],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1148,21045,21046,21049],{},[1108,21047,21048],{},"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.",[1148,21051,21052,21053,21056,21057,21060],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1108,21054,21055],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1108,21058,21059],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1148,21062,21063],{},"Postup při konstrukci regulačního diagramu:",[1237,21065,21066,21069,21072,21075,21078,21081,21084,21087,21090],{},[1105,21067,21068],{},"volba regulované veličiny,",[1105,21070,21071],{},"sběr a záznam dat,",[1105,21073,21074],{},"ověření požadovaných předpokladů o datech,",[1105,21076,21077],{},"volba rozsahu logických podskupin,",[1105,21079,21080],{},"volba vhodného regulačního diagramu,",[1105,21082,21083],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1105,21085,21086],{},"ověření a zajištění statistické zvládnutosti procesu,",[1105,21088,21089],{},"ověření způsobilosti procesu,",[1105,21091,21092],{},"vlastní regulace procesu.",[1143,21094,21096],{"id":21095},"regulace-měřením","Regulace měřením",[1148,21098,21099],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1102,21101,21102,21105],{},[1105,21103,21104],{},"jednotlivá měření byla vzájemně nezávislá,",[1105,21106,21107,21108,21121,21122,21135,21136,21149,21150,21163],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1296,21109,21111],{"className":21110},[1299],[1301,21112,21113],{"xmlns":1303},[1305,21114,21115,21119],{},[1308,21116,21117],{},[1314,21118,6887],{},[1319,21120,8791],{"encoding":1321}," a směrodatnou odchylkou ",[1296,21123,21125],{"className":21124},[1299],[1301,21126,21127],{"xmlns":1303},[1305,21128,21129,21133],{},[1308,21130,21131],{},[1314,21132,6895],{},[1319,21134,6927],{"encoding":1321}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1296,21137,21139],{"className":21138},[1299],[1301,21140,21141],{"xmlns":1303},[1305,21142,21143,21147],{},[1308,21144,21145],{},[1314,21146,6887],{},[1319,21148,8791],{"encoding":1321}," je hodnota, na niž je proces nastaven, ",[1296,21151,21153],{"className":21152},[1299],[1301,21154,21155],{"xmlns":1303},[1305,21156,21157,21161],{},[1308,21158,21159],{},[1314,21160,6895],{},[1319,21162,6927],{"encoding":1321}," charakterizuje jeho přesnost.",[1148,21165,21166,21167,1323,21192,1370,21217,21254],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1296,21168,21170],{"className":21169},[1299],[1301,21171,21172],{"xmlns":1303},[1305,21173,21174,21190],{},[1308,21175,21176,21178,21184,21186,21188],{},[1685,21177,1873],{"stretchy":1872},[2722,21179,21180,21182],{"accent":1530},[1314,21181,6716],{},[1685,21183,11454],{},[1685,21185,1795],{"separator":1530},[1314,21187,10218],{},[1685,21189,1884],{"stretchy":1872},[1319,21191,20646],{"encoding":1321},[1296,21193,21195],{"className":21194},[1299],[1301,21196,21197],{"xmlns":1303},[1305,21198,21199,21215],{},[1308,21200,21201,21203,21209,21211,21213],{},[1685,21202,1873],{"stretchy":1872},[2722,21204,21205,21207],{"accent":1530},[1314,21206,6716],{},[1685,21208,11454],{},[1685,21210,1795],{"separator":1530},[1314,21212,1852],{},[1685,21214,1884],{"stretchy":1872},[1319,21216,20672],{"encoding":1321},[1296,21218,21220],{"className":21219},[1299],[1301,21221,21222],{"xmlns":1303},[1305,21223,21224,21252],{},[1308,21225,21226,21228,21234,21236,21250],{},[1685,21227,1873],{"stretchy":1872},[1311,21229,21230,21232],{},[1314,21231,6716],{},[1314,21233,1876],{},[1685,21235,1795],{"separator":1530},[1311,21237,21238,21240],{},[1314,21239,10218],{},[1308,21241,21242,21244,21246,21248],{},[1314,21243,1343],{},[1314,21245,20702],{},[1685,21247,1795],{"separator":1530},[1314,21249,1876],{},[1685,21251,1884],{"stretchy":1872},[1319,21253,20711],{"encoding":1321},". Výsledkem jsou vždy dva diagramy.",[16742,21256,21258,21259],{"id":21257},"diagram-xˉrbarx-r","Diagram ",[1296,21260,21262],{"className":21261},[1299],[1301,21263,21264],{"xmlns":1303},[1305,21265,21266,21282],{},[1308,21267,21268,21270,21276,21278,21280],{},[1685,21269,1873],{"stretchy":1872},[2722,21271,21272,21274],{"accent":1530},[1314,21273,6716],{},[1685,21275,11454],{},[1685,21277,1795],{"separator":1530},[1314,21279,10218],{},[1685,21281,1884],{"stretchy":1872},[1319,21283,20646],{"encoding":1321},[1148,21285,21286,21287,21309,21310,21328],{},"Regulované veličiny jsou výběrové průměry ",[1296,21288,21290],{"className":21289},[1299],[1301,21291,21292],{"xmlns":1303},[1305,21293,21294,21306],{},[1308,21295,21296],{},[1311,21297,21298,21304],{},[2722,21299,21300,21302],{"accent":1530},[1314,21301,6716],{},[1685,21303,11454],{},[1314,21305,1876],{},[1319,21307,21308],{"encoding":1321},"\\bar{x}_i"," a výběrová rozpětí ",[1296,21311,21313],{"className":21312},[1299],[1301,21314,21315],{"xmlns":1303},[1305,21316,21317,21325],{},[1308,21318,21319],{},[1311,21320,21321,21323],{},[1314,21322,10218],{},[1314,21324,1876],{},[1319,21326,21327],{"encoding":1321},"R_i"," v logických podskupinách:",[1296,21330,21332],{"className":21331},[1299],[1301,21333,21334],{"xmlns":1303,"display":1962},[1305,21335,21336,21437],{},[1308,21337,21338,21348,21350,21356,21370,21380,21382,21384,21390,21392,21403,21413,21415,21425,21435],{},[1311,21339,21340,21346],{},[2722,21341,21342,21344],{"accent":1530},[1314,21343,6716],{},[1685,21345,11454],{},[1314,21347,1876],{},[1685,21349,1980],{},[2738,21351,21352,21354],{},[1562,21353,1792],{},[1314,21355,1683],{},[1982,21357,21358,21360,21368],{},[1685,21359,1986],{},[1308,21361,21362,21364,21366],{},[1314,21363,1881],{},[1685,21365,1980],{},[1562,21367,1792],{},[1314,21369,1683],{},[1311,21371,21372,21374],{},[1314,21373,6716],{},[1308,21375,21376,21378],{},[1314,21377,1876],{},[1314,21379,1881],{},[1685,21381,1795],{"separator":1530},[2010,21383],{"width":2012},[1311,21385,21386,21388],{},[1314,21387,10218],{},[1314,21389,1876],{},[1685,21391,1980],{},[21393,21394,21395,21401],"munder",{},[1308,21396,21397,21399],{},[1314,21398,11714],{},[1685,21400,4489],{},[1314,21402,1881],{},[1311,21404,21405,21407],{},[1314,21406,6716],{},[1308,21408,21409,21411],{},[1314,21410,1876],{},[1314,21412,1881],{},[1685,21414,3062],{},[21393,21416,21417,21423],{},[1308,21418,21419,21421],{},[1314,21420,4486],{},[1685,21422,4489],{},[1314,21424,1881],{},[1311,21426,21427,21429],{},[1314,21428,6716],{},[1308,21430,21431,21433],{},[1314,21432,1876],{},[1314,21434,1881],{},[1314,21436,1395],{"mathvariant":2119},[1319,21438,21439],{"encoding":1321},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1148,21441,21442],{},"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.",[1148,21444,21445,21446,21472,21473,21486,21487,1370,21508,21525,21526,21539,21540,21558,21559,1395],{},"Data se zapisují do tabulky: řádek ",[1296,21447,21449],{"className":21448},[1299],[1301,21450,21451],{"xmlns":1303},[1305,21452,21453,21469],{},[1308,21454,21455,21457,21459,21461,21463,21465,21467],{},[1314,21456,1876],{},[1685,21458,1980],{},[1562,21460,1792],{},[1685,21462,1795],{"separator":1530},[1685,21464,1798],{},[1685,21466,1795],{"separator":1530},[1314,21468,1343],{},[1319,21470,21471],{"encoding":1321},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1296,21474,21476],{"className":21475},[1299],[1301,21477,21478],{"xmlns":1303},[1305,21479,21480,21484],{},[1308,21481,21482],{},[1314,21483,1683],{},[1319,21485,1683],{"encoding":1321}," naměřených hodnot a poslední dva sloupce ",[1296,21488,21490],{"className":21489},[1299],[1301,21491,21492],{"xmlns":1303},[1305,21493,21494,21506],{},[1308,21495,21496],{},[1311,21497,21498,21504],{},[2722,21499,21500,21502],{"accent":1530},[1314,21501,6716],{},[1685,21503,11454],{},[1314,21505,1876],{},[1319,21507,21308],{"encoding":1321},[1296,21509,21511],{"className":21510},[1299],[1301,21512,21513],{"xmlns":1303},[1305,21514,21515,21523],{},[1308,21516,21517],{},[1311,21518,21519,21521],{},[1314,21520,10218],{},[1314,21522,1876],{},[1319,21524,21327],{"encoding":1321},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1296,21527,21529],{"className":21528},[1299],[1301,21530,21531],{"xmlns":1303},[1305,21532,21533,21537],{},[1308,21534,21535],{},[1314,21536,10218],{},[1319,21538,10218],{"encoding":1321},", potom diagram ",[1296,21541,21543],{"className":21542},[1299],[1301,21544,21545],{"xmlns":1303},[1305,21546,21547,21555],{},[1308,21548,21549],{},[2722,21550,21551,21553],{"accent":1530},[1314,21552,6716],{},[1685,21554,11454],{},[1319,21556,21557],{"encoding":1321},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3468,21560,21561],{},"qcc()",[1514,21563,21565,21572],{"className":21564,"dataCallout":3475},[1517,3474],[1148,21566,21568,21571],{"className":21567},[1523],[1296,21569],{"className":21570,"ariaHidden":1530},[1527,3482,1529],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1148,21573,21574,21575,21588,21589,1323,21607,21625,21626,1395],{},"Naměřená data znaku jakosti ",[1296,21576,21578],{"className":21577},[1299],[1301,21579,21580],{"xmlns":1303},[1305,21581,21582,21586],{},[1308,21583,21584],{},[1314,21585,6728],{},[1319,21587,6728],{"encoding":1321}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1296,21590,21592],{"className":21591},[1299],[1301,21593,21594],{"xmlns":1303},[1305,21595,21596,21604],{},[1308,21597,21598,21600,21602],{},[1314,21599,1343],{},[1685,21601,1980],{},[1562,21603,4044],{},[1319,21605,21606],{"encoding":1321},"k=20",[1296,21608,21610],{"className":21609},[1299],[1301,21611,21612],{"xmlns":1303},[1305,21613,21614,21622],{},[1308,21615,21616,21618,21620],{},[1314,21617,1683],{},[1685,21619,1980],{},[1562,21621,3540],{},[1319,21623,21624],{"encoding":1321},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1296,21627,21629],{"className":21628},[1299],[1301,21630,21631],{"xmlns":1303},[1305,21632,21633,21649],{},[1308,21634,21635,21637,21643,21645,21647],{},[1685,21636,1873],{"stretchy":1872},[2722,21638,21639,21641],{"accent":1530},[1314,21640,6716],{},[1685,21642,11454],{},[1685,21644,1795],{"separator":1530},[1314,21646,10218],{},[1685,21648,1884],{"stretchy":1872},[1319,21650,20646],{"encoding":1321},[1162,21652,21653,21768],{},[1165,21654,21655],{},[1168,21656,21657,21672,21696,21720,21744],{},[1171,21658,21659],{},[1296,21660,21662],{"className":21661},[1299],[1301,21663,21664],{"xmlns":1303},[1305,21665,21666,21670],{},[1308,21667,21668],{},[1314,21669,1876],{},[1319,21671,1876],{"encoding":1321},[1171,21673,21674],{},[1296,21675,21677],{"className":21676},[1299],[1301,21678,21679],{"xmlns":1303},[1305,21680,21681,21693],{},[1308,21682,21683],{},[1311,21684,21685,21687],{},[1314,21686,6716],{},[1308,21688,21689,21691],{},[1314,21690,1876],{},[1562,21692,1792],{},[1319,21694,21695],{"encoding":1321},"x_{i1}",[1171,21697,21698],{},[1296,21699,21701],{"className":21700},[1299],[1301,21702,21703],{"xmlns":1303},[1305,21704,21705,21717],{},[1308,21706,21707],{},[1311,21708,21709,21711],{},[1314,21710,6716],{},[1308,21712,21713,21715],{},[1314,21714,1876],{},[1562,21716,1586],{},[1319,21718,21719],{"encoding":1321},"x_{i2}",[1171,21721,21722],{},[1296,21723,21725],{"className":21724},[1299],[1301,21726,21727],{"xmlns":1303},[1305,21728,21729,21741],{},[1308,21730,21731],{},[1311,21732,21733,21735],{},[1314,21734,6716],{},[1308,21736,21737,21739],{},[1314,21738,1876],{},[1562,21740,3590],{},[1319,21742,21743],{"encoding":1321},"x_{i3}",[1171,21745,21746],{},[1296,21747,21749],{"className":21748},[1299],[1301,21750,21751],{"xmlns":1303},[1305,21752,21753,21765],{},[1308,21754,21755],{},[1311,21756,21757,21759],{},[1314,21758,6716],{},[1308,21760,21761,21763],{},[1314,21762,1876],{},[1562,21764,3540],{},[1319,21766,21767],{"encoding":1321},"x_{i4}",[1178,21769,21770,21784,21799,21815,21830,21842,21856,21868,21881],{},[1168,21771,21772,21774,21777,21780,21782],{},[1183,21773,1792],{},[1183,21775,21776],{},"106",[1183,21778,21779],{},"98",[1183,21781,14080],{},[1183,21783,14080],{},[1168,21785,21786,21788,21791,21794,21797],{},[1183,21787,1586],{},[1183,21789,21790],{},"95",[1183,21792,21793],{},"94",[1183,21795,21796],{},"108",[1183,21798,6120],{},[1168,21800,21801,21803,21806,21809,21812],{},[1183,21802,3590],{},[1183,21804,21805],{},"122",[1183,21807,21808],{},"105",[1183,21810,21811],{},"103",[1183,21813,21814],{},"133",[1168,21816,21817,21819,21822,21824,21827],{},[1183,21818,3540],{},[1183,21820,21821],{},"113",[1183,21823,3562],{},[1183,21825,21826],{},"128",[1183,21828,21829],{},"135",[1168,21831,21832,21834,21836,21838,21840],{},[1183,21833,9921],{},[1183,21835,14080],{},[1183,21837,6120],{},[1183,21839,21811],{},[1183,21841,6120],{},[1168,21843,21844,21846,21848,21850,21853],{},[1183,21845,3963],{},[1183,21847,21779],{},[1183,21849,21811],{},[1183,21851,21852],{},"97",[1183,21854,21855],{},"99",[1168,21857,21858,21860,21862,21864,21866],{},[1183,21859,1798],{},[1183,21861,1798],{},[1183,21863,1798],{},[1183,21865,1798],{},[1183,21867,1798],{},[1168,21869,21870,21872,21874,21876,21879],{},[1183,21871,14714],{},[1183,21873,21826],{},[1183,21875,21814],{},[1183,21877,21878],{},"120",[1183,21880,14742],{},[1168,21882,21883,21885,21887,21889,21891],{},[1183,21884,4044],{},[1183,21886,21779],{},[1183,21888,21811],{},[1183,21890,21852],{},[1183,21892,21855],{},[1148,21894,21895,21896,21917,21918,1956],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1296,21897,21899],{"className":21898},[1299],[1301,21900,21901],{"xmlns":1303},[1305,21902,21903,21915],{},[1308,21904,21905],{},[1311,21906,21907,21913],{},[2722,21908,21909,21911],{"accent":1530},[1314,21910,6716],{},[1685,21912,11454],{},[1314,21914,1876],{},[1319,21916,21308],{"encoding":1321}," a rozpětí ",[1296,21919,21921],{"className":21920},[1299],[1301,21922,21923],{"xmlns":1303},[1305,21924,21925,21933],{},[1308,21926,21927],{},[1311,21928,21929,21931],{},[1314,21930,10218],{},[1314,21932,1876],{},[1319,21934,21327],{"encoding":1321},[1162,21936,21937,21998],{},[1165,21938,21939],{},[1168,21940,21941,21956,21979],{},[1171,21942,21943],{},[1296,21944,21946],{"className":21945},[1299],[1301,21947,21948],{"xmlns":1303},[1305,21949,21950,21954],{},[1308,21951,21952],{},[1314,21953,1876],{},[1319,21955,1876],{"encoding":1321},[1171,21957,21958],{},[1296,21959,21961],{"className":21960},[1299],[1301,21962,21963],{"xmlns":1303},[1305,21964,21965,21977],{},[1308,21966,21967],{},[1311,21968,21969,21975],{},[2722,21970,21971,21973],{"accent":1530},[1314,21972,6716],{},[1685,21974,11454],{},[1314,21976,1876],{},[1319,21978,21308],{"encoding":1321},[1171,21980,21981],{},[1296,21982,21984],{"className":21983},[1299],[1301,21985,21986],{"xmlns":1303},[1305,21987,21988,21996],{},[1308,21989,21990],{},[1311,21991,21992,21994],{},[1314,21993,10218],{},[1314,21995,1876],{},[1319,21997,21327],{"encoding":1321},[1178,21999,22000,22009,22019,22029,22039,22048,22057,22065,22074],{},[1168,22001,22002,22004,22007],{},[1183,22003,1792],{},[1183,22005,22006],{},"101,50",[1183,22008,14809],{},[1168,22010,22011,22013,22016],{},[1183,22012,1586],{},[1183,22014,22015],{},"97,25",[1183,22017,22018],{},"16",[1168,22020,22021,22023,22026],{},[1183,22022,3590],{},[1183,22024,22025],{},"115,75",[1183,22027,22028],{},"30",[1168,22030,22031,22033,22036],{},[1183,22032,3540],{},[1183,22034,22035],{},"111,75",[1183,22037,22038],{},"64",[1168,22040,22041,22043,22046],{},[1183,22042,9921],{},[1183,22044,22045],{},"97,00",[1183,22047,2253],{},[1168,22049,22050,22052,22055],{},[1183,22051,3963],{},[1183,22053,22054],{},"99,25",[1183,22056,3963],{},[1168,22058,22059,22061,22063],{},[1183,22060,1798],{},[1183,22062,1798],{},[1183,22064,1798],{},[1168,22066,22067,22069,22072],{},[1183,22068,14714],{},[1183,22070,22071],{},"126,50",[1183,22073,3543],{},[1168,22075,22076,22078,22080],{},[1183,22077,4044],{},[1183,22079,22054],{},[1183,22081,3963],{},[1148,22083,22084,22085,22098,22099,1323,22127,1323,22157,22185,22186,22208,22209,1323,22236,1323,22265,22292,22293,1395],{},"Nejprve se posoudí diagram ",[1296,22086,22088],{"className":22087},[1299],[1301,22089,22090],{"xmlns":1303},[1305,22091,22092,22096],{},[1308,22093,22094],{},[1314,22095,10218],{},[1319,22097,10218],{"encoding":1321}," na všech 20 podskupinách: ",[1296,22100,22102],{"className":22101},[1299],[1301,22103,22104],{"xmlns":1303},[1305,22105,22106,22124],{},[1308,22107,22108,22110,22113,22115,22117,22119,22121],{},[1314,22109,1201],{},[1314,22111,22112],{},"L",[1685,22114,1873],{"stretchy":1872},[1314,22116,10218],{},[1685,22118,1884],{"stretchy":1872},[1685,22120,1980],{},[1562,22122,22123],{},"15,8",[1319,22125,22126],{"encoding":1321},"CL(R)=15{,}8",[1296,22128,22130],{"className":22129},[1299],[1301,22131,22132],{"xmlns":1303},[1305,22133,22134,22154],{},[1308,22135,22136,22139,22141,22143,22145,22147,22149,22151],{},[1314,22137,22138],{},"U",[1314,22140,1201],{},[1314,22142,22112],{},[1685,22144,1873],{"stretchy":1872},[1314,22146,10218],{},[1685,22148,1884],{"stretchy":1872},[1685,22150,1980],{},[1562,22152,22153],{},"36,06",[1319,22155,22156],{"encoding":1321},"UCL(R)=36{,}06",[1296,22158,22160],{"className":22159},[1299],[1301,22161,22162],{"xmlns":1303},[1305,22163,22164,22182],{},[1308,22165,22166,22168,22170,22172,22174,22176,22178,22180],{},[1314,22167,22112],{},[1314,22169,1201],{},[1314,22171,22112],{},[1685,22173,1873],{"stretchy":1872},[1314,22175,10218],{},[1685,22177,1884],{"stretchy":1872},[1685,22179,1980],{},[1562,22181,1564],{},[1319,22183,22184],{"encoding":1321},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1296,22187,22189],{"className":22188},[1299],[1301,22190,22191],{"xmlns":1303},[1305,22192,22193,22205],{},[1308,22194,22195,22201,22203],{},[1311,22196,22197,22199],{},[1314,22198,10218],{},[1562,22200,3540],{},[1685,22202,1980],{},[1562,22204,22038],{},[1319,22206,22207],{"encoding":1321},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1296,22210,22212],{"className":22211},[1299],[1301,22213,22214],{"xmlns":1303},[1305,22215,22216,22233],{},[1308,22217,22218,22220,22222,22224,22226,22228,22230],{},[1314,22219,1201],{},[1314,22221,22112],{},[1685,22223,1873],{"stretchy":1872},[1314,22225,10218],{},[1685,22227,1884],{"stretchy":1872},[1685,22229,1980],{},[1562,22231,22232],{},"13,26",[1319,22234,22235],{"encoding":1321},"CL(R)=13{,}26",[1296,22237,22239],{"className":22238},[1299],[1301,22240,22241],{"xmlns":1303},[1305,22242,22243,22262],{},[1308,22244,22245,22247,22249,22251,22253,22255,22257,22259],{},[1314,22246,22138],{},[1314,22248,1201],{},[1314,22250,22112],{},[1685,22252,1873],{"stretchy":1872},[1314,22254,10218],{},[1685,22256,1884],{"stretchy":1872},[1685,22258,1980],{},[1562,22260,22261],{},"30,27",[1319,22263,22264],{"encoding":1321},"UCL(R)=30{,}27",[1296,22266,22268],{"className":22267},[1299],[1301,22269,22270],{"xmlns":1303},[1305,22271,22272,22290],{},[1308,22273,22274,22276,22278,22280,22282,22284,22286,22288],{},[1314,22275,22112],{},[1314,22277,1201],{},[1314,22279,22112],{},[1685,22281,1873],{"stretchy":1872},[1314,22283,10218],{},[1685,22285,1884],{"stretchy":1872},[1685,22287,1980],{},[1562,22289,1564],{},[1319,22291,22184],{"encoding":1321},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1296,22294,22296],{"className":22295},[1299],[1301,22297,22298],{"xmlns":1303},[1305,22299,22300,22308],{},[1308,22301,22302],{},[2722,22303,22304,22306],{"accent":1530},[1314,22305,6716],{},[1685,22307,11454],{},[1319,22309,21557],{"encoding":1321},[1148,22311,21258,22312,22329,22330,1323,22361,1323,22394,22427,22428,22441,22442,1323,22469,1323,22498,22525],{},[1296,22313,22315],{"className":22314},[1299],[1301,22316,22317],{"xmlns":1303},[1305,22318,22319,22327],{},[1308,22320,22321],{},[2722,22322,22323,22325],{"accent":1530},[1314,22324,6716],{},[1685,22326,11454],{},[1319,22328,21557],{"encoding":1321}," bez čtvrté podskupiny dává ",[1296,22331,22333],{"className":22332},[1299],[1301,22334,22335],{"xmlns":1303},[1305,22336,22337,22358],{},[1308,22338,22339,22341,22343,22345,22351,22353,22355],{},[1314,22340,1201],{},[1314,22342,22112],{},[1685,22344,1873],{"stretchy":1872},[2722,22346,22347,22349],{"accent":1530},[1314,22348,6716],{},[1685,22350,11454],{},[1685,22352,1884],{"stretchy":1872},[1685,22354,1980],{},[1562,22356,22357],{},"102,01",[1319,22359,22360],{"encoding":1321},"CL(\\bar{x})=102{,}01",[1296,22362,22364],{"className":22363},[1299],[1301,22365,22366],{"xmlns":1303},[1305,22367,22368,22391],{},[1308,22369,22370,22372,22374,22376,22378,22384,22386,22388],{},[1314,22371,22138],{},[1314,22373,1201],{},[1314,22375,22112],{},[1685,22377,1873],{"stretchy":1872},[2722,22379,22380,22382],{"accent":1530},[1314,22381,6716],{},[1685,22383,11454],{},[1685,22385,1884],{"stretchy":1872},[1685,22387,1980],{},[1562,22389,22390],{},"111,68",[1319,22392,22393],{"encoding":1321},"UCL(\\bar{x})=111{,}68",[1296,22395,22397],{"className":22396},[1299],[1301,22398,22399],{"xmlns":1303},[1305,22400,22401,22424],{},[1308,22402,22403,22405,22407,22409,22411,22417,22419,22421],{},[1314,22404,22112],{},[1314,22406,1201],{},[1314,22408,22112],{},[1685,22410,1873],{"stretchy":1872},[2722,22412,22413,22415],{"accent":1530},[1314,22414,6716],{},[1685,22416,11454],{},[1685,22418,1884],{"stretchy":1872},[1685,22420,1980],{},[1562,22422,22423],{},"92,34",[1319,22425,22426],{"encoding":1321},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1296,22429,22431],{"className":22430},[1299],[1301,22432,22433],{"xmlns":1303},[1305,22434,22435,22439],{},[1308,22436,22437],{},[1314,22438,10218],{},[1319,22440,10218],{"encoding":1321}," se přepočítají bez podskupin 3, 4 a 19: ",[1296,22443,22445],{"className":22444},[1299],[1301,22446,22447],{"xmlns":1303},[1305,22448,22449,22466],{},[1308,22450,22451,22453,22455,22457,22459,22461,22463],{},[1314,22452,1201],{},[1314,22454,22112],{},[1685,22456,1873],{"stretchy":1872},[1314,22458,10218],{},[1685,22460,1884],{"stretchy":1872},[1685,22462,1980],{},[1562,22464,22465],{},"12,29",[1319,22467,22468],{"encoding":1321},"CL(R)=12{,}29",[1296,22470,22472],{"className":22471},[1299],[1301,22473,22474],{"xmlns":1303},[1305,22475,22476,22495],{},[1308,22477,22478,22480,22482,22484,22486,22488,22490,22492],{},[1314,22479,22138],{},[1314,22481,1201],{},[1314,22483,22112],{},[1685,22485,1873],{"stretchy":1872},[1314,22487,10218],{},[1685,22489,1884],{"stretchy":1872},[1685,22491,1980],{},[1562,22493,22494],{},"28,06",[1319,22496,22497],{"encoding":1321},"UCL(R)=28{,}06",[1296,22499,22501],{"className":22500},[1299],[1301,22502,22503],{"xmlns":1303},[1305,22504,22505,22523],{},[1308,22506,22507,22509,22511,22513,22515,22517,22519,22521],{},[1314,22508,22112],{},[1314,22510,1201],{},[1314,22512,22112],{},[1685,22514,1873],{"stretchy":1872},[1314,22516,10218],{},[1685,22518,1884],{"stretchy":1872},[1685,22520,1980],{},[1562,22522,1564],{},[1319,22524,22184],{"encoding":1321}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1148,22527,22528,22529,22546,22547,1323,22578,1323,22611,22644],{},"Konečný diagram ",[1296,22530,22532],{"className":22531},[1299],[1301,22533,22534],{"xmlns":1303},[1305,22535,22536,22544],{},[1308,22537,22538],{},[2722,22539,22540,22542],{"accent":1530},[1314,22541,6716],{},[1685,22543,11454],{},[1319,22545,21557],{"encoding":1321}," na stejných 17 podskupinách má ",[1296,22548,22550],{"className":22549},[1299],[1301,22551,22552],{"xmlns":1303},[1305,22553,22554,22575],{},[1308,22555,22556,22558,22560,22562,22568,22570,22572],{},[1314,22557,1201],{},[1314,22559,22112],{},[1685,22561,1873],{"stretchy":1872},[2722,22563,22564,22566],{"accent":1530},[1314,22565,6716],{},[1685,22567,11454],{},[1685,22569,1884],{"stretchy":1872},[1685,22571,1980],{},[1562,22573,22574],{},"99,76",[1319,22576,22577],{"encoding":1321},"CL(\\bar{x})=99{,}76",[1296,22579,22581],{"className":22580},[1299],[1301,22582,22583],{"xmlns":1303},[1305,22584,22585,22608],{},[1308,22586,22587,22589,22591,22593,22595,22601,22603,22605],{},[1314,22588,22138],{},[1314,22590,1201],{},[1314,22592,22112],{},[1685,22594,1873],{"stretchy":1872},[2722,22596,22597,22599],{"accent":1530},[1314,22598,6716],{},[1685,22600,11454],{},[1685,22602,1884],{"stretchy":1872},[1685,22604,1980],{},[1562,22606,22607],{},"108,73",[1319,22609,22610],{"encoding":1321},"UCL(\\bar{x})=108{,}73",[1296,22612,22614],{"className":22613},[1299],[1301,22615,22616],{"xmlns":1303},[1305,22617,22618,22641],{},[1308,22619,22620,22622,22624,22626,22628,22634,22636,22638],{},[1314,22621,22112],{},[1314,22623,1201],{},[1314,22625,22112],{},[1685,22627,1873],{"stretchy":1872},[2722,22629,22630,22632],{"accent":1530},[1314,22631,6716],{},[1685,22633,11454],{},[1685,22635,1884],{"stretchy":1872},[1685,22637,1980],{},[1562,22639,22640],{},"90,80",[1319,22642,22643],{"encoding":1321},"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.",[1148,22646,22647],{},[4382,22648],{"alt":22649,"className":22650,"src":22651},"mask-rd-priklad1-meze",[1245,4386],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1148,22653,22654,22655,22657,22658,22660],{},"V R se diagramy sestrojí funkcí ",[3468,22656,21561],{}," z balíčku ",[3468,22659,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3692,22662,22664],{"className":3694,"code":22663,"language":71,"meta":1452,"style":1452},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3468,22665,22666,22676,22699,22722],{"__ignoreMap":1452},[1296,22667,22668,22670,22672,22674],{"class":3700,"line":10},[1296,22669,17392],{"class":3707},[1296,22671,1873],{"class":3715},[1296,22673,360],{"class":3703},[1296,22675,3900],{"class":3715},[1296,22677,22678,22680,22682,22684,22686,22689,22691,22693,22695,22697],{"class":3700,"line":27},[1296,22679,20103],{"class":3703},[1296,22681,3708],{"class":3707},[1296,22683,20108],{"class":3711},[1296,22685,1873],{"class":3715},[1296,22687,22688],{"class":3839},"\"3_2.txt\"",[1296,22690,1795],{"class":3707},[1296,22692,20118],{"class":3703},[1296,22694,3796],{"class":3707},[1296,22696,3809],{"class":3723},[1296,22698,3900],{"class":3715},[1296,22700,22701,22703,22705,22707,22709,22711,22713,22716,22719],{"class":3700,"line":148},[1296,22702,360],{"class":3711},[1296,22704,1873],{"class":3715},[1296,22706,20103],{"class":3703},[1296,22708,1795],{"class":3707},[1296,22710,12218],{"class":3703},[1296,22712,3796],{"class":3707},[1296,22714,22715],{"class":3839}," \"R\"",[1296,22717,22718],{"class":3715},")      ",[1296,22720,22721],{"class":12028},"# diagram R\n",[1296,22723,22724,22726,22728,22730,22732,22734,22736,22739,22741],{"class":3700,"line":111},[1296,22725,360],{"class":3711},[1296,22727,1873],{"class":3715},[1296,22729,20103],{"class":3703},[1296,22731,1795],{"class":3707},[1296,22733,12218],{"class":3703},[1296,22735,3796],{"class":3707},[1296,22737,22738],{"class":3839}," \"xbar\"",[1296,22740,12025],{"class":3715},[1296,22742,22743],{"class":12028},"# diagram x̄\n",[1148,22745,22746,22747,22750],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3468,22748,22749],{},"data[-4, ]",") a diagram se sestrojí znovu.",[16742,22752,21258,22754],{"id":22753},"diagram-xˉsbarx-s",[1296,22755,22757],{"className":22756},[1299],[1301,22758,22759],{"xmlns":1303},[1305,22760,22761,22777],{},[1308,22762,22763,22765,22771,22773,22775],{},[1685,22764,1873],{"stretchy":1872},[2722,22766,22767,22769],{"accent":1530},[1314,22768,6716],{},[1685,22770,11454],{},[1685,22772,1795],{"separator":1530},[1314,22774,1852],{},[1685,22776,1884],{"stretchy":1872},[1319,22778,20672],{"encoding":1321},[1148,22780,21286,22781,22802,22803,22821,22822,22847],{},[1296,22782,22784],{"className":22783},[1299],[1301,22785,22786],{"xmlns":1303},[1305,22787,22788,22800],{},[1308,22789,22790],{},[1311,22791,22792,22798],{},[2722,22793,22794,22796],{"accent":1530},[1314,22795,6716],{},[1685,22797,11454],{},[1314,22799,1876],{},[1319,22801,21308],{"encoding":1321}," a výběrové směrodatné odchylky ",[1296,22804,22806],{"className":22805},[1299],[1301,22807,22808],{"xmlns":1303},[1305,22809,22810,22818],{},[1308,22811,22812],{},[1311,22813,22814,22816],{},[1314,22815,1852],{},[1314,22817,1876],{},[1319,22819,22820],{"encoding":1321},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1296,22823,22825],{"className":22824},[1299],[1301,22826,22827],{"xmlns":1303},[1305,22828,22829,22845],{},[1308,22830,22831,22833,22839,22841,22843],{},[1685,22832,1873],{"stretchy":1872},[2722,22834,22835,22837],{"accent":1530},[1314,22836,6716],{},[1685,22838,11454],{},[1685,22840,1795],{"separator":1530},[1314,22842,10218],{},[1685,22844,1884],{"stretchy":1872},[1319,22846,20646],{"encoding":1321},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3692,22849,22851],{"className":3694,"code":22850,"language":71,"meta":1452,"style":1452},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3468,22852,22853,22875,22897],{"__ignoreMap":1452},[1296,22854,22855,22857,22859,22861,22863,22865,22867,22869,22871,22873],{"class":3700,"line":10},[1296,22856,20103],{"class":3703},[1296,22858,3708],{"class":3707},[1296,22860,20108],{"class":3711},[1296,22862,1873],{"class":3715},[1296,22864,22688],{"class":3839},[1296,22866,1795],{"class":3707},[1296,22868,20118],{"class":3703},[1296,22870,3796],{"class":3707},[1296,22872,3809],{"class":3723},[1296,22874,3900],{"class":3715},[1296,22876,22877,22879,22881,22883,22885,22887,22889,22892,22894],{"class":3700,"line":27},[1296,22878,360],{"class":3711},[1296,22880,1873],{"class":3715},[1296,22882,20103],{"class":3703},[1296,22884,1795],{"class":3707},[1296,22886,12218],{"class":3703},[1296,22888,3796],{"class":3707},[1296,22890,22891],{"class":3839}," \"S\"",[1296,22893,22718],{"class":3715},[1296,22895,22896],{"class":12028},"# diagram s\n",[1296,22898,22899,22901,22903,22905,22907,22909,22911,22913,22915],{"class":3700,"line":148},[1296,22900,360],{"class":3711},[1296,22902,1873],{"class":3715},[1296,22904,20103],{"class":3703},[1296,22906,1795],{"class":3707},[1296,22908,12218],{"class":3703},[1296,22910,3796],{"class":3707},[1296,22912,22738],{"class":3839},[1296,22914,12025],{"class":3715},[1296,22916,22743],{"class":12028},[16742,22918,21258,22920],{"id":22919},"diagram-xirklix_i-r_kli",[1296,22921,22923],{"className":22922},[1299],[1301,22924,22925],{"xmlns":1303},[1305,22926,22927,22955],{},[1308,22928,22929,22931,22937,22939,22953],{},[1685,22930,1873],{"stretchy":1872},[1311,22932,22933,22935],{},[1314,22934,6716],{},[1314,22936,1876],{},[1685,22938,1795],{"separator":1530},[1311,22940,22941,22943],{},[1314,22942,10218],{},[1308,22944,22945,22947,22949,22951],{},[1314,22946,1343],{},[1314,22948,20702],{},[1685,22950,1795],{"separator":1530},[1314,22952,1876],{},[1685,22954,1884],{"stretchy":1872},[1319,22956,20711],{"encoding":1321},[1148,22958,22959,22960,22985,22986,1956],{},"Používá se za stejných podmínek jako ",[1296,22961,22963],{"className":22962},[1299],[1301,22964,22965],{"xmlns":1303},[1305,22966,22967,22983],{},[1308,22968,22969,22971,22977,22979,22981],{},[1685,22970,1873],{"stretchy":1872},[2722,22972,22973,22975],{"accent":1530},[1314,22974,6716],{},[1685,22976,11454],{},[1685,22978,1795],{"separator":1530},[1314,22980,10218],{},[1685,22982,1884],{"stretchy":1872},[1319,22984,20646],{"encoding":1321},", 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 ",[1108,22987,22988],{},"klouzavé rozpětí",[1296,22990,22992],{"className":22991},[1299],[1301,22993,22994],{"xmlns":1303,"display":1962},[1305,22995,22996,23123],{},[1308,22997,22998,23012,23014,23017,23023,23025,23037,23039,23041,23043,23045,23047,23049,23051,23053,23055,23057,23059,23061,23063,23065,23079,23081,23093,23107,23121],{},[1311,22999,23000,23002],{},[1314,23001,10218],{},[1308,23003,23004,23006,23008,23010],{},[1314,23005,1343],{},[1314,23007,20702],{},[1685,23009,1795],{"separator":1530},[1314,23011,1876],{},[1685,23013,1980],{},[1314,23015,23016],{"mathvariant":2119},"∣",[1311,23018,23019,23021],{},[1314,23020,6716],{},[1314,23022,1876],{},[1685,23024,3062],{},[1311,23026,23027,23029],{},[1314,23028,6716],{},[1308,23030,23031,23033,23035],{},[1314,23032,1876],{},[1685,23034,3062],{},[1562,23036,1792],{},[1314,23038,23016],{"mathvariant":2119},[1685,23040,1795],{"separator":1530},[2010,23042],{"width":18013},[1314,23044,1876],{},[1685,23046,1980],{},[1562,23048,1586],{},[1685,23050,1795],{"separator":1530},[1562,23052,3590],{},[1685,23054,1795],{"separator":1530},[1685,23056,1798],{},[1685,23058,1795],{"separator":1530},[1314,23060,1343],{},[1685,23062,1795],{"separator":1530},[2010,23064],{"width":2012},[1311,23066,23067,23073],{},[2722,23068,23069,23071],{"accent":1530},[1314,23070,10218],{},[1685,23072,11454],{},[1308,23074,23075,23077],{},[1314,23076,1343],{},[1314,23078,20702],{},[1685,23080,1980],{},[2738,23082,23083,23085],{},[1562,23084,1792],{},[1308,23086,23087,23089,23091],{},[1314,23088,1343],{},[1685,23090,3062],{},[1562,23092,1792],{},[1982,23094,23095,23097,23105],{},[1685,23096,1986],{},[1308,23098,23099,23101,23103],{},[1314,23100,1876],{},[1685,23102,1980],{},[1562,23104,1586],{},[1314,23106,1343],{},[1311,23108,23109,23111],{},[1314,23110,10218],{},[1308,23112,23113,23115,23117,23119],{},[1314,23114,1343],{},[1314,23116,20702],{},[1685,23118,1795],{"separator":1530},[1314,23120,1876],{},[1314,23122,1395],{"mathvariant":2119},[1319,23124,23125],{"encoding":1321},"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}.",[1148,23127,23128,23129,1370,23146,23172,23173,23198,23199,23216],{},"Regulované veličiny jsou hodnoty ",[1296,23130,23132],{"className":23131},[1299],[1301,23133,23134],{"xmlns":1303},[1305,23135,23136,23144],{},[1308,23137,23138],{},[1311,23139,23140,23142],{},[1314,23141,6716],{},[1314,23143,1876],{},[1319,23145,17129],{"encoding":1321},[1296,23147,23149],{"className":23148},[1299],[1301,23150,23151],{"xmlns":1303},[1305,23152,23153,23169],{},[1308,23154,23155],{},[1311,23156,23157,23159],{},[1314,23158,10218],{},[1308,23160,23161,23163,23165,23167],{},[1314,23162,1343],{},[1314,23164,20702],{},[1685,23166,1795],{"separator":1530},[1314,23168,1876],{},[1319,23170,23171],{"encoding":1321},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1296,23174,23176],{"className":23175},[1299],[1301,23177,23178],{"xmlns":1303},[1305,23179,23180,23196],{},[1308,23181,23182],{},[1311,23183,23184,23186],{},[1314,23185,10218],{},[1308,23187,23188,23190,23192,23194],{},[1314,23189,1343],{},[1314,23191,20702],{},[1685,23193,1795],{"separator":1530},[1314,23195,1876],{},[1319,23197,23171],{"encoding":1321},", potom diagramu ",[1296,23200,23202],{"className":23201},[1299],[1301,23203,23204],{"xmlns":1303},[1305,23205,23206,23214],{},[1308,23207,23208],{},[1311,23209,23210,23212],{},[1314,23211,6716],{},[1314,23213,1876],{},[1319,23215,17129],{"encoding":1321},". Data jsou jeden vektor naměřených hodnot:",[3692,23218,23220],{"className":3694,"code":23219,"language":71,"meta":1452,"style":1452},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3468,23221,23222,23245],{"__ignoreMap":1452},[1296,23223,23224,23226,23228,23230,23232,23235,23237,23239,23241,23243],{"class":3700,"line":10},[1296,23225,20103],{"class":3703},[1296,23227,3708],{"class":3707},[1296,23229,20108],{"class":3711},[1296,23231,1873],{"class":3715},[1296,23233,23234],{"class":3839},"\"3_3.txt\"",[1296,23236,1795],{"class":3707},[1296,23238,20118],{"class":3703},[1296,23240,3796],{"class":3707},[1296,23242,3809],{"class":3723},[1296,23244,3900],{"class":3715},[1296,23246,23247,23249,23251,23253,23255,23257,23259,23261,23263,23265,23267,23270],{"class":3700,"line":27},[1296,23248,360],{"class":3711},[1296,23250,1873],{"class":3715},[1296,23252,20103],{"class":3703},[1296,23254,8170],{"class":3715},[1296,23256,1795],{"class":3707},[1296,23258,4638],{"class":3723},[1296,23260,8187],{"class":3715},[1296,23262,1795],{"class":3707},[1296,23264,12218],{"class":3703},[1296,23266,3796],{"class":3707},[1296,23268,23269],{"class":3839}," \"xbar.one\"",[1296,23271,3900],{"class":3715},[1143,23273,23275],{"id":23274},"regulace-srovnáváním","Regulace srovnáváním",[1148,23277,23278],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1162,23280,23281,23294],{},[1165,23282,23283],{},[1168,23284,23285,23288,23291],{},[1171,23286,23287],{},"Sleduje se",[1171,23289,23290],{},"Konstantní rozsah podskupin",[1171,23292,23293],{},"Nekonstantní rozsah podskupin",[1178,23295,23296,23331],{},[1168,23297,23298,23301,23316],{},[1183,23299,23300],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1183,23302,23303],{},[1296,23304,23306],{"className":23305},[1299],[1301,23307,23308],{"xmlns":1303},[1305,23309,23310,23314],{},[1308,23311,23312],{},[1314,23313,3718],{},[1319,23315,3718],{"encoding":1321},[1183,23317,23318],{},[1296,23319,23321],{"className":23320},[1299],[1301,23322,23323],{"xmlns":1303},[1305,23324,23325,23329],{},[1308,23326,23327],{},[1314,23328,11523],{},[1319,23330,11523],{"encoding":1321},[1168,23332,23333,23336,23353],{},[1183,23334,23335],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1183,23337,23338],{},[1296,23339,23341],{"className":23340},[1299],[1301,23342,23343],{"xmlns":1303},[1305,23344,23345,23351],{},[1308,23346,23347,23349],{},[1314,23348,1683],{},[1314,23350,1148],{},[1319,23352,20758],{"encoding":1321},[1183,23354,23355],{},[1296,23356,23358],{"className":23357},[1299],[1301,23359,23360],{"xmlns":1303},[1305,23361,23362,23366],{},[1308,23363,23364],{},[1314,23365,1148],{},[1319,23367,1148],{"encoding":1321},[16742,23369,21258,23371],{"id":23370},"diagram-cc",[1296,23372,23374],{"className":23373},[1299],[1301,23375,23376],{"xmlns":1303},[1305,23377,23378,23382],{},[1308,23379,23380],{},[1314,23381,3718],{},[1319,23383,3718],{"encoding":1321},[1148,23385,23386,23387,23405,23406,23419,23420,23445,23446,23459],{},"Regulovanou veličinou ",[1296,23388,23390],{"className":23389},[1299],[1301,23391,23392],{"xmlns":1303},[1305,23393,23394,23402],{},[1308,23395,23396],{},[1311,23397,23398,23400],{},[1314,23399,3718],{},[1314,23401,1876],{},[1319,23403,23404],{"encoding":1321},"c_i"," je počet neshod na produktech v ",[1296,23407,23409],{"className":23408},[1299],[1301,23410,23411],{"xmlns":1303},[1305,23412,23413,23417],{},[1308,23414,23415],{},[1314,23416,1876],{},[1319,23418,1876],{"encoding":1321},"-té logické podskupině, ",[1296,23421,23423],{"className":23422},[1299],[1301,23424,23425],{"xmlns":1303},[1305,23426,23427,23443],{},[1308,23428,23429,23431,23433,23435,23437,23439,23441],{},[1314,23430,1876],{},[1685,23432,1980],{},[1562,23434,1792],{},[1685,23436,1795],{"separator":1530},[1685,23438,1798],{},[1685,23440,1795],{"separator":1530},[1314,23442,1343],{},[1319,23444,21471],{"encoding":1321},"; v každé podskupině je stejný počet ",[1296,23447,23449],{"className":23448},[1299],[1301,23450,23451],{"xmlns":1303},[1305,23452,23453,23457],{},[1308,23454,23455],{},[1314,23456,1683],{},[1319,23458,1683],{"encoding":1321}," 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.",[1514,23461,23463,23470],{"className":23462,"dataCallout":3475},[1517,3474],[1148,23464,23466,23469],{"className":23465},[1523],[1296,23467],{"className":23468,"ariaHidden":1530},[1527,3482,1529],"Příklad: bodové vady na pásech látky",[1148,23471,23472,23473,23490,23491,1395],{},"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 ",[1296,23474,23476],{"className":23475},[1299],[1301,23477,23478],{"xmlns":1303},[1305,23479,23480,23488],{},[1308,23481,23482],{},[1311,23483,23484,23486],{},[1314,23485,3718],{},[1314,23487,1876],{},[1319,23489,23404],{"encoding":1321},". Sestrojte regulační diagram ",[1296,23492,23494],{"className":23493},[1299],[1301,23495,23496],{"xmlns":1303},[1305,23497,23498,23502],{},[1308,23499,23500],{},[1314,23501,3718],{},[1319,23503,3718],{"encoding":1321},[3692,23505,23507],{"className":3694,"code":23506,"language":71,"meta":1452,"style":1452},"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",[3468,23508,23509,23599,23603,23628],{"__ignoreMap":1452},[1296,23510,23511,23513,23515,23517,23519,23521,23523,23525,23527,23529,23531,23533,23535,23537,23539,23541,23543,23545,23547,23549,23551,23553,23555,23557,23559,23561,23563,23565,23567,23569,23571,23573,23575,23577,23579,23581,23583,23585,23587,23589,23591,23593,23595,23597],{"class":3700,"line":10},[1296,23512,23404],{"class":3703},[1296,23514,3708],{"class":3707},[1296,23516,3834],{"class":3711},[1296,23518,1873],{"class":3715},[1296,23520,13325],{"class":3723},[1296,23522,1795],{"class":3707},[1296,23524,4638],{"class":3723},[1296,23526,1795],{"class":3707},[1296,23528,4179],{"class":3723},[1296,23530,1795],{"class":3707},[1296,23532,9989],{"class":3723},[1296,23534,1795],{"class":3707},[1296,23536,9965],{"class":3723},[1296,23538,1795],{"class":3707},[1296,23540,12223],{"class":3723},[1296,23542,1795],{"class":3707},[1296,23544,4179],{"class":3723},[1296,23546,1795],{"class":3707},[1296,23548,9965],{"class":3723},[1296,23550,1795],{"class":3707},[1296,23552,3799],{"class":3723},[1296,23554,1795],{"class":3707},[1296,23556,3799],{"class":3723},[1296,23558,1795],{"class":3707},[1296,23560,12223],{"class":3723},[1296,23562,1795],{"class":3707},[1296,23564,10850],{"class":3723},[1296,23566,1795],{"class":3707},[1296,23568,10850],{"class":3723},[1296,23570,1795],{"class":3707},[1296,23572,10850],{"class":3723},[1296,23574,1795],{"class":3707},[1296,23576,4638],{"class":3723},[1296,23578,1795],{"class":3707},[1296,23580,12223],{"class":3723},[1296,23582,1795],{"class":3707},[1296,23584,10850],{"class":3723},[1296,23586,1795],{"class":3707},[1296,23588,4638],{"class":3723},[1296,23590,1795],{"class":3707},[1296,23592,9989],{"class":3723},[1296,23594,1795],{"class":3707},[1296,23596,12223],{"class":3723},[1296,23598,3900],{"class":3715},[1296,23600,23601],{"class":3700,"line":27},[1296,23602,10036],{"emptyLinePlaceholder":1464},[1296,23604,23605,23608,23610,23613,23615,23617,23619,23621,23623,23626],{"class":3700,"line":148},[1296,23606,23607],{"class":3703},"q_c",[1296,23609,3708],{"class":3707},[1296,23611,23612],{"class":3711}," qcc",[1296,23614,1873],{"class":3715},[1296,23616,23404],{"class":3703},[1296,23618,1795],{"class":3707},[1296,23620,12218],{"class":3703},[1296,23622,3796],{"class":3707},[1296,23624,23625],{"class":3839}," \"c\"",[1296,23627,3900],{"class":3715},[1296,23629,23630,23632,23634,23636],{"class":3700,"line":111},[1296,23631,16863],{"class":3711},[1296,23633,1873],{"class":3715},[1296,23635,23607],{"class":3703},[1296,23637,3900],{"class":3715},[3692,23639,23642],{"className":23640,"code":23641,"language":3922,"meta":1452},[3920],"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",[3468,23643,23641],{"__ignoreMap":1452},[1148,23645,23646,23647,23676,23677,23700,23701,23723],{},"Průměrný počet vad na pás je ",[1296,23648,23650],{"className":23649},[1299],[1301,23651,23652],{"xmlns":1303},[1305,23653,23654,23673],{},[1308,23655,23656,23658,23660,23662,23668,23670],{},[1314,23657,1201],{},[1314,23659,22112],{},[1685,23661,1980],{},[2722,23663,23664,23666],{"accent":1530},[1314,23665,3718],{},[1685,23667,11454],{},[1685,23669,1980],{},[1562,23671,23672],{},"3,4",[1319,23674,23675],{"encoding":1321},"CL = \\bar{c} = 3{,}4",", horní mez ",[1296,23678,23680],{"className":23679},[1299],[1301,23681,23682],{"xmlns":1303},[1305,23683,23684,23697],{},[1308,23685,23686,23688,23690,23692,23694],{},[1314,23687,22138],{},[1314,23689,1201],{},[1314,23691,22112],{},[1685,23693,1980],{},[1562,23695,23696],{},"8,93",[1319,23698,23699],{"encoding":1321},"UCL = 8{,}93"," a dolní mez ",[1296,23702,23704],{"className":23703},[1299],[1301,23705,23706],{"xmlns":1303},[1305,23707,23708,23720],{},[1308,23709,23710,23712,23714,23716,23718],{},[1314,23711,22112],{},[1314,23713,1201],{},[1314,23715,22112],{},[1685,23717,1980],{},[1562,23719,1564],{},[1319,23721,23722],{"encoding":1321},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1148,23725,23726],{},[4382,23727],{"alt":23728,"className":23729,"src":23730},"mask-rd-priklad2-c",[1245,4386],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[16742,23732,21258,23734],{"id":23733},"diagram-uu",[1296,23735,23737],{"className":23736},[1299],[1301,23738,23739],{"xmlns":1303},[1305,23740,23741,23745],{},[1308,23742,23743],{},[1314,23744,11523],{},[1319,23746,11523],{"encoding":1321},[1148,23748,23386,23749,23783,23784,23802],{},[1296,23750,23752],{"className":23751},[1299],[1301,23753,23754],{"xmlns":1303},[1305,23755,23756,23780],{},[1308,23757,23758,23764,23766,23772,23774],{},[1311,23759,23760,23762],{},[1314,23761,11523],{},[1314,23763,1876],{},[1685,23765,1980],{},[1311,23767,23768,23770],{},[1314,23769,3718],{},[1314,23771,1876],{},[1314,23773,1502],{"mathvariant":2119},[1311,23775,23776,23778],{},[1314,23777,1683],{},[1314,23779,1876],{},[1319,23781,23782],{"encoding":1321},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1296,23785,23787],{"className":23786},[1299],[1301,23788,23789],{"xmlns":1303},[1305,23790,23791,23799],{},[1308,23792,23793],{},[1311,23794,23795,23797],{},[1314,23796,1683],{},[1314,23798,1876],{},[1319,23800,23801],{"encoding":1321},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1148,23804,23805,23806,23809],{},"Za ",[3468,23807,23808],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3692,23811,23813],{"className":3694,"code":23812,"language":71,"meta":1452,"style":1452},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3468,23814,23815,23841],{"__ignoreMap":1452},[1296,23816,23817,23819,23821,23823,23825,23828,23830,23832,23834,23836,23838],{"class":3700,"line":10},[1296,23818,20103],{"class":3703},[1296,23820,3708],{"class":3707},[1296,23822,20108],{"class":3711},[1296,23824,1873],{"class":3715},[1296,23826,23827],{"class":3839},"\"3_4.txt\"",[1296,23829,1795],{"class":3707},[1296,23831,20118],{"class":3703},[1296,23833,3796],{"class":3707},[1296,23835,3809],{"class":3723},[1296,23837,12025],{"class":3715},[1296,23839,23840],{"class":12028},"# počty suků a rozměry prken\n",[1296,23842,23843,23845,23847,23849,23851,23853,23855,23857,23859,23861,23863,23866,23868,23871,23873,23875,23877,23879,23881],{"class":3700,"line":27},[1296,23844,360],{"class":3711},[1296,23846,1873],{"class":3715},[1296,23848,20103],{"class":3703},[1296,23850,8170],{"class":3715},[1296,23852,1795],{"class":3707},[1296,23854,4638],{"class":3723},[1296,23856,8187],{"class":3715},[1296,23858,1795],{"class":3707},[1296,23860,12218],{"class":3703},[1296,23862,3796],{"class":3707},[1296,23864,23865],{"class":3839}," \"u\"",[1296,23867,1795],{"class":3707},[1296,23869,23870],{"class":3703}," sizes",[1296,23872,3796],{"class":3707},[1296,23874,20162],{"class":3703},[1296,23876,8170],{"class":3715},[1296,23878,1795],{"class":3707},[1296,23880,4179],{"class":3723},[1296,23882,23883],{"class":3715},"])\n",[16742,23885,21258,23887],{"id":23886},"diagram-npnp",[1296,23888,23890],{"className":23889},[1299],[1301,23891,23892],{"xmlns":1303},[1305,23893,23894,23900],{},[1308,23895,23896,23898],{},[1314,23897,1683],{},[1314,23899,1148],{},[1319,23901,20758],{"encoding":1321},[1148,23903,23904,23905,6777,23920,23933],{},"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 ",[1296,23906,23908],{"className":23907},[1299],[1301,23909,23910],{"xmlns":1303},[1305,23911,23912,23918],{},[1308,23913,23914,23916],{},[1314,23915,1683],{},[1314,23917,1148],{},[1319,23919,20758],{"encoding":1321},[1296,23921,23923],{"className":23922},[1299],[1301,23924,23925],{"xmlns":1303},[1305,23926,23927,23931],{},[1308,23928,23929],{},[1314,23930,1148],{},[1319,23932,1148],{"encoding":1321}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1148,23935,23936,23937,1956],{},"Pro konstantní rozsah ",[1296,23938,23940],{"className":23939},[1299],[1301,23941,23942],{"xmlns":1303},[1305,23943,23944,23948],{},[1308,23945,23946],{},[1314,23947,1683],{},[1319,23949,1683],{"encoding":1321},[3692,23951,23953],{"className":3694,"code":23952,"language":71,"meta":1452,"style":1452},"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",[3468,23954,23955,23981],{"__ignoreMap":1452},[1296,23956,23957,23959,23961,23963,23965,23968,23970,23972,23974,23976,23978],{"class":3700,"line":10},[1296,23958,20103],{"class":3703},[1296,23960,3708],{"class":3707},[1296,23962,20108],{"class":3711},[1296,23964,1873],{"class":3715},[1296,23966,23967],{"class":3839},"\"3_7.txt\"",[1296,23969,1795],{"class":3707},[1296,23971,20118],{"class":3703},[1296,23973,3796],{"class":3707},[1296,23975,3809],{"class":3723},[1296,23977,12025],{"class":3715},[1296,23979,23980],{"class":12028},"# počty vadných tabletů v sériích po 100 kusech\n",[1296,23982,23983,23985,23987,23989,23991,23993,23995,23997,23999,24001,24003,24006,24008,24010,24012,24014],{"class":3700,"line":27},[1296,23984,360],{"class":3711},[1296,23986,1873],{"class":3715},[1296,23988,20103],{"class":3703},[1296,23990,8170],{"class":3715},[1296,23992,1795],{"class":3707},[1296,23994,4638],{"class":3723},[1296,23996,8187],{"class":3715},[1296,23998,1795],{"class":3707},[1296,24000,12218],{"class":3703},[1296,24002,3796],{"class":3707},[1296,24004,24005],{"class":3839}," \"np\"",[1296,24007,1795],{"class":3707},[1296,24009,23870],{"class":3703},[1296,24011,3796],{"class":3707},[1296,24013,15334],{"class":3723},[1296,24015,3900],{"class":3715},[16742,24017,21258,24019],{"id":24018},"diagram-pp",[1296,24020,24022],{"className":24021},[1299],[1301,24023,24024],{"xmlns":1303},[1305,24025,24026,24030],{},[1308,24027,24028],{},[1314,24029,1148],{},[1319,24031,1148],{"encoding":1321},[1148,24033,24034,24035,24071],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1296,24036,24038],{"className":24037},[1299],[1301,24039,24040],{"xmlns":1303},[1305,24041,24042,24068],{},[1308,24043,24044,24050,24052,24054,24060,24062],{},[1311,24045,24046,24048],{},[1314,24047,1148],{},[1314,24049,1876],{},[1685,24051,1980],{},[1314,24053,1683],{},[1311,24055,24056,24058],{},[1314,24057,1148],{},[1314,24059,1876],{},[1314,24061,1502],{"mathvariant":2119},[1311,24063,24064,24066],{},[1314,24065,1683],{},[1314,24067,1876],{},[1319,24069,24070],{"encoding":1321},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1148,24073,23805,24074,24076],{},[3468,24075,23808],{}," se dosadí vektor rozsahů logických podskupin:",[3692,24078,24080],{"className":3694,"code":24079,"language":71,"meta":1452,"style":1452},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3468,24081,24082,24108],{"__ignoreMap":1452},[1296,24083,24084,24086,24088,24090,24092,24095,24097,24099,24101,24103,24105],{"class":3700,"line":10},[1296,24085,20103],{"class":3703},[1296,24087,3708],{"class":3707},[1296,24089,20108],{"class":3711},[1296,24091,1873],{"class":3715},[1296,24093,24094],{"class":3839},"\"3_6.txt\"",[1296,24096,1795],{"class":3707},[1296,24098,20118],{"class":3703},[1296,24100,3796],{"class":3707},[1296,24102,3809],{"class":3723},[1296,24104,12025],{"class":3715},[1296,24106,24107],{"class":12028},"# počty vadných tabletů a rozsahy sérií\n",[1296,24109,24110,24112,24114,24116,24118,24120,24122,24124,24126,24128,24130,24133,24135,24137,24139,24141,24143,24145,24147],{"class":3700,"line":27},[1296,24111,360],{"class":3711},[1296,24113,1873],{"class":3715},[1296,24115,20103],{"class":3703},[1296,24117,8170],{"class":3715},[1296,24119,1795],{"class":3707},[1296,24121,4638],{"class":3723},[1296,24123,8187],{"class":3715},[1296,24125,1795],{"class":3707},[1296,24127,12218],{"class":3703},[1296,24129,3796],{"class":3707},[1296,24131,24132],{"class":3839}," \"p\"",[1296,24134,1795],{"class":3707},[1296,24136,23870],{"class":3703},[1296,24138,3796],{"class":3707},[1296,24140,20162],{"class":3703},[1296,24142,8170],{"class":3715},[1296,24144,1795],{"class":3707},[1296,24146,4179],{"class":3723},[1296,24148,23883],{"class":3715},[1143,24150,24152],{"id":24151},"indexy-způsobilosti","Indexy způsobilosti",[1148,24154,24155,24156,24175,24176,24194],{},"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 ",[1296,24157,24159],{"className":24158},[1299],[1301,24160,24161],{"xmlns":1303},[1305,24162,24163,24172],{},[1308,24164,24165,24167,24170],{},[1314,24166,22112],{},[1314,24168,24169],{},"S",[1314,24171,22112],{},[1319,24173,24174],{"encoding":1321},"LSL"," a horní meze ",[1296,24177,24179],{"className":24178},[1299],[1301,24180,24181],{"xmlns":1303},[1305,24182,24183,24191],{},[1308,24184,24185,24187,24189],{},[1314,24186,22138],{},[1314,24188,24169],{},[1314,24190,22112],{},[1319,24192,24193],{"encoding":1321},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[16742,24196,24198,24215],{"id":24197},"cpc_p-index-způsobilosti",[1296,24199,24201],{"className":24200},[1299],[1301,24202,24203],{"xmlns":1303},[1305,24204,24205,24213],{},[1308,24206,24207],{},[1311,24208,24209,24211],{},[1314,24210,1201],{},[1314,24212,1148],{},[1319,24214,1322],{"encoding":1321}," — index způsobilosti",[1148,24217,24218,24219,1956],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1296,24220,24222],{"className":24221},[1299],[1301,24223,24224],{"xmlns":1303},[1305,24225,24226,24232],{},[1308,24227,24228,24230],{},[1562,24229,3963],{},[1314,24231,6895],{},[1319,24233,24234],{"encoding":1321},"6\\sigma",[1296,24236,24238],{"className":24237},[1299],[1301,24239,24240],{"xmlns":1303,"display":1962},[1305,24241,24242,24278],{},[1308,24243,24244,24250,24252,24276],{},[1311,24245,24246,24248],{},[1314,24247,1201],{},[1314,24249,1148],{},[1685,24251,1980],{},[2738,24253,24254,24270],{},[1308,24255,24256,24258,24260,24262,24264,24266,24268],{},[1314,24257,22138],{},[1314,24259,24169],{},[1314,24261,22112],{},[1685,24263,3062],{},[1314,24265,22112],{},[1314,24267,24169],{},[1314,24269,22112],{},[1308,24271,24272,24274],{},[1562,24273,3963],{},[1314,24275,6895],{},[1314,24277,1395],{"mathvariant":2119},[1319,24279,24280],{"encoding":1321},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1148,24282,24283,24300,24301,24314,24315,1395],{},[1296,24284,24286],{"className":24285},[1299],[1301,24287,24288],{"xmlns":1303},[1305,24289,24290,24298],{},[1308,24291,24292],{},[1311,24293,24294,24296],{},[1314,24295,1201],{},[1314,24297,1148],{},[1319,24299,1322],{"encoding":1321}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1296,24302,24304],{"className":24303},[1299],[1301,24305,24306],{"xmlns":1303},[1305,24307,24308,24312],{},[1308,24309,24310],{},[1314,24311,6895],{},[1319,24313,6927],{"encoding":1321}," mají stejné ",[1296,24316,24318],{"className":24317},[1299],[1301,24319,24320],{"xmlns":1303},[1305,24321,24322,24330],{},[1308,24323,24324],{},[1311,24325,24326,24328],{},[1314,24327,1201],{},[1314,24329,1148],{},[1319,24331,1322],{"encoding":1321},[1148,24333,24334],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1102,24336,24337,24371,24459],{},[1105,24338,24339,3987,24342,24370],{},[1108,24340,24341],{},"míra využití tolerančního intervalu",[1296,24343,24345],{"className":24344},[1299],[1301,24346,24347],{"xmlns":1303},[1305,24348,24349,24367],{},[1308,24350,24351,24363,24365],{},[3239,24352,24353],{"scriptlevel":1564,"displaystyle":1530},[2738,24354,24355,24357],{},[1562,24356,11813],{},[1311,24358,24359,24361],{},[1314,24360,1201],{},[1314,24362,1148],{},[2907,24364,2909],{},[1314,24366,11820],{"mathvariant":2119},[1319,24368,24369],{"encoding":1321},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1105,24372,24373,24376,24377,24394,24395,1370,24427,1795],{},[1108,24374,24375],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1296,24378,24380],{"className":24379},[1299],[1301,24381,24382],{"xmlns":1303},[1305,24383,24384,24392],{},[1308,24385,24386],{},[1311,24387,24388,24390],{},[1314,24389,1201],{},[1314,24391,1148],{},[1319,24393,1322],{"encoding":1321}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1296,24396,24398],{"className":24397},[1299],[1301,24399,24400],{"xmlns":1303},[1305,24401,24402,24424],{},[1308,24403,24404,24406,24408,24410,24412,24414,24416,24418,24420,24422],{},[1314,24405,22138],{},[1314,24407,24169],{},[1314,24409,22112],{},[1685,24411,3062],{},[1685,24413,1873],{"stretchy":1872},[1314,24415,6887],{},[1685,24417,5474],{},[1562,24419,3590],{},[1314,24421,6895],{},[1685,24423,1884],{"stretchy":1872},[1319,24425,24426],{"encoding":1321},"USL-(\\mu+3\\sigma)",[1296,24428,24430],{"className":24429},[1299],[1301,24431,24432],{"xmlns":1303},[1305,24433,24434,24456],{},[1308,24435,24436,24438,24440,24442,24444,24446,24448,24450,24452,24454],{},[1685,24437,1873],{"stretchy":1872},[1314,24439,6887],{},[1685,24441,3062],{},[1562,24443,3590],{},[1314,24445,6895],{},[1685,24447,1884],{"stretchy":1872},[1685,24449,3062],{},[1314,24451,22112],{},[1314,24453,24169],{},[1314,24455,22112],{},[1319,24457,24458],{"encoding":1321},"(\\mu-3\\sigma)-LSL",[1105,24460,24461,3987,24464,6777,24504,24518],{},[1108,24462,24463],{},"podíl zmetků",[1296,24465,24467],{"className":24466},[1299],[1301,24468,24469],{"xmlns":1303},[1305,24470,24471,24501],{},[1308,24472,24473,24480,24482,24484,24487,24489,24491,24493,24499],{},[1311,24474,24475,24477],{},[1314,24476,6723],{},[1314,24478,24479],{},"z",[1685,24481,1980],{},[1562,24483,1586],{},[1314,24485,24486],{"mathvariant":2119},"Φ",[1685,24488,1873],{"stretchy":1872},[1685,24490,3062],{},[1562,24492,3590],{},[1311,24494,24495,24497],{},[1314,24496,1201],{},[1314,24498,1148],{},[1685,24500,1884],{"stretchy":1872},[1319,24502,24503],{"encoding":1321},"P_z = 2\\Phi(-3C_p)",[1296,24505,24507],{"className":24506},[1299],[1301,24508,24509],{"xmlns":1303},[1305,24510,24511,24515],{},[1308,24512,24513],{},[1314,24514,24486],{"mathvariant":2119},[1319,24516,24517],{"encoding":1321},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[16742,24520,24522,24543],{"id":24521},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1296,24523,24525],{"className":24524},[1299],[1301,24526,24527],{"xmlns":1303},[1305,24528,24529,24541],{},[1308,24530,24531],{},[1311,24532,24533,24535],{},[1314,24534,1201],{},[1308,24536,24537,24539],{},[1314,24538,1148],{},[1314,24540,1343],{},[1319,24542,1346],{"encoding":1321}," — index způsobilosti s ohledem na vychýlení",[1148,24545,24546],{},"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:",[1296,24548,24550],{"className":24549},[1299],[1301,24551,24552],{"xmlns":1303,"display":1962},[1305,24553,24554,24624],{},[1308,24555,24556,24566,24568,24570,24572,24622],{},[1311,24557,24558,24560],{},[1314,24559,1201],{},[1308,24561,24562,24564],{},[1314,24563,1148],{},[1314,24565,1343],{},[1685,24567,1980],{},[1314,24569,4486],{},[1685,24571,4489],{},[1308,24573,24574,24576,24596,24598,24600,24620],{},[1685,24575,1873],{"fence":1530},[2738,24577,24578,24590],{},[1308,24579,24580,24582,24584,24586,24588],{},[1314,24581,22138],{},[1314,24583,24169],{},[1314,24585,22112],{},[1685,24587,3062],{},[1314,24589,6887],{},[1308,24591,24592,24594],{},[1562,24593,3590],{},[1314,24595,6895],{},[1685,24597,1795],{"separator":1530},[2907,24599,11309],{},[2738,24601,24602,24614],{},[1308,24603,24604,24606,24608,24610,24612],{},[1314,24605,6887],{},[1685,24607,3062],{},[1314,24609,22112],{},[1314,24611,24169],{},[1314,24613,22112],{},[1308,24615,24616,24618],{},[1562,24617,3590],{},[1314,24619,6895],{},[1685,24621,1884],{"fence":1530},[1314,24623,1395],{"mathvariant":2119},[1319,24625,24626],{"encoding":1321},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1148,24628,24629,24630,24643,24644,24674,24675,24696,24697,1395],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1296,24631,24633],{"className":24632},[1299],[1301,24634,24635],{"xmlns":1303},[1305,24636,24637,24641],{},[1308,24638,24639],{},[1314,24640,6887],{},[1319,24642,8791],{"encoding":1321}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1296,24645,24647],{"className":24646},[1299],[1301,24648,24649],{"xmlns":1303},[1305,24650,24651,24671],{},[1308,24652,24653,24663,24665],{},[1311,24654,24655,24657],{},[1314,24656,1201],{},[1308,24658,24659,24661],{},[1314,24660,1148],{},[1314,24662,1343],{},[1685,24664,1980],{},[1311,24666,24667,24669],{},[1314,24668,1201],{},[1314,24670,1148],{},[1319,24672,24673],{"encoding":1321},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1296,24676,24678],{"className":24677},[1299],[1301,24679,24680],{"xmlns":1303},[1305,24681,24682,24694],{},[1308,24683,24684],{},[1311,24685,24686,24688],{},[1314,24687,1201],{},[1308,24689,24690,24692],{},[1314,24691,1148],{},[1314,24693,1343],{},[1319,24695,1346],{"encoding":1321}," menší než ",[1296,24698,24700],{"className":24699},[1299],[1301,24701,24702],{"xmlns":1303},[1305,24703,24704,24712],{},[1308,24705,24706],{},[1311,24707,24708,24710],{},[1314,24709,1201],{},[1314,24711,1148],{},[1319,24713,1322],{"encoding":1321},[16742,24715,24717,1370,24738,24761],{"id":24716},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1296,24718,24720],{"className":24719},[1299],[1301,24721,24722],{"xmlns":1303},[1305,24723,24724,24736],{},[1308,24725,24726],{},[1311,24727,24728,24730],{},[1314,24729,1201],{},[1308,24731,24732,24734],{},[1314,24733,1148],{},[1314,24735,1366],{},[1319,24737,1369],{"encoding":1321},[1296,24739,24741],{"className":24740},[1299],[1301,24742,24743],{"xmlns":1303},[1305,24744,24745,24759],{},[1308,24746,24747],{},[1311,24748,24749,24751],{},[1314,24750,1201],{},[1308,24752,24753,24755,24757],{},[1314,24754,1148],{},[1314,24756,1366],{},[1314,24758,1343],{},[1319,24760,1394],{"encoding":1321}," — indexy vztažené k cíli",[1148,24763,24764,24765,24778,24779,24792,24793,24836,24837,1956],{},"Pokud má proces zadaný cílový střed ",[1296,24766,24768],{"className":24767},[1299],[1301,24769,24770],{"xmlns":1303},[1305,24771,24772,24776],{},[1308,24773,24774],{},[1314,24775,7098],{},[1319,24777,7098],{"encoding":1321}," (ne nutně střed tolerance), nahradí se ",[1296,24780,24782],{"className":24781},[1299],[1301,24783,24784],{"xmlns":1303},[1305,24785,24786,24790],{},[1308,24787,24788],{},[1314,24789,6895],{},[1319,24791,6927],{"encoding":1321}," odmocninou ze střední čtvercové odchylky od cíle ",[1296,24794,24796],{"className":24795},[1299],[1301,24797,24798],{"xmlns":1303},[1305,24799,24800,24833],{},[1308,24801,24802,24805,24807],{},[1314,24803,24804],{},"τ",[1685,24806,1980],{},[4452,24808,24809],{},[1308,24810,24811,24817,24819,24821,24823,24825,24827],{},[1579,24812,24813,24815],{},[1314,24814,6895],{},[1562,24816,1586],{},[1685,24818,5474],{},[1685,24820,1873],{"stretchy":1872},[1314,24822,6887],{},[1685,24824,3062],{},[1314,24826,7098],{},[1579,24828,24829,24831],{},[1685,24830,1884],{"stretchy":1872},[1562,24832,1586],{},[1319,24834,24835],{"encoding":1321},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1296,24838,24840],{"className":24839},[1299],[1301,24841,24842],{"xmlns":1303},[1305,24843,24844,24848],{},[1308,24845,24846],{},[1314,24847,7098],{},[1319,24849,7098],{"encoding":1321},[1296,24851,24853],{"className":24852},[1299],[1301,24854,24855],{"xmlns":1303,"display":1962},[1305,24856,24857,24969],{},[1308,24858,24859,24869,24871,24895,24897,24899,24911,24913,24915,24917,24967],{},[1311,24860,24861,24863],{},[1314,24862,1201],{},[1308,24864,24865,24867],{},[1314,24866,1148],{},[1314,24868,1366],{},[1685,24870,1980],{},[2738,24872,24873,24889],{},[1308,24874,24875,24877,24879,24881,24883,24885,24887],{},[1314,24876,22138],{},[1314,24878,24169],{},[1314,24880,22112],{},[1685,24882,3062],{},[1314,24884,22112],{},[1314,24886,24169],{},[1314,24888,22112],{},[1308,24890,24891,24893],{},[1562,24892,3963],{},[1314,24894,24804],{},[1685,24896,1795],{"separator":1530},[2010,24898],{"width":2012},[1311,24900,24901,24903],{},[1314,24902,1201],{},[1308,24904,24905,24907,24909],{},[1314,24906,1148],{},[1314,24908,1366],{},[1314,24910,1343],{},[1685,24912,1980],{},[1314,24914,4486],{},[1685,24916,4489],{},[1308,24918,24919,24921,24941,24943,24945,24965],{},[1685,24920,1873],{"fence":1530},[2738,24922,24923,24935],{},[1308,24924,24925,24927,24929,24931,24933],{},[1314,24926,22138],{},[1314,24928,24169],{},[1314,24930,22112],{},[1685,24932,3062],{},[1314,24934,6887],{},[1308,24936,24937,24939],{},[1562,24938,3590],{},[1314,24940,24804],{},[1685,24942,1795],{"separator":1530},[2907,24944,11309],{},[2738,24946,24947,24959],{},[1308,24948,24949,24951,24953,24955,24957],{},[1314,24950,6887],{},[1685,24952,3062],{},[1314,24954,22112],{},[1314,24956,24169],{},[1314,24958,22112],{},[1308,24960,24961,24963],{},[1562,24962,3590],{},[1314,24964,24804],{},[1685,24966,1884],{"fence":1530},[1314,24968,1395],{"mathvariant":2119},[1319,24970,24971],{"encoding":1321},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[16742,24973,24975],{"id":24974},"interpretace","Interpretace",[1162,24977,24978,25005],{},[1165,24979,24980],{},[1168,24981,24982,25002],{},[1171,24983,24984,24985],{},"Hodnota ",[1296,24986,24988],{"className":24987},[1299],[1301,24989,24990],{"xmlns":1303},[1305,24991,24992,25000],{},[1308,24993,24994],{},[1311,24995,24996,24998],{},[1314,24997,1201],{},[1314,24999,1148],{},[1319,25001,1322],{"encoding":1321},[1171,25003,25004],{},"Způsobilost procesu",[1178,25006,25007,25036,25079],{},[1168,25008,25009,25033],{},[1183,25010,25011],{},[1296,25012,25014],{"className":25013},[1299],[1301,25015,25016],{"xmlns":1303},[1305,25017,25018,25030],{},[1308,25019,25020,25026,25028],{},[1311,25021,25022,25024],{},[1314,25023,1201],{},[1314,25025,1148],{},[1685,25027,4331],{},[1562,25029,1792],{},[1319,25031,25032],{"encoding":1321},"C_p \u003C 1",[1183,25034,25035],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1168,25037,25038,25062],{},[1183,25039,25040],{},[1296,25041,25043],{"className":25042},[1299],[1301,25044,25045],{"xmlns":1303},[1305,25046,25047,25059],{},[1308,25048,25049,25055,25057],{},[1311,25050,25051,25053],{},[1314,25052,1201],{},[1314,25054,1148],{},[1685,25056,1980],{},[1562,25058,1792],{},[1319,25060,25061],{"encoding":1321},"C_p = 1",[1183,25063,25064,25065,25078],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1296,25066,25068],{"className":25067},[1299],[1301,25069,25070],{"xmlns":1303},[1305,25071,25072,25076],{},[1308,25073,25074],{},[1314,25075,6895],{},[1319,25077,6927],{"encoding":1321}," jej posune na nezpůsobilý",[1168,25080,25081,25105],{},[1183,25082,25083],{},[1296,25084,25086],{"className":25085},[1299],[1301,25087,25088],{"xmlns":1303},[1305,25089,25090,25102],{},[1308,25091,25092,25098,25100],{},[1311,25093,25094,25096],{},[1314,25095,1201],{},[1314,25097,1148],{},[1685,25099,1687],{},[1562,25101,1792],{},[1319,25103,25104],{"encoding":1321},"C_p > 1",[1183,25106,25107],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1148,25109,25110,25111,25132,25133,1395],{},"U indexu ",[1296,25112,25114],{"className":25113},[1299],[1301,25115,25116],{"xmlns":1303},[1305,25117,25118,25130],{},[1308,25119,25120],{},[1311,25121,25122,25124],{},[1314,25123,1201],{},[1308,25125,25126,25128],{},[1314,25127,1148],{},[1314,25129,1343],{},[1319,25131,1346],{"encoding":1321}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1296,25134,25136],{"className":25135},[1299],[1301,25137,25138],{"xmlns":1303},[1305,25139,25140,25145],{},[1308,25141,25142],{},[1562,25143,25144],{},"1,5",[1319,25146,25147],{"encoding":1321},"1{,}5",[1148,25149,25150],{},[4382,25151],{"alt":25152,"className":25153,"src":25154},"mask-rd-cp-panely",[1245,4386],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1148,25156,25157],{},[4382,25158],{"alt":25159,"className":25160,"src":25161},"mask-rd-cpk-off-centre",[1245,4386],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[16742,25163,25165],{"id":25164},"výpočet-v-r","Výpočet v R",[1148,25167,25168,25169,25172,25173,25176,25177,25180,25181,1370,25198,1323,25215,25218,25219,25232],{},"Indexy způsobilosti počítá ",[3468,25170,25171],{},"process.capability()"," z výstupu regulačního diagramu ",[3468,25174,25175],{},"q","; ",[3468,25178,25179],{},"spec.limits"," jsou toleranční meze ",[1296,25182,25184],{"className":25183},[1299],[1301,25185,25186],{"xmlns":1303},[1305,25187,25188,25196],{},[1308,25189,25190,25192,25194],{},[1314,25191,22112],{},[1314,25193,24169],{},[1314,25195,22112],{},[1319,25197,24174],{"encoding":1321},[1296,25199,25201],{"className":25200},[1299],[1301,25202,25203],{"xmlns":1303},[1305,25204,25205,25213],{},[1308,25206,25207,25209,25211],{},[1314,25208,22138],{},[1314,25210,24169],{},[1314,25212,22112],{},[1319,25214,24193],{"encoding":1321},[3468,25216,25217],{},"target"," cílová hodnota ",[1296,25220,25222],{"className":25221},[1299],[1301,25223,25224],{"xmlns":1303},[1305,25225,25226,25230],{},[1308,25227,25228],{},[1314,25229,7098],{},[1319,25231,7098],{"encoding":1321},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3692,25234,25236],{"className":3694,"code":25235,"language":71,"meta":1452,"style":1452},"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",[3468,25237,25238,25248,25271,25286,25308],{"__ignoreMap":1452},[1296,25239,25240,25242,25244,25246],{"class":3700,"line":10},[1296,25241,17392],{"class":3707},[1296,25243,1873],{"class":3715},[1296,25245,360],{"class":3703},[1296,25247,3900],{"class":3715},[1296,25249,25250,25252,25254,25256,25258,25261,25263,25265,25267,25269],{"class":3700,"line":27},[1296,25251,20103],{"class":3703},[1296,25253,3708],{"class":3707},[1296,25255,20108],{"class":3711},[1296,25257,1873],{"class":3715},[1296,25259,25260],{"class":3839},"\"3_8.txt\"",[1296,25262,1795],{"class":3707},[1296,25264,20118],{"class":3703},[1296,25266,3796],{"class":3707},[1296,25268,3809],{"class":3723},[1296,25270,3900],{"class":3715},[1296,25272,25273,25275,25277,25280,25282,25284],{"class":3700,"line":148},[1296,25274,6716],{"class":3703},[1296,25276,3708],{"class":3707},[1296,25278,25279],{"class":3711}," as.matrix",[1296,25281,1873],{"class":3715},[1296,25283,20103],{"class":3703},[1296,25285,3900],{"class":3715},[1296,25287,25288,25290,25292,25294,25296,25298,25300,25302,25304,25306],{"class":3700,"line":111},[1296,25289,25175],{"class":3703},[1296,25291,3708],{"class":3707},[1296,25293,23612],{"class":3711},[1296,25295,1873],{"class":3715},[1296,25297,6716],{"class":3703},[1296,25299,1795],{"class":3707},[1296,25301,12218],{"class":3703},[1296,25303,3796],{"class":3707},[1296,25305,22738],{"class":3839},[1296,25307,3900],{"class":3715},[1296,25309,25310,25313,25315,25317,25319,25322,25324,25326,25328,25330,25332,25334,25336,25338,25341,25343,25346,25348,25351,25353,25355,25357,25359],{"class":3700,"line":96},[1296,25311,25312],{"class":3711},"process.capability",[1296,25314,1873],{"class":3715},[1296,25316,25175],{"class":3703},[1296,25318,1795],{"class":3707},[1296,25320,25321],{"class":3703}," spec.limits",[1296,25323,3796],{"class":3707},[1296,25325,3834],{"class":3711},[1296,25327,1873],{"class":3715},[1296,25329,11813],{"class":3723},[1296,25331,1795],{"class":3707},[1296,25333,14263],{"class":3723},[1296,25335,1884],{"class":3715},[1296,25337,1795],{"class":3707},[1296,25339,25340],{"class":3703}," target",[1296,25342,3796],{"class":3707},[1296,25344,25345],{"class":3723}," 105",[1296,25347,1795],{"class":3707},[1296,25349,25350],{"class":3703}," std.dev",[1296,25352,3796],{"class":3707},[1296,25354,9236],{"class":3711},[1296,25356,1873],{"class":3715},[1296,25358,6716],{"class":3703},[1296,25360,9488],{"class":3715},[1148,25362,25363,25364,1323,25367,1323,25370,1323,25373,1370,25376,25379,25380,1370,25382,25384,25385,25406,25407,25430],{},"Výpis obsahuje řádky ",[3468,25365,25366],{},"Cp",[3468,25368,25369],{},"Cp_l",[3468,25371,25372],{},"Cp_u",[3468,25374,25375],{},"Cp_k",[3468,25377,25378],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3468,25381,25369],{},[3468,25383,25372],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1296,25386,25388],{"className":25387},[1299],[1301,25389,25390],{"xmlns":1303},[1305,25391,25392,25404],{},[1308,25393,25394],{},[1311,25395,25396,25398],{},[1314,25397,1201],{},[1308,25399,25400,25402],{},[1314,25401,1148],{},[1314,25403,1343],{},[1319,25405,1346],{"encoding":1321},". Index ",[1296,25408,25410],{"className":25409},[1299],[1301,25411,25412],{"xmlns":1303},[1305,25413,25414,25428],{},[1308,25415,25416],{},[1311,25417,25418,25420],{},[1314,25419,1201],{},[1308,25421,25422,25424,25426],{},[1314,25423,1148],{},[1314,25425,1366],{},[1314,25427,1343],{},[1319,25429,1394],{"encoding":1321}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3692,25432,25434],{"className":3694,"code":25433,"language":71,"meta":1452,"style":1452},"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",[3468,25435,25436,25463,25488,25525,25555,25613,25627,25678],{"__ignoreMap":1452},[1296,25437,25438,25441,25443,25445,25447,25449,25451,25453,25455,25457,25459,25461],{"class":3700,"line":10},[1296,25439,25440],{"class":3703},"mu",[1296,25442,3708],{"class":3707},[1296,25444,9226],{"class":3711},[1296,25446,1873],{"class":3715},[1296,25448,6716],{"class":3703},[1296,25450,12172],{"class":3715},[1296,25452,380],{"class":3703},[1296,25454,3708],{"class":3707},[1296,25456,9236],{"class":3711},[1296,25458,1873],{"class":3715},[1296,25460,6716],{"class":3703},[1296,25462,3900],{"class":3715},[1296,25464,25465,25467,25469,25471,25473,25475,25477,25479,25481,25483,25485],{"class":3700,"line":27},[1296,25466,24174],{"class":3703},[1296,25468,3708],{"class":3707},[1296,25470,15334],{"class":3723},[1296,25472,25176],{"class":3715},[1296,25474,24193],{"class":3703},[1296,25476,3708],{"class":3707},[1296,25478,14263],{"class":3723},[1296,25480,25176],{"class":3715},[1296,25482,7098],{"class":3703},[1296,25484,3708],{"class":3707},[1296,25486,25487],{"class":3723}," 105\n",[1296,25489,25490,25493,25495,25497,25499,25501,25503,25505,25507,25509,25511,25514,25517,25519,25521,25523],{"class":3700,"line":148},[1296,25491,25492],{"class":3703},"tau",[1296,25494,3708],{"class":3707},[1296,25496,4576],{"class":3711},[1296,25498,1873],{"class":3715},[1296,25500,380],{"class":3703},[1296,25502,2728],{"class":3707},[1296,25504,1586],{"class":3723},[1296,25506,18511],{"class":3707},[1296,25508,4604],{"class":3715},[1296,25510,25440],{"class":3703},[1296,25512,25513],{"class":3707}," -",[1296,25515,25516],{"class":3703}," T",[1296,25518,1884],{"class":3715},[1296,25520,2728],{"class":3707},[1296,25522,1586],{"class":3723},[1296,25524,3900],{"class":3715},[1296,25526,25527,25529,25531,25533,25535,25537,25540,25542,25544,25546,25548,25550,25553],{"class":3700,"line":111},[1296,25528,25366],{"class":3703},[1296,25530,3708],{"class":3707},[1296,25532,4604],{"class":3715},[1296,25534,24193],{"class":3703},[1296,25536,25513],{"class":3707},[1296,25538,25539],{"class":3703}," LSL",[1296,25541,4599],{"class":3715},[1296,25543,1502],{"class":3707},[1296,25545,4604],{"class":3715},[1296,25547,3963],{"class":3723},[1296,25549,18636],{"class":3707},[1296,25551,25552],{"class":3703}," sigma",[1296,25554,3900],{"class":3715},[1296,25556,25557,25560,25562,25564,25567,25569,25571,25574,25576,25578,25580,25582,25584,25587,25589,25591,25593,25595,25597,25599,25601,25603,25605,25607,25609,25611],{"class":3700,"line":96},[1296,25558,25559],{"class":3703},"Cpmk",[1296,25561,3708],{"class":3707},[1296,25563,12193],{"class":3711},[1296,25565,25566],{"class":3715},"((",[1296,25568,24193],{"class":3703},[1296,25570,25513],{"class":3707},[1296,25572,25573],{"class":3703}," mu",[1296,25575,4599],{"class":3715},[1296,25577,1502],{"class":3707},[1296,25579,4604],{"class":3715},[1296,25581,3590],{"class":3723},[1296,25583,18636],{"class":3707},[1296,25585,25586],{"class":3703}," tau",[1296,25588,1884],{"class":3715},[1296,25590,1795],{"class":3707},[1296,25592,4604],{"class":3715},[1296,25594,25440],{"class":3703},[1296,25596,25513],{"class":3707},[1296,25598,25539],{"class":3703},[1296,25600,4599],{"class":3715},[1296,25602,1502],{"class":3707},[1296,25604,4604],{"class":3715},[1296,25606,3590],{"class":3723},[1296,25608,18636],{"class":3707},[1296,25610,25586],{"class":3703},[1296,25612,9488],{"class":3715},[1296,25614,25615,25618,25620,25622,25624],{"class":3700,"line":89},[1296,25616,25617],{"class":3703},"miravyuziti",[1296,25619,3708],{"class":3707},[1296,25621,15334],{"class":3723},[1296,25623,10070],{"class":3707},[1296,25625,25626],{"class":3703}," Cp\n",[1296,25628,25629,25632,25634,25636,25638,25640,25642,25644,25646,25648,25650,25652,25654,25656,25658,25660,25662,25664,25666,25668,25670,25672,25674,25676],{"class":3700,"line":82},[1296,25630,25631],{"class":3703},"robustnost",[1296,25633,3708],{"class":3707},[1296,25635,12193],{"class":3711},[1296,25637,1873],{"class":3715},[1296,25639,24193],{"class":3703},[1296,25641,25513],{"class":3707},[1296,25643,4604],{"class":3715},[1296,25645,25440],{"class":3703},[1296,25647,18511],{"class":3707},[1296,25649,10850],{"class":3723},[1296,25651,18636],{"class":3707},[1296,25653,25552],{"class":3703},[1296,25655,1884],{"class":3715},[1296,25657,1795],{"class":3707},[1296,25659,4604],{"class":3715},[1296,25661,25440],{"class":3703},[1296,25663,25513],{"class":3707},[1296,25665,10850],{"class":3723},[1296,25667,18636],{"class":3707},[1296,25669,25552],{"class":3703},[1296,25671,4599],{"class":3715},[1296,25673,4635],{"class":3707},[1296,25675,25539],{"class":3703},[1296,25677,3900],{"class":3715},[1296,25679,25680,25683,25685,25687,25689,25691,25693,25695,25697,25699,25702],{"class":3700,"line":75},[1296,25681,25682],{"class":3703},"Pz",[1296,25684,3708],{"class":3707},[1296,25686,4179],{"class":3723},[1296,25688,18636],{"class":3707},[1296,25690,9346],{"class":3711},[1296,25692,1873],{"class":3715},[1296,25694,4635],{"class":3707},[1296,25696,3590],{"class":3723},[1296,25698,18636],{"class":3707},[1296,25700,25701],{"class":3703}," Cp",[1296,25703,3900],{"class":3715},[1143,25705,6404],{"id":6403},[1102,25707,25708,25711,25771,25862,25928],{},[1105,25709,25710],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1105,25712,25713,25714,25731,25732,25749,25750,1395],{},"Posuzovat jen ",[1296,25715,25717],{"className":25716},[1299],[1301,25718,25719],{"xmlns":1303},[1305,25720,25721,25729],{},[1308,25722,25723],{},[1311,25724,25725,25727],{},[1314,25726,1201],{},[1314,25728,1148],{},[1319,25730,1322],{"encoding":1321}," u vychýleného procesu — ",[1296,25733,25735],{"className":25734},[1299],[1301,25736,25737],{"xmlns":1303},[1305,25738,25739,25747],{},[1308,25740,25741],{},[1311,25742,25743,25745],{},[1314,25744,1201],{},[1314,25746,1148],{},[1319,25748,1322],{"encoding":1321}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1296,25751,25753],{"className":25752},[1299],[1301,25754,25755],{"xmlns":1303},[1305,25756,25757,25769],{},[1308,25758,25759],{},[1311,25760,25761,25763],{},[1314,25762,1201],{},[1308,25764,25765,25767],{},[1314,25766,1148],{},[1314,25768,1343],{},[1319,25770,1346],{"encoding":1321},[1105,25772,25773,25774,25787,25788,25801,25802,25787,25817,25830,25831,25844,25845,25858,25859,25861],{},"Zaměnit diagram ",[1296,25775,25777],{"className":25776},[1299],[1301,25778,25779],{"xmlns":1303},[1305,25780,25781,25785],{},[1308,25782,25783],{},[1314,25784,3718],{},[1319,25786,3718],{"encoding":1321}," s diagramem ",[1296,25789,25791],{"className":25790},[1299],[1301,25792,25793],{"xmlns":1303},[1305,25794,25795,25799],{},[1308,25796,25797],{},[1314,25798,11523],{},[1319,25800,11523],{"encoding":1321}," nebo diagram ",[1296,25803,25805],{"className":25804},[1299],[1301,25806,25807],{"xmlns":1303},[1305,25808,25809,25815],{},[1308,25810,25811,25813],{},[1314,25812,1683],{},[1314,25814,1148],{},[1319,25816,20758],{"encoding":1321},[1296,25818,25820],{"className":25819},[1299],[1301,25821,25822],{"xmlns":1303},[1305,25823,25824,25828],{},[1308,25825,25826],{},[1314,25827,1148],{},[1319,25829,1148],{"encoding":1321}," — při nekonstantním rozsahu podskupin se volí ",[1296,25832,25834],{"className":25833},[1299],[1301,25835,25836],{"xmlns":1303},[1305,25837,25838,25842],{},[1308,25839,25840],{},[1314,25841,11523],{},[1319,25843,11523],{"encoding":1321},", resp. ",[1296,25846,25848],{"className":25847},[1299],[1301,25849,25850],{"xmlns":1303},[1305,25851,25852,25856],{},[1308,25853,25854],{},[1314,25855,1148],{},[1319,25857,1148],{"encoding":1321},", a do ",[3468,25860,23808],{}," se zadává vektor rozsahů.",[1105,25863,25864,25865,25882,25883,25896,25897,25910,25911,1395],{},"Posuzovat diagram ",[1296,25866,25868],{"className":25867},[1299],[1301,25869,25870],{"xmlns":1303},[1305,25871,25872,25880],{},[1308,25873,25874],{},[2722,25875,25876,25878],{"accent":1530},[1314,25877,6716],{},[1685,25879,11454],{},[1319,25881,21557],{"encoding":1321}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1296,25884,25886],{"className":25885},[1299],[1301,25887,25888],{"xmlns":1303},[1305,25889,25890,25894],{},[1308,25891,25892],{},[1314,25893,10218],{},[1319,25895,10218],{"encoding":1321}," (resp. ",[1296,25898,25900],{"className":25899},[1299],[1301,25901,25902],{"xmlns":1303},[1305,25903,25904,25908],{},[1308,25905,25906],{},[1314,25907,1852],{},[1319,25909,1852],{"encoding":1321},"), potom diagram ",[1296,25912,25914],{"className":25913},[1299],[1301,25915,25916],{"xmlns":1303},[1305,25917,25918,25926],{},[1308,25919,25920],{},[2722,25921,25922,25924],{"accent":1530},[1314,25923,6716],{},[1685,25925,11454],{},[1319,25927,21557],{"encoding":1321},[1105,25929,25930],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1143,25932,6592],{"id":6591},[1102,25934,25935,25940,25945,25950,25955,25960,25965],{},[1105,25936,25937],{},[1242,25938,1717],{"className":25939,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,25941,25942],{},[1242,25943,886],{"className":25944,"dataFsResolvedFilePath":1255,"href":1256},[1245],[1105,25946,25947],{},[1242,25948,1498],{"className":25949,"dataFsResolvedFilePath":1246,"href":1247},[1245],[1105,25951,25952],{},[1242,25953,141],{"className":25954,"dataFsResolvedFilePath":1264,"href":1265},[1245],[1105,25956,25957],{},[1242,25958,11080],{"className":25959,"dataFsResolvedFilePath":1273,"href":1274},[1245],[1105,25961,25962],{},[1242,25963,716],{"className":25964,"dataFsResolvedFilePath":1282,"href":1283},[1245],[1105,25966,25967],{},[1242,25968,6630],{"className":25969,"dataFsResolvedFilePath":1447,"href":1448},[1245],[1143,25971,6633],{"id":934},[1148,25973,6636,25974,6641],{},[6638,25975,6640],{},[1148,25977,25978,25979,25982],{},"MONTGOMERY, D. C. ",[6638,25980,25981],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1148,25984,25985,25986,25989],{},"ČSN ISO 8258. ",[6638,25987,25988],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1148,25991,25992,25993,25996],{},"KUPKA, K. ",[6638,25994,25995],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6643,25998,25999],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: 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pp",{"id":24151,"depth":27,"text":24152,"children":26023},[26024,26026,26028,26030,26031],{"id":24197,"depth":148,"text":26025},"CpC_p — index způsobilosti",{"id":24521,"depth":148,"text":26027},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":24716,"depth":148,"text":26029},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":24974,"depth":148,"text":24975},{"id":25164,"depth":148,"text":25165},{"id":6403,"depth":27,"text":6404},{"id":6591,"depth":27,"text":6592},{"id":934,"depth":27,"text":6633},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":1293,"description":1452},[26039,26040,26041,26042],"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":26047,"title":1266,"body":26048,"course":23,"courses":1459,"created":1460,"description":1452,"extension":1461,"meta":35859,"navigation":1464,"path":35860,"seo":35861,"sources":35862,"stem":35868,"tags":35869,"type":6664,"updated":1460,"__hash__":35870},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1095,"value":26049,"toc":35832},[26050,26053,26252,26296,26300,26310,26313,26379,26429,26582,26586,26589,26683,26833,26852,26859,26948,26952,26987,27024,27062,27097,27101,27108,27326,27445,27449,27581,27635,27657,27999,28006,28094,28100,28141,28426,28435,28550,28556,28563,28568,28574,28668,28674,28700,28706,28798,28804,28854,28858,29054,29114,29476,29815,29914,29920,30148,30152,30418,30422,30425,30491,30538,30994,30998,31001,31188,31221,31443,31762,31801,31808,32465,32604,32610,32766,32772,32779,32832,32838,33011,33017,33081,33086,33271,33277,33322,33326,33329,33333,33380,33608,33624,33713,33719,33745,33749,33752,33824,33917,33986,33992,34015,34462,34469,34473,34503,34507,34757,34776,34837,34846,35002,35008,35034,35209,35213,35234,35265,35269,35293,35323,35327,35387,35445,35449,35456,35629,35631,35784,35786,35823,35825,35829],[1098,26051,1266],{"id":26052},"testování-statistických-hypotéz",[1514,26054,26056,26062],{"className":26055,"dataCallout":1519},[1517,1518],[1148,26057,26059,1531],{"className":26058},[1523],[1296,26060],{"className":26061,"ariaHidden":1530},[1527,1528,1529],[1102,26063,26064,26134,26216,26219,26222],{},[1105,26065,26066,26067,26084,26085,26102,26103,1323,26116,26133],{},"Test porovnává tvrzení ",[1296,26068,26070],{"className":26069},[1299],[1301,26071,26072],{"xmlns":1303},[1305,26073,26074,26082],{},[1308,26075,26076],{},[1311,26077,26078,26080],{},[1314,26079,1560],{},[1562,26081,1564],{},[1319,26083,1567],{"encoding":1321}," s alternativou ",[1296,26086,26088],{"className":26087},[1299],[1301,26089,26090],{"xmlns":1303},[1305,26091,26092,26100],{},[1308,26093,26094],{},[1311,26095,26096,26098],{},[1314,26097,1560],{},[1562,26099,1792],{},[1319,26101,2994],{"encoding":1321}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1296,26104,26106],{"className":26105},[1299],[1301,26107,26108],{"xmlns":1303},[1305,26109,26110,26114],{},[1308,26111,26112],{},[1314,26113,1602],{},[1319,26115,1602],{"encoding":1321},[1296,26117,26119],{"className":26118},[1299],[1301,26120,26121],{"xmlns":1303},[1305,26122,26123,26131],{},[1308,26124,26125],{},[1311,26126,26127,26129],{},[1314,26128,1560],{},[1562,26130,1564],{},[1319,26132,1567],{"encoding":1321}," zamítáme.",[1105,26135,26136,26137,26150,26151,26168,26169,26183,26184,26201,26202,26215],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1296,26138,26140],{"className":26139},[1299],[1301,26141,26142],{"xmlns":1303},[1305,26143,26144,26148],{},[1308,26145,26146],{},[1314,26147,3363],{},[1319,26149,3426],{"encoding":1321},", zamítnutí platné ",[1296,26152,26154],{"className":26153},[1299],[1301,26155,26156],{"xmlns":1303},[1305,26157,26158,26166],{},[1308,26159,26160],{},[1311,26161,26162,26164],{},[1314,26163,1560],{},[1562,26165,1564],{},[1319,26167,1567],{"encoding":1321},") a chybu II. druhu (",[1296,26170,26172],{"className":26171},[1299],[1301,26173,26174],{"xmlns":1303},[1305,26175,26176,26180],{},[1308,26177,26178],{},[1314,26179,16333],{},[1319,26181,26182],{"encoding":1321},"\\beta",", přijetí neplatné ",[1296,26185,26187],{"className":26186},[1299],[1301,26188,26189],{"xmlns":1303},[1305,26190,26191,26199],{},[1308,26192,26193],{},[1311,26194,26195,26197],{},[1314,26196,1560],{},[1562,26198,1564],{},[1319,26200,1567],{"encoding":1321},"). Hladina významnosti ",[1296,26203,26205],{"className":26204},[1299],[1301,26206,26207],{"xmlns":1303},[1305,26208,26209,26213],{},[1308,26210,26211],{},[1314,26212,3363],{},[1319,26214,3426],{"encoding":1321}," se volí předem, obvykle 0,05.",[1105,26217,26218],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1105,26220,26221],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1105,26223,26224,26225,26238,26239,1395],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1296,26226,26228],{"className":26227},[1299],[1301,26229,26230],{"xmlns":1303},[1305,26231,26232,26236],{},[1308,26233,26234],{},[1314,26235,1602],{},[1319,26237,1602],{"encoding":1321},", nebo podle p-hodnoty vůči ",[1296,26240,26242],{"className":26241},[1299],[1301,26243,26244],{"xmlns":1303},[1305,26245,26246,26250],{},[1308,26247,26248],{},[1314,26249,3363],{},[1319,26251,3426],{"encoding":1321},[1148,26253,26254,26255,26259,26260,26264,26265,26269,26270,1323,26283,16089],{},"Testy statistických hypotéz jsou nástroj ",[1242,26256,26258],{"className":26257,"dataFsResolvedFilePath":1715,"href":1716},[1245],"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 ",[1242,26261,26263],{"className":26262,"dataFsResolvedFilePath":1255,"href":1256},[1245],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1242,26266,26268],{"className":26267,"dataFsResolvedFilePath":1246,"href":1247},[1245],"náhodných veličin"," (normální, ",[1296,26271,26273],{"className":26272},[1299],[1301,26274,26275],{"xmlns":1303},[1305,26276,26277,26281],{},[1308,26278,26279],{},[1314,26280,7140],{},[1319,26282,7140],{"encoding":1321},[1296,26284,26286],{"className":26285},[1299],[1301,26287,26288],{"xmlns":1303},[1305,26289,26290,26294],{},[1308,26291,26292],{},[1314,26293,1225],{},[1319,26295,1225],{"encoding":1321},[1143,26297,26299],{"id":26298},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1148,26301,26302,26305,26306,26309],{},[1108,26303,26304],{},"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. ",[1108,26307,26308],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1148,26311,26312],{},"Proti sobě stojí dvě hypotézy:",[1102,26314,26315,26338],{},[1105,26316,26317,26337],{},[1108,26318,26319,26320],{},"Nulová hypotéza ",[1296,26321,26323],{"className":26322},[1299],[1301,26324,26325],{"xmlns":1303},[1305,26326,26327,26335],{},[1308,26328,26329],{},[1311,26330,26331,26333],{},[1314,26332,1560],{},[1562,26334,1564],{},[1319,26336,1567],{"encoding":1321}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1105,26339,26340,26360,26361,26378],{},[1108,26341,26342,26343],{},"Alternativní hypotéza ",[1296,26344,26346],{"className":26345},[1299],[1301,26347,26348],{"xmlns":1303},[1305,26349,26350,26358],{},[1308,26351,26352],{},[1311,26353,26354,26356],{},[1314,26355,1560],{},[1562,26357,1792],{},[1319,26359,2994],{"encoding":1321}," — staví se proti ",[1296,26362,26364],{"className":26363},[1299],[1301,26365,26366],{"xmlns":1303},[1305,26367,26368,26376],{},[1308,26369,26370],{},[1311,26371,26372,26374],{},[1314,26373,1560],{},[1562,26375,1564],{},[1319,26377,1567],{"encoding":1321}," a určitým způsobem popírá její tvrzení.",[1148,26380,1696,26381,26411,26412,1956],{},[1296,26382,26384],{"className":26383},[1299],[1301,26385,26386],{"xmlns":1303},[1305,26387,26388,26408],{},[1308,26389,26390,26396,26398,26400,26402],{},[1311,26391,26392,26394],{},[1314,26393,1560],{},[1562,26395,1564],{},[1685,26397,1956],{},[1314,26399,6887],{},[1685,26401,1980],{},[1311,26403,26404,26406],{},[1314,26405,6887],{},[1562,26407,1564],{},[1319,26409,26410],{"encoding":1321},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1296,26413,26415],{"className":26414},[1299],[1301,26416,26417],{"xmlns":1303},[1305,26418,26419,26427],{},[1308,26420,26421],{},[1311,26422,26423,26425],{},[1314,26424,1560],{},[1562,26426,1792],{},[1319,26428,2994],{"encoding":1321},[1162,26430,26431,26461],{},[1165,26432,26433],{},[1168,26434,26435,26455,26458],{},[1171,26436,26437,26438],{},"Tvar ",[1296,26439,26441],{"className":26440},[1299],[1301,26442,26443],{"xmlns":1303},[1305,26444,26445,26453],{},[1308,26446,26447],{},[1311,26448,26449,26451],{},[1314,26450,1560],{},[1562,26452,1792],{},[1319,26454,2994],{"encoding":1321},[1171,26456,26457],{},"Zápis",[1171,26459,26460],{},"Typ",[1178,26462,26463,26503,26543],{},[1168,26464,26465,26468,26500],{},[1183,26466,26467],{},"nerovnost",[1183,26469,26470],{},[1296,26471,26473],{"className":26472},[1299],[1301,26474,26475],{"xmlns":1303},[1305,26476,26477,26497],{},[1308,26478,26479,26485,26487,26489,26491],{},[1311,26480,26481,26483],{},[1314,26482,1560],{},[1562,26484,1792],{},[1685,26486,1956],{},[1314,26488,6887],{},[1685,26490,10951],{"mathvariant":2119},[1311,26492,26493,26495],{},[1314,26494,6887],{},[1562,26496,1564],{},[1319,26498,26499],{"encoding":1321},"H_1: \\mu \\neq \\mu_0",[1183,26501,26502],{},"dvoustranná",[1168,26504,26505,26508,26540],{},[1183,26506,26507],{},"větší",[1183,26509,26510],{},[1296,26511,26513],{"className":26512},[1299],[1301,26514,26515],{"xmlns":1303},[1305,26516,26517,26537],{},[1308,26518,26519,26525,26527,26529,26531],{},[1311,26520,26521,26523],{},[1314,26522,1560],{},[1562,26524,1792],{},[1685,26526,1956],{},[1314,26528,6887],{},[1685,26530,1687],{},[1311,26532,26533,26535],{},[1314,26534,6887],{},[1562,26536,1564],{},[1319,26538,26539],{"encoding":1321},"H_1: \\mu > \\mu_0",[1183,26541,26542],{},"jednostranná",[1168,26544,26545,26548,26580],{},[1183,26546,26547],{},"menší",[1183,26549,26550],{},[1296,26551,26553],{"className":26552},[1299],[1301,26554,26555],{"xmlns":1303},[1305,26556,26557,26577],{},[1308,26558,26559,26565,26567,26569,26571],{},[1311,26560,26561,26563],{},[1314,26562,1560],{},[1562,26564,1792],{},[1685,26566,1956],{},[1314,26568,6887],{},[1685,26570,4331],{},[1311,26572,26573,26575],{},[1314,26574,6887],{},[1562,26576,1564],{},[1319,26578,26579],{"encoding":1321},"H_1: \\mu \u003C \\mu_0",[1183,26581,26542],{},[16742,26583,26585],{"id":26584},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1148,26587,26588],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1102,26590,26591,26628],{},[1105,26592,26593,26596,26597,26614,26615,1395],{},[1108,26594,26595],{},"Chyba I. druhu"," — zamítnutí ",[1296,26598,26600],{"className":26599},[1299],[1301,26601,26602],{"xmlns":1303},[1305,26603,26604,26612],{},[1308,26605,26606],{},[1311,26607,26608,26610],{},[1314,26609,1560],{},[1562,26611,1564],{},[1319,26613,1567],{"encoding":1321},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1296,26616,26618],{"className":26617},[1299],[1301,26619,26620],{"xmlns":1303},[1305,26621,26622,26626],{},[1308,26623,26624],{},[1314,26625,3363],{},[1319,26627,3426],{"encoding":1321},[1105,26629,26630,26633,26634,26651,26652,26669,26670,1395],{},[1108,26631,26632],{},"Chyba II. druhu"," — přijetí ",[1296,26635,26637],{"className":26636},[1299],[1301,26638,26639],{"xmlns":1303},[1305,26640,26641,26649],{},[1308,26642,26643],{},[1311,26644,26645,26647],{},[1314,26646,1560],{},[1562,26648,1564],{},[1319,26650,1567],{"encoding":1321},", ačkoliv platí ",[1296,26653,26655],{"className":26654},[1299],[1301,26656,26657],{"xmlns":1303},[1305,26658,26659,26667],{},[1308,26660,26661],{},[1311,26662,26663,26665],{},[1314,26664,1560],{},[1562,26666,1792],{},[1319,26668,2994],{"encoding":1321},". Pravděpodobnost ",[1296,26671,26673],{"className":26672},[1299],[1301,26674,26675],{"xmlns":1303},[1305,26676,26677,26681],{},[1308,26678,26679],{},[1314,26680,16333],{},[1319,26682,26182],{"encoding":1321},[1162,26684,26685,26748],{},[1165,26686,26687],{},[1168,26688,26689,26709,26728],{},[1171,26690,26691,26692],{},"Úsudek o ",[1296,26693,26695],{"className":26694},[1299],[1301,26696,26697],{"xmlns":1303},[1305,26698,26699,26707],{},[1308,26700,26701],{},[1311,26702,26703,26705],{},[1314,26704,1560],{},[1562,26706,1564],{},[1319,26708,1567],{"encoding":1321},[1171,26710,26711,8346],{},[1296,26712,26714],{"className":26713},[1299],[1301,26715,26716],{"xmlns":1303},[1305,26717,26718,26726],{},[1308,26719,26720],{},[1311,26721,26722,26724],{},[1314,26723,1560],{},[1562,26725,1564],{},[1319,26727,1567],{"encoding":1321},[1171,26729,26730,26747],{},[1296,26731,26733],{"className":26732},[1299],[1301,26734,26735],{"xmlns":1303},[1305,26736,26737,26745],{},[1308,26738,26739],{},[1311,26740,26741,26743],{},[1314,26742,1560],{},[1562,26744,1564],{},[1319,26746,1567],{"encoding":1321}," neplatí",[1178,26749,26750,26792],{},[1168,26751,26752,26755,26776],{},[1183,26753,26754],{},"Nezamítá se",[1183,26756,26757,26758],{},"správné rozhodnutí, ",[1296,26759,26761],{"className":26760},[1299],[1301,26762,26763],{"xmlns":1303},[1305,26764,26765,26773],{},[1308,26766,26767,26769,26771],{},[1562,26768,1792],{},[1685,26770,3062],{},[1314,26772,3363],{},[1319,26774,26775],{"encoding":1321},"1-\\alpha",[1183,26777,26778,26779],{},"chyba II. druhu, ",[1296,26780,26782],{"className":26781},[1299],[1301,26783,26784],{"xmlns":1303},[1305,26785,26786,26790],{},[1308,26787,26788],{},[1314,26789,16333],{},[1319,26791,26182],{"encoding":1321},[1168,26793,26794,26797,26813],{},[1183,26795,26796],{},"Zamítá se",[1183,26798,26799,26800],{},"chyba I. druhu, ",[1296,26801,26803],{"className":26802},[1299],[1301,26804,26805],{"xmlns":1303},[1305,26806,26807,26811],{},[1308,26808,26809],{},[1314,26810,3363],{},[1319,26812,3426],{"encoding":1321},[1183,26814,26757,26815],{},[1296,26816,26818],{"className":26817},[1299],[1301,26819,26820],{"xmlns":1303},[1305,26821,26822,26830],{},[1308,26823,26824,26826,26828],{},[1562,26825,1792],{},[1685,26827,3062],{},[1314,26829,16333],{},[1319,26831,26832],{"encoding":1321},"1-\\beta",[1148,26834,26835,1651,26838,26851],{},[1108,26836,26837],{},"Hladina významnosti",[1296,26839,26841],{"className":26840},[1299],[1301,26842,26843],{"xmlns":1303},[1305,26844,26845,26849],{},[1308,26846,26847],{},[1314,26848,3363],{},[1319,26850,3426],{"encoding":1321}," 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.",[1148,26853,26854],{},[4382,26855],{"alt":26856,"className":26857,"src":26858},"mask-th-chyba-i-ii",[1245,4386],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1148,26860,26861,26862,26875,26876,26889,26890,26903,26904,1888,26917,26930,26931,1395],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1296,26863,26865],{"className":26864},[1299],[1301,26866,26867],{"xmlns":1303},[1305,26868,26869,26873],{},[1308,26870,26871],{},[1314,26872,3718],{},[1319,26874,3718],{"encoding":1321}," doleva zmenší ",[1296,26877,26879],{"className":26878},[1299],[1301,26880,26881],{"xmlns":1303},[1305,26882,26883,26887],{},[1308,26884,26885],{},[1314,26886,16333],{},[1319,26888,26182],{"encoding":1321},", ale zvětší ",[1296,26891,26893],{"className":26892},[1299],[1301,26894,26895],{"xmlns":1303},[1305,26896,26897,26901],{},[1308,26898,26899],{},[1314,26900,3363],{},[1319,26902,3426],{"encoding":1321},", a naopak. Pro danou hladinu ",[1296,26905,26907],{"className":26906},[1299],[1301,26908,26909],{"xmlns":1303},[1305,26910,26911,26915],{},[1308,26912,26913],{},[1314,26914,3363],{},[1319,26916,3426],{"encoding":1321},[1296,26918,26920],{"className":26919},[1299],[1301,26921,26922],{"xmlns":1303},[1305,26923,26924,26928],{},[1308,26925,26926],{},[1314,26927,3718],{},[1319,26929,3718],{"encoding":1321}," jednoznačně určena rozdělením kritéria za platnosti ",[1296,26932,26934],{"className":26933},[1299],[1301,26935,26936],{"xmlns":1303},[1305,26937,26938,26946],{},[1308,26939,26940],{},[1311,26941,26942,26944],{},[1314,26943,1560],{},[1562,26945,1564],{},[1319,26947,1567],{"encoding":1321},[16742,26949,26951],{"id":26950},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1148,26953,26954,1651,26956,26969,26970,1395],{},[1108,26955,2998],{},[1296,26957,26959],{"className":26958},[1299],[1301,26960,26961],{"xmlns":1303},[1305,26962,26963,26967],{},[1308,26964,26965],{},[1314,26966,7098],{},[1319,26968,7098],{"encoding":1321}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1296,26971,26973],{"className":26972},[1299],[1301,26974,26975],{"xmlns":1303},[1305,26976,26977,26985],{},[1308,26978,26979],{},[1311,26980,26981,26983],{},[1314,26982,1560],{},[1562,26984,1564],{},[1319,26986,1567],{"encoding":1321},[1148,26988,26989,1651,26992,27005,27006,27023],{},[1108,26990,26991],{},"Kritický obor",[1296,26993,26995],{"className":26994},[1299],[1301,26996,26997],{"xmlns":1303},[1305,26998,26999,27003],{},[1308,27000,27001],{},[1314,27002,1602],{},[1319,27004,1602],{"encoding":1321}," je množina hodnot svědčících pro ",[1296,27007,27009],{"className":27008},[1299],[1301,27010,27011],{"xmlns":1303},[1305,27012,27013,27021],{},[1308,27014,27015],{},[1311,27016,27017,27019],{},[1314,27018,1560],{},[1562,27020,1792],{},[1319,27022,2994],{"encoding":1321},". Je zkonstruován tak, aby",[1296,27025,27027],{"className":27026},[1299],[1301,27028,27029],{"xmlns":1303,"display":1962},[1305,27030,27031,27059],{},[1308,27032,27033,27035,27037,27039,27041,27043,27045,27051,27053,27055,27057],{},[1314,27034,6723],{},[1685,27036,1873],{"stretchy":1872},[1314,27038,7098],{},[1685,27040,7015],{},[1314,27042,1602],{},[1685,27044,23016],{},[1311,27046,27047,27049],{},[1314,27048,1560],{},[1562,27050,1564],{},[1685,27052,1884],{"stretchy":1872},[1685,27054,1980],{},[1314,27056,3363],{},[1685,27058,1795],{"separator":1530},[1319,27060,27061],{"encoding":1321},"P(T \\in W \\mid H_0) = \\alpha,",[1148,27063,27064,27065,27078,27079,27096],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1296,27066,27068],{"className":27067},[1299],[1301,27069,27070],{"xmlns":1303},[1305,27071,27072,27076],{},[1308,27073,27074],{},[1314,27075,1602],{},[1319,27077,1602],{"encoding":1321}," i při platné ",[1296,27080,27082],{"className":27081},[1299],[1301,27083,27084],{"xmlns":1303},[1305,27085,27086,27094],{},[1308,27087,27088],{},[1311,27089,27090,27092],{},[1314,27091,1560],{},[1562,27093,1564],{},[1319,27095,1567],{"encoding":1321},", byla rovna zvolené hladině významnosti.",[16742,27098,27100],{"id":27099},"postup-testování-hypotézy","Postup testování hypotézy",[1148,27102,27103],{},[4382,27104],{"alt":27105,"className":27106,"src":27107},"mask-ilu-postup-testovani",[1245,4386],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[1237,27109,27110,27147,27150,27166],{},[1105,27111,27112,27113,1370,27130,1395],{},"Formulace hypotéz ",[1296,27114,27116],{"className":27115},[1299],[1301,27117,27118],{"xmlns":1303},[1305,27119,27120,27128],{},[1308,27121,27122],{},[1311,27123,27124,27126],{},[1314,27125,1560],{},[1562,27127,1564],{},[1319,27129,1567],{"encoding":1321},[1296,27131,27133],{"className":27132},[1299],[1301,27134,27135],{"xmlns":1303},[1305,27136,27137,27145],{},[1308,27138,27139],{},[1311,27140,27141,27143],{},[1314,27142,1560],{},[1562,27144,1792],{},[1319,27146,2994],{"encoding":1321},[1105,27148,27149],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1105,27151,27152,27153,1395],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1296,27154,27156],{"className":27155},[1299],[1301,27157,27158],{"xmlns":1303},[1305,27159,27160,27164],{},[1308,27161,27162],{},[1314,27163,1602],{},[1319,27165,1602],{"encoding":1321},[1105,27167,27168,27169],{},"Formulace závěru:\n",[1102,27170,27171,27249],{},[1105,27172,27173,27174,3987,27192,27209,27210,27230,27231,27248],{},"pokud ",[1296,27175,27177],{"className":27176},[1299],[1301,27178,27179],{"xmlns":1303},[1305,27180,27181,27189],{},[1308,27182,27183,27185,27187],{},[1314,27184,7098],{},[1685,27186,7015],{},[1314,27188,1602],{},[1319,27190,27191],{"encoding":1321},"T \\in W",[1296,27193,27195],{"className":27194},[1299],[1301,27196,27197],{"xmlns":1303},[1305,27198,27199,27207],{},[1308,27200,27201],{},[1311,27202,27203,27205],{},[1314,27204,1560],{},[1562,27206,1792],{},[1319,27208,2994],{"encoding":1321}," je testem prokázána na hladině významnosti ",[1296,27211,27213],{"className":27212},[1299],[1301,27214,27215],{"xmlns":1303},[1305,27216,27217,27227],{},[1308,27218,27219,27221,27223,27225],{},[1562,27220,11813],{},[1314,27222,3363],{},[2907,27224,2909],{},[1314,27226,11820],{"mathvariant":2119},[1319,27228,27229],{"encoding":1321},"100\\alpha\\,\\%"," (zamítáme ",[1296,27232,27234],{"className":27233},[1299],[1301,27235,27236],{"xmlns":1303},[1305,27237,27238,27246],{},[1308,27239,27240],{},[1311,27241,27242,27244],{},[1314,27243,1560],{},[1562,27245,1564],{},[1319,27247,1567],{"encoding":1321},");",[1105,27250,27173,27251,3987,27270,27287,27288,27307,27308,27325],{},[1296,27252,27254],{"className":27253},[1299],[1301,27255,27256],{"xmlns":1303},[1305,27257,27258,27267],{},[1308,27259,27260,27262,27265],{},[1314,27261,7098],{},[1685,27263,27264],{"mathvariant":2119},"∉",[1314,27266,1602],{},[1319,27268,27269],{"encoding":1321},"T \\notin W",[1296,27271,27273],{"className":27272},[1299],[1301,27274,27275],{"xmlns":1303},[1305,27276,27277,27285],{},[1308,27278,27279],{},[1311,27280,27281,27283],{},[1314,27282,1560],{},[1562,27284,1792],{},[1319,27286,2994],{"encoding":1321}," není testem prokázána na hladině významnosti ",[1296,27289,27291],{"className":27290},[1299],[1301,27292,27293],{"xmlns":1303},[1305,27294,27295,27305],{},[1308,27296,27297,27299,27301,27303],{},[1562,27298,11813],{},[1314,27300,3363],{},[2907,27302,2909],{},[1314,27304,11820],{"mathvariant":2119},[1319,27306,27229],{"encoding":1321}," ; ",[1296,27309,27311],{"className":27310},[1299],[1301,27312,27313],{"xmlns":1303},[1305,27314,27315,27323],{},[1308,27316,27317],{},[1311,27318,27319,27321],{},[1314,27320,1560],{},[1562,27322,1564],{},[1319,27324,1567],{"encoding":1321}," nezamítáme.",[1148,27327,27328,27329,27332,27333,27350,27351,27368,27369,27389,27390,25176,27407,1651,27427,27444],{},"Rovnocennou alternativou je ",[1108,27330,27331],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1296,27334,27336],{"className":27335},[1299],[1301,27337,27338],{"xmlns":1303},[1305,27339,27340,27348],{},[1308,27341,27342],{},[1311,27343,27344,27346],{},[1314,27345,1560],{},[1562,27347,1564],{},[1319,27349,1567],{"encoding":1321},". Čím menší p-hodnota, tím více data svědčí proti ",[1296,27352,27354],{"className":27353},[1299],[1301,27355,27356],{"xmlns":1303},[1305,27357,27358,27366],{},[1308,27359,27360],{},[1311,27361,27362,27364],{},[1314,27363,1560],{},[1562,27365,1564],{},[1319,27367,1567],{"encoding":1321},". Rozhodovací pravidlo: ",[1296,27370,27372],{"className":27371},[1299],[1301,27373,27374],{"xmlns":1303},[1305,27375,27376,27386],{},[1308,27377,27378,27380,27382,27384],{},[1314,27379,1148],{},[1685,27381,6731],{},[1314,27383,3363],{},[1685,27385,7545],{},[1319,27387,27388],{"encoding":1321},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1296,27391,27393],{"className":27392},[1299],[1301,27394,27395],{"xmlns":1303},[1305,27396,27397,27405],{},[1308,27398,27399],{},[1311,27400,27401,27403],{},[1314,27402,1560],{},[1562,27404,1564],{},[1319,27406,1567],{"encoding":1321},[1296,27408,27410],{"className":27409},[1299],[1301,27411,27412],{"xmlns":1303},[1305,27413,27414,27424],{},[1308,27415,27416,27418,27420,27422],{},[1314,27417,1148],{},[1685,27419,1687],{},[1314,27421,3363],{},[1685,27423,7545],{},[1319,27425,27426],{"encoding":1321},"p > \\alpha \\Rightarrow",[1296,27428,27430],{"className":27429},[1299],[1301,27431,27432],{"xmlns":1303},[1305,27433,27434,27442],{},[1308,27435,27436],{},[1311,27437,27438,27440],{},[1314,27439,1560],{},[1562,27441,1564],{},[1319,27443,1567],{"encoding":1321}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1143,27446,27448],{"id":27447},"jednovýběrový-t-test","Jednovýběrový t-test",[1148,27450,27451,27452,27465,27466,27498,27499,27512,27513,1370,27530,27547,27548,27566,27567,27580],{},"Test o střední hodnotě ",[1296,27453,27455],{"className":27454},[1299],[1301,27456,27457],{"xmlns":1303},[1305,27458,27459,27463],{},[1308,27460,27461],{},[1314,27462,6887],{},[1319,27464,8791],{"encoding":1321}," rozdělení ",[1296,27467,27469],{"className":27468},[1299],[1301,27470,27471],{"xmlns":1303},[1305,27472,27473,27495],{},[1308,27474,27475,27477,27479,27481,27483,27485,27487,27493],{},[1314,27476,6728],{},[1685,27478,9178],{},[1314,27480,6882],{},[1685,27482,1873],{"stretchy":1872},[1314,27484,6887],{},[1685,27486,1795],{"separator":1530},[1579,27488,27489,27491],{},[1314,27490,6895],{},[1562,27492,1586],{},[1685,27494,1884],{"stretchy":1872},[1319,27496,27497],{"encoding":1321},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1296,27500,27502],{"className":27501},[1299],[1301,27503,27504],{"xmlns":1303},[1305,27505,27506,27510],{},[1308,27507,27508],{},[1314,27509,1683],{},[1319,27511,1683],{"encoding":1321}," se určí charakteristiky ",[1296,27514,27516],{"className":27515},[1299],[1301,27517,27518],{"xmlns":1303},[1305,27519,27520,27528],{},[1308,27521,27522],{},[2722,27523,27524,27526],{"accent":1530},[1314,27525,6716],{},[1685,27527,11454],{},[1319,27529,21557],{"encoding":1321},[1296,27531,27533],{"className":27532},[1299],[1301,27534,27535],{"xmlns":1303},[1305,27536,27537,27545],{},[1308,27538,27539],{},[1579,27540,27541,27543],{},[1314,27542,1852],{},[1562,27544,1586],{},[1319,27546,15772],{"encoding":1321},"; testem se posuzuje vztah mezi zvoleným číslem ",[1296,27549,27551],{"className":27550},[1299],[1301,27552,27553],{"xmlns":1303},[1305,27554,27555,27563],{},[1308,27556,27557],{},[1311,27558,27559,27561],{},[1314,27560,6887],{},[1562,27562,1564],{},[1319,27564,27565],{"encoding":1321},"\\mu_0"," a neznámou hodnotou ",[1296,27568,27570],{"className":27569},[1299],[1301,27571,27572],{"xmlns":1303},[1305,27573,27574,27578],{},[1308,27575,27576],{},[1314,27577,6887],{},[1319,27579,8791],{"encoding":1321},". Testové kritérium",[1296,27582,27584],{"className":27583},[1299],[1301,27585,27586],{"xmlns":1303,"display":1962},[1305,27587,27588,27632],{},[1308,27589,27590,27592,27594,27614,27618,27620],{},[1314,27591,7098],{},[1685,27593,1980],{},[2738,27595,27596,27612],{},[1308,27597,27598,27604,27606],{},[2722,27599,27600,27602],{"accent":1530},[1314,27601,6716],{},[1685,27603,11454],{},[1685,27605,3062],{},[1311,27607,27608,27610],{},[1314,27609,6887],{},[1562,27611,1564],{},[1314,27613,1852],{},[4452,27615,27616],{},[1314,27617,1683],{},[1685,27619,9178],{},[1311,27621,27622,27624],{},[1314,27623,7140],{},[1308,27625,27626,27628,27630],{},[1314,27627,1683],{},[1685,27629,3062],{},[1562,27631,1792],{},[1319,27633,27634],{"encoding":1321},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1148,27636,27637,27638,27656],{},"má Studentovo rozdělení o ",[1296,27639,27641],{"className":27640},[1299],[1301,27642,27643],{"xmlns":1303},[1305,27644,27645,27653],{},[1308,27646,27647,27649,27651],{},[1314,27648,1683],{},[1685,27650,3062],{},[1562,27652,1792],{},[1319,27654,27655],{"encoding":1321},"n-1"," stupních volnosti.",[1162,27658,27659,27717],{},[1165,27660,27661],{},[1168,27662,27663,27682,27701],{},[1171,27664,27665],{},[1296,27666,27668],{"className":27667},[1299],[1301,27669,27670],{"xmlns":1303},[1305,27671,27672,27680],{},[1308,27673,27674],{},[1311,27675,27676,27678],{},[1314,27677,1560],{},[1562,27679,1564],{},[1319,27681,1567],{"encoding":1321},[1171,27683,27684],{},[1296,27685,27687],{"className":27686},[1299],[1301,27688,27689],{"xmlns":1303},[1305,27690,27691,27699],{},[1308,27692,27693],{},[1311,27694,27695,27697],{},[1314,27696,1560],{},[1562,27698,1792],{},[1319,27700,2994],{"encoding":1321},[1171,27702,27703,27704],{},"Kritický obor ",[1296,27705,27707],{"className":27706},[1299],[1301,27708,27709],{"xmlns":1303},[1305,27710,27711,27715],{},[1308,27712,27713],{},[1314,27714,1602],{},[1319,27716,1602],{"encoding":1321},[1178,27718,27719,27809,27907],{},[1168,27720,27721,27745,27769],{},[1183,27722,27723],{},[1296,27724,27726],{"className":27725},[1299],[1301,27727,27728],{"xmlns":1303},[1305,27729,27730,27742],{},[1308,27731,27732,27734,27736],{},[1314,27733,6887],{},[1685,27735,6731],{},[1311,27737,27738,27740],{},[1314,27739,6887],{},[1562,27741,1564],{},[1319,27743,27744],{"encoding":1321},"\\mu \\le \\mu_0",[1183,27746,27747],{},[1296,27748,27750],{"className":27749},[1299],[1301,27751,27752],{"xmlns":1303},[1305,27753,27754,27766],{},[1308,27755,27756,27758,27760],{},[1314,27757,6887],{},[1685,27759,1687],{},[1311,27761,27762,27764],{},[1314,27763,6887],{},[1562,27765,1564],{},[1319,27767,27768],{"encoding":1321},"\\mu > \\mu_0",[1183,27770,27771],{},[1296,27772,27774],{"className":27773},[1299],[1301,27775,27776],{"xmlns":1303},[1305,27777,27778,27806],{},[1308,27779,27780,27782,27784,27796,27798,27800,27802,27804],{},[1314,27781,7140],{},[1685,27783,3349],{},[1311,27785,27786,27788],{},[1314,27787,7140],{},[1308,27789,27790,27792,27794],{},[1562,27791,1792],{},[1685,27793,3062],{},[1314,27795,3363],{},[1685,27797,1873],{"stretchy":1872},[1314,27799,1683],{},[1685,27801,3062],{},[1562,27803,1792],{},[1685,27805,1884],{"stretchy":1872},[1319,27807,27808],{"encoding":1321},"t \\ge t_{1-\\alpha}(n-1)",[1168,27810,27811,27835,27859],{},[1183,27812,27813],{},[1296,27814,27816],{"className":27815},[1299],[1301,27817,27818],{"xmlns":1303},[1305,27819,27820,27832],{},[1308,27821,27822,27824,27826],{},[1314,27823,6887],{},[1685,27825,1980],{},[1311,27827,27828,27830],{},[1314,27829,6887],{},[1562,27831,1564],{},[1319,27833,27834],{"encoding":1321},"\\mu = \\mu_0",[1183,27836,27837],{},[1296,27838,27840],{"className":27839},[1299],[1301,27841,27842],{"xmlns":1303},[1305,27843,27844,27856],{},[1308,27845,27846,27848,27850],{},[1314,27847,6887],{},[1685,27849,10951],{"mathvariant":2119},[1311,27851,27852,27854],{},[1314,27853,6887],{},[1562,27855,1564],{},[1319,27857,27858],{"encoding":1321},"\\mu \\neq \\mu_0",[1183,27860,27861],{},[1296,27862,27864],{"className":27863},[1299],[1301,27865,27866],{"xmlns":1303},[1305,27867,27868,27904],{},[1308,27869,27870,27872,27874,27876,27878,27894,27896,27898,27900,27902],{},[1685,27871,23016],{"stretchy":1872},[1314,27873,7140],{},[1685,27875,23016],{"stretchy":1872},[1685,27877,3349],{},[1311,27879,27880,27882],{},[1314,27881,7140],{},[1308,27883,27884,27886,27888,27890,27892],{},[1562,27885,1792],{},[1685,27887,3062],{},[1314,27889,3363],{},[1314,27891,1502],{"mathvariant":2119},[1562,27893,1586],{},[1685,27895,1873],{"stretchy":1872},[1314,27897,1683],{},[1685,27899,3062],{},[1562,27901,1792],{},[1685,27903,1884],{"stretchy":1872},[1319,27905,27906],{"encoding":1321},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1168,27908,27909,27933,27957],{},[1183,27910,27911],{},[1296,27912,27914],{"className":27913},[1299],[1301,27915,27916],{"xmlns":1303},[1305,27917,27918,27930],{},[1308,27919,27920,27922,27924],{},[1314,27921,6887],{},[1685,27923,3349],{},[1311,27925,27926,27928],{},[1314,27927,6887],{},[1562,27929,1564],{},[1319,27931,27932],{"encoding":1321},"\\mu \\ge \\mu_0",[1183,27934,27935],{},[1296,27936,27938],{"className":27937},[1299],[1301,27939,27940],{"xmlns":1303},[1305,27941,27942,27954],{},[1308,27943,27944,27946,27948],{},[1314,27945,6887],{},[1685,27947,4331],{},[1311,27949,27950,27952],{},[1314,27951,6887],{},[1562,27953,1564],{},[1319,27955,27956],{"encoding":1321},"\\mu \u003C \\mu_0",[1183,27958,27959],{},[1296,27960,27962],{"className":27961},[1299],[1301,27963,27964],{"xmlns":1303},[1305,27965,27966,27996],{},[1308,27967,27968,27970,27972,27974,27986,27988,27990,27992,27994],{},[1314,27969,7140],{},[1685,27971,6731],{},[1685,27973,3062],{},[1311,27975,27976,27978],{},[1314,27977,7140],{},[1308,27979,27980,27982,27984],{},[1562,27981,1792],{},[1685,27983,3062],{},[1314,27985,3363],{},[1685,27987,1873],{"stretchy":1872},[1314,27989,1683],{},[1685,27991,3062],{},[1562,27993,1792],{},[1685,27995,1884],{"stretchy":1872},[1319,27997,27998],{"encoding":1321},"t \\le -t_{1-\\alpha}(n-1)",[1148,28000,28001,28002,28005],{},"V R test provádí ",[3468,28003,28004],{},"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?",[3692,28007,28009],{"className":3694,"code":28008,"language":71,"meta":1452,"style":1452},"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",[3468,28010,28011,28065],{"__ignoreMap":1452},[1296,28012,28013,28015,28017,28019,28021,28024,28026,28029,28031,28034,28036,28039,28041,28044,28046,28049,28051,28053,28055,28058,28060,28063],{"class":3700,"line":10},[1296,28014,6716],{"class":3703},[1296,28016,3708],{"class":3707},[1296,28018,3834],{"class":3711},[1296,28020,1873],{"class":3715},[1296,28022,28023],{"class":3723},"12.5",[1296,28025,1795],{"class":3707},[1296,28027,28028],{"class":3723}," 13.5",[1296,28030,1795],{"class":3707},[1296,28032,28033],{"class":3723}," 11.9",[1296,28035,1795],{"class":3707},[1296,28037,28038],{"class":3723}," 12.2",[1296,28040,1795],{"class":3707},[1296,28042,28043],{"class":3723}," 13.0",[1296,28045,1795],{"class":3707},[1296,28047,28048],{"class":3723}," 14.3",[1296,28050,1795],{"class":3707},[1296,28052,28038],{"class":3723},[1296,28054,1795],{"class":3707},[1296,28056,28057],{"class":3723}," 11.8",[1296,28059,1795],{"class":3707},[1296,28061,28062],{"class":3723}," 14.0",[1296,28064,3900],{"class":3715},[1296,28066,28067,28070,28072,28074,28076,28078,28080,28082,28084,28087,28089,28092],{"class":3700,"line":27},[1296,28068,28069],{"class":3711},"t.test",[1296,28071,1873],{"class":3715},[1296,28073,6716],{"class":3703},[1296,28075,1795],{"class":3707},[1296,28077,25573],{"class":3703},[1296,28079,3796],{"class":3707},[1296,28081,3733],{"class":3723},[1296,28083,1795],{"class":3707},[1296,28085,28086],{"class":3703}," alternative",[1296,28088,3796],{"class":3707},[1296,28090,28091],{"class":3839}," \"two.sided\"",[1296,28093,3900],{"class":3715},[3692,28095,28098],{"className":28096,"code":28097,"language":3922,"meta":1452},[3920],"    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",[3468,28099,28097],{"__ignoreMap":1452},[1148,28101,28102,28104,28105,28108,28109,28112,28113,28116,28117,28140],{},[3468,28103,7140],{}," je testové kritérium, ",[3468,28106,28107],{},"df"," stupně volnosti, ",[3468,28110,28111],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3468,28114,28115],{},"mean of x"," výběrový průměr. Zde ",[1296,28118,28120],{"className":28119},[1299],[1301,28121,28122],{"xmlns":1303},[1305,28123,28124,28137],{},[1308,28125,28126,28128,28130,28133,28135],{},[1314,28127,1148],{},[1685,28129,1980],{},[1562,28131,28132],{},"0,02843",[1685,28134,4331],{},[1562,28136,3983],{},[1319,28138,28139],{"encoding":1321},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1514,28142,28144,28151,28239,28295,28387],{"className":28143,"dataCallout":3475},[1517,3474],[1148,28145,28147,28150],{"className":28146},[1523],[1296,28148],{"className":28149,"ariaHidden":1530},[1527,3482,1529],"Příklad: Kontrola objemu lahví",[1148,28152,28153,28154,28176,28177,28195,28196,28219,28220,28238],{},"Pivovar plní lahve, deklarovaný objem je ",[1296,28155,28157],{"className":28156},[1299],[1301,28158,28159],{"xmlns":1303},[1305,28160,28161,28173],{},[1308,28162,28163,28169,28171],{},[1311,28164,28165,28167],{},[1314,28166,6887],{},[1562,28168,1564],{},[1685,28170,1980],{},[1562,28172,8452],{},[1319,28174,28175],{"encoding":1321},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1296,28178,28180],{"className":28179},[1299],[1301,28181,28182],{"xmlns":1303},[1305,28183,28184,28192],{},[1308,28185,28186,28188,28190],{},[1314,28187,1683],{},[1685,28189,1980],{},[1562,28191,4044],{},[1319,28193,28194],{"encoding":1321},"n = 20"," lahví dal ",[1296,28197,28199],{"className":28198},[1299],[1301,28200,28201],{"xmlns":1303},[1305,28202,28203,28216],{},[1308,28204,28205,28211,28213],{},[2722,28206,28207,28209],{"accent":1530},[1314,28208,6716],{},[1685,28210,11454],{},[1685,28212,1980],{},[1562,28214,28215],{},"0,492",[1319,28217,28218],{"encoding":1321},"\\bar{x} = 0{,}492"," l, ",[1296,28221,28223],{"className":28222},[1299],[1301,28224,28225],{"xmlns":1303},[1305,28226,28227,28235],{},[1308,28228,28229,28231,28233],{},[1314,28230,1852],{},[1685,28232,1980],{},[1562,28234,14790],{},[1319,28236,28237],{"encoding":1321},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1148,28240,28241,28267,28268,28294],{},[1296,28242,28244],{"className":28243},[1299],[1301,28245,28246],{"xmlns":1303},[1305,28247,28248,28264],{},[1308,28249,28250,28256,28258,28260,28262],{},[1311,28251,28252,28254],{},[1314,28253,1560],{},[1562,28255,1564],{},[1685,28257,1956],{},[1314,28259,6887],{},[1685,28261,3349],{},[1562,28263,8452],{},[1319,28265,28266],{"encoding":1321},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1296,28269,28271],{"className":28270},[1299],[1301,28272,28273],{"xmlns":1303},[1305,28274,28275,28291],{},[1308,28276,28277,28283,28285,28287,28289],{},[1311,28278,28279,28281],{},[1314,28280,1560],{},[1562,28282,1792],{},[1685,28284,1956],{},[1314,28286,6887],{},[1685,28288,4331],{},[1562,28290,8452],{},[1319,28292,28293],{"encoding":1321},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1148,28296,28297],{},[1296,28298,28300],{"className":28299},[1299],[1301,28301,28302],{"xmlns":1303},[1305,28303,28304,28384],{},[1308,28305,28306,28308,28310,28322,28326,28328,28330,28333,28335,28337,28339,28341,28343,28345,28347,28349,28361,28363,28365,28367,28369,28371,28373,28375,28377,28379,28382],{},[1314,28307,7140],{},[1685,28309,1980],{},[2738,28311,28312,28320],{},[1308,28313,28314,28316,28318],{},[1562,28315,28215],{},[1685,28317,3062],{},[1562,28319,8452],{},[1562,28321,14790],{},[4452,28323,28324],{},[1562,28325,4044],{},[1685,28327,1980],{},[1685,28329,3062],{},[1562,28331,28332],{},"2,385",[1685,28334,1795],{"separator":1530},[2010,28336],{"width":2012},[1314,28338,1602],{},[1685,28340,1980],{},[1685,28342,3332],{"stretchy":1872},[1314,28344,7140],{},[1685,28346,6731],{},[1685,28348,3062],{},[1311,28350,28351,28353],{},[1314,28352,7140],{},[1308,28354,28355,28357,28359],{},[1562,28356,1564],{},[1685,28358,1795],{"separator":1530},[1562,28360,21790],{},[1685,28362,1873],{"stretchy":1872},[1562,28364,14714],{},[1685,28366,1884],{"stretchy":1872},[1685,28368,3392],{"stretchy":1872},[1685,28370,1980],{},[1685,28372,3332],{"stretchy":1872},[1314,28374,7140],{},[1685,28376,6731],{},[1685,28378,3062],{},[1562,28380,28381],{},"1,729",[1685,28383,3392],{"stretchy":1872},[1319,28385,28386],{"encoding":1321},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1148,28388,28389,28390,6003,28408,28425],{},"Protože ",[1296,28391,28393],{"className":28392},[1299],[1301,28394,28395],{"xmlns":1303},[1305,28396,28397,28405],{},[1308,28398,28399,28401,28403],{},[1314,28400,7140],{},[1685,28402,7015],{},[1314,28404,1602],{},[1319,28406,28407],{"encoding":1321},"t \\in W",[1296,28409,28411],{"className":28410},[1299],[1301,28412,28413],{"xmlns":1303},[1305,28414,28415,28423],{},[1308,28416,28417],{},[1311,28418,28419,28421],{},[1314,28420,1560],{},[1562,28422,1564],{},[1319,28424,1567],{"encoding":1321},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1148,28427,28428,28429,28431,28432,1956],{},"Ze souhrnných charakteristik bez surových dat ",[3468,28430,28004],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3468,28433,28434],{},"qt()",[3692,28436,28438],{"className":3694,"code":28437,"language":71,"meta":1452,"style":1452},"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",[3468,28439,28440,28478,28510,28540,28545],{"__ignoreMap":1452},[1296,28441,28442,28445,28447,28450,28452,28454,28456,28459,28461,28463,28465,28468,28470,28473,28475],{"class":3700,"line":10},[1296,28443,28444],{"class":3703},"xbar",[1296,28446,3708],{"class":3707},[1296,28448,28449],{"class":3723}," 0.492",[1296,28451,25176],{"class":3715},[1296,28453,1852],{"class":3703},[1296,28455,3708],{"class":3707},[1296,28457,28458],{"class":3723}," 0.015",[1296,28460,25176],{"class":3715},[1296,28462,1683],{"class":3703},[1296,28464,3708],{"class":3707},[1296,28466,28467],{"class":3723}," 20",[1296,28469,25176],{"class":3715},[1296,28471,28472],{"class":3703},"mu0",[1296,28474,3708],{"class":3707},[1296,28476,28477],{"class":3723}," 0.5\n",[1296,28479,28480,28482,28484,28486,28488,28490,28493,28495,28497,28500,28502,28504,28506,28508],{"class":3700,"line":27},[1296,28481,7140],{"class":3703},[1296,28483,3708],{"class":3707},[1296,28485,4604],{"class":3715},[1296,28487,28444],{"class":3703},[1296,28489,25513],{"class":3707},[1296,28491,28492],{"class":3703}," mu0",[1296,28494,4599],{"class":3715},[1296,28496,1502],{"class":3707},[1296,28498,28499],{"class":3703}," s",[1296,28501,18636],{"class":3707},[1296,28503,4576],{"class":3711},[1296,28505,1873],{"class":3715},[1296,28507,1683],{"class":3703},[1296,28509,3900],{"class":3715},[1296,28511,28512,28515,28517,28520,28522,28525,28527,28529,28531,28534,28536,28538],{"class":3700,"line":148},[1296,28513,28514],{"class":3703},"t_krit",[1296,28516,3708],{"class":3707},[1296,28518,28519],{"class":3711}," qt",[1296,28521,1873],{"class":3715},[1296,28523,28524],{"class":3723},"0.05",[1296,28526,1795],{"class":3707},[1296,28528,10804],{"class":3703},[1296,28530,3796],{"class":3707},[1296,28532,28533],{"class":3703}," n",[1296,28535,25513],{"class":3707},[1296,28537,4638],{"class":3723},[1296,28539,3900],{"class":3715},[1296,28541,28542],{"class":3700,"line":111},[1296,28543,28544],{"class":3703},"t\n",[1296,28546,28547],{"class":3700,"line":96},[1296,28548,28549],{"class":3703},"t_krit\n",[3692,28551,28554],{"className":28552,"code":28553,"language":3922,"meta":1452},[3920],"[1] -2.385139\n[1] -1.729133\n",[3468,28555,28553],{"__ignoreMap":1452},[1148,28557,28558],{},[4382,28559],{"alt":28560,"className":28561,"src":28562},"mask-th-t-jednostranny",[1245,4386],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1148,28564,28565,28566,1956],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3468,28567,28004],{},[1148,28569,28570,28573],{},[1108,28571,28572],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3692,28575,28577],{"className":3694,"code":28576,"language":71,"meta":1452,"style":1452},"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",[3468,28578,28579,28642],{"__ignoreMap":1452},[1296,28580,28581,28584,28586,28588,28590,28593,28595,28598,28600,28603,28605,28608,28610,28613,28615,28618,28620,28622,28624,28627,28629,28631,28633,28636,28638,28640],{"class":3700,"line":10},[1296,28582,28583],{"class":3703},"x2",[1296,28585,3708],{"class":3707},[1296,28587,3834],{"class":3711},[1296,28589,1873],{"class":3715},[1296,28591,28592],{"class":3723},"9.5",[1296,28594,1795],{"class":3707},[1296,28596,28597],{"class":3723}," 10.5",[1296,28599,1795],{"class":3707},[1296,28601,28602],{"class":3723}," 8.9",[1296,28604,1795],{"class":3707},[1296,28606,28607],{"class":3723}," 9.2",[1296,28609,1795],{"class":3707},[1296,28611,28612],{"class":3723}," 10.0",[1296,28614,1795],{"class":3707},[1296,28616,28617],{"class":3723}," 8.5",[1296,28619,1795],{"class":3707},[1296,28621,28607],{"class":3723},[1296,28623,1795],{"class":3707},[1296,28625,28626],{"class":3723}," 8.8",[1296,28628,1795],{"class":3707},[1296,28630,28612],{"class":3723},[1296,28632,1795],{"class":3707},[1296,28634,28635],{"class":3723}," 9.5",[1296,28637,1795],{"class":3707},[1296,28639,28607],{"class":3723},[1296,28641,3900],{"class":3715},[1296,28643,28644,28646,28648,28650,28652,28654,28656,28658,28660,28662,28664,28666],{"class":3700,"line":27},[1296,28645,28069],{"class":3711},[1296,28647,1873],{"class":3715},[1296,28649,28583],{"class":3703},[1296,28651,1795],{"class":3707},[1296,28653,25573],{"class":3703},[1296,28655,3796],{"class":3707},[1296,28657,9472],{"class":3723},[1296,28659,1795],{"class":3707},[1296,28661,28086],{"class":3703},[1296,28663,3796],{"class":3707},[1296,28665,28091],{"class":3839},[1296,28667,3900],{"class":3715},[3692,28669,28672],{"className":28670,"code":28671,"language":3922,"meta":1452},[3920],"    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",[3468,28673,28671],{"__ignoreMap":1452},[1148,28675,28676,28699],{},[1296,28677,28679],{"className":28678},[1299],[1301,28680,28681],{"xmlns":1303},[1305,28682,28683,28696],{},[1308,28684,28685,28687,28689,28692,28694],{},[1314,28686,1148],{},[1685,28688,1980],{},[1562,28690,28691],{},"0,006548",[1685,28693,4331],{},[1562,28695,3983],{},[1319,28697,28698],{"encoding":1321},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1148,28701,28702,28705],{},[1108,28703,28704],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3692,28707,28709],{"className":3694,"code":28708,"language":71,"meta":1452,"style":1452},"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",[3468,28710,28711,28762,28788],{"__ignoreMap":1452},[1296,28712,28713,28716,28718,28720,28722,28724,28726,28728,28730,28732,28734,28736,28738,28740,28742,28744,28746,28748,28750,28752,28754,28756,28758,28760],{"class":3700,"line":10},[1296,28714,28715],{"class":3703},"x3",[1296,28717,3708],{"class":3707},[1296,28719,3834],{"class":3711},[1296,28721,1873],{"class":3715},[1296,28723,11981],{"class":3723},[1296,28725,1795],{"class":3707},[1296,28727,11986],{"class":3723},[1296,28729,1795],{"class":3707},[1296,28731,11991],{"class":3723},[1296,28733,1795],{"class":3707},[1296,28735,11996],{"class":3723},[1296,28737,1795],{"class":3707},[1296,28739,11991],{"class":3723},[1296,28741,1795],{"class":3707},[1296,28743,11991],{"class":3723},[1296,28745,1795],{"class":3707},[1296,28747,12009],{"class":3723},[1296,28749,1795],{"class":3707},[1296,28751,12014],{"class":3723},[1296,28753,1795],{"class":3707},[1296,28755,11986],{"class":3723},[1296,28757,1795],{"class":3707},[1296,28759,11986],{"class":3723},[1296,28761,3900],{"class":3715},[1296,28763,28764,28766,28768,28770,28772,28774,28776,28778,28780,28782,28784,28786],{"class":3700,"line":27},[1296,28765,28069],{"class":3711},[1296,28767,1873],{"class":3715},[1296,28769,28715],{"class":3703},[1296,28771,1795],{"class":3707},[1296,28773,25573],{"class":3703},[1296,28775,3796],{"class":3707},[1296,28777,3799],{"class":3723},[1296,28779,1795],{"class":3707},[1296,28781,28086],{"class":3703},[1296,28783,3796],{"class":3707},[1296,28785,28091],{"class":3839},[1296,28787,3900],{"class":3715},[1296,28789,28790,28792,28794,28796],{"class":3700,"line":148},[1296,28791,17572],{"class":3711},[1296,28793,1873],{"class":3715},[1296,28795,28715],{"class":3703},[1296,28797,3900],{"class":3715},[3692,28799,28802],{"className":28800,"code":28801,"language":3922,"meta":1452},[3920],"    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",[3468,28803,28801],{"__ignoreMap":1452},[1148,28805,28806,28829,28830,28853],{},[1296,28807,28809],{"className":28808},[1299],[1301,28810,28811],{"xmlns":1303},[1305,28812,28813,28826],{},[1308,28814,28815,28817,28819,28822,28824],{},[1314,28816,1148],{},[1685,28818,1980],{},[1562,28820,28821],{},"0,0343",[1685,28823,4331],{},[1562,28825,3983],{},[1319,28827,28828],{"encoding":1321},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1296,28831,28833],{"className":28832},[1299],[1301,28834,28835],{"xmlns":1303},[1305,28836,28837,28850],{},[1308,28838,28839,28841,28843,28846,28848],{},[1314,28840,1148],{},[1685,28842,1980],{},[1562,28844,28845],{},"0,4634",[1685,28847,1687],{},[1562,28849,3983],{},[1319,28851,28852],{"encoding":1321},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1143,28855,28857],{"id":28856},"párový-t-test","Párový t-test",[1148,28859,28860,28861,28891,28892,6777,28926,28964,28965,28978,28979,1370,28997,29017,29018,29035,29036,27580],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1296,28862,28864],{"className":28863},[1299],[1301,28865,28866],{"xmlns":1303},[1305,28867,28868,28888],{},[1308,28869,28870,28872,28878,28880,28886],{},[1685,28871,1873],{"stretchy":1872},[1311,28873,28874,28876],{},[1314,28875,6728],{},[1314,28877,1876],{},[1685,28879,1795],{"separator":1530},[1311,28881,28882,28884],{},[1314,28883,7084],{},[1314,28885,1876],{},[1685,28887,1884],{"stretchy":1872},[1319,28889,28890],{"encoding":1321},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1296,28893,28895],{"className":28894},[1299],[1301,28896,28897],{"xmlns":1303},[1305,28898,28899,28923],{},[1308,28900,28901,28907,28909,28915,28917],{},[1311,28902,28903,28905],{},[1314,28904,1209],{},[1314,28906,1876],{},[1685,28908,1980],{},[1311,28910,28911,28913],{},[1314,28912,6728],{},[1314,28914,1876],{},[1685,28916,3062],{},[1311,28918,28919,28921],{},[1314,28920,7084],{},[1314,28922,1876],{},[1319,28924,28925],{"encoding":1321},"D_i = X_i - Y_i",[1296,28927,28929],{"className":28928},[1299],[1301,28930,28931],{"xmlns":1303},[1305,28932,28933,28961],{},[1308,28934,28935,28937,28939,28941,28943,28949,28951,28959],{},[1314,28936,1209],{},[1685,28938,9178],{},[1314,28940,6882],{},[1685,28942,1873],{"stretchy":1872},[1311,28944,28945,28947],{},[1314,28946,6887],{},[1314,28948,1209],{},[1685,28950,1795],{"separator":1530},[3351,28952,28953,28955,28957],{},[1314,28954,6895],{},[1314,28956,1209],{},[1562,28958,1586],{},[1685,28960,1884],{"stretchy":1872},[1319,28962,28963],{"encoding":1321},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1296,28966,28968],{"className":28967},[1299],[1301,28969,28970],{"xmlns":1303},[1305,28971,28972,28976],{},[1308,28973,28974],{},[1314,28975,1683],{},[1319,28977,1683],{"encoding":1321}," dvojic se určí ",[1296,28980,28982],{"className":28981},[1299],[1301,28983,28984],{"xmlns":1303},[1305,28985,28986,28994],{},[1308,28987,28988],{},[2722,28989,28990,28992],{"accent":1530},[1314,28991,7792],{},[1685,28993,11454],{},[1319,28995,28996],{"encoding":1321},"\\bar{d}",[1296,28998,29000],{"className":28999},[1299],[1301,29001,29002],{"xmlns":1303},[1305,29003,29004,29014],{},[1308,29005,29006],{},[3351,29007,29008,29010,29012],{},[1314,29009,1852],{},[1314,29011,7792],{},[1562,29013,1586],{},[1319,29015,29016],{"encoding":1321},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1296,29019,29021],{"className":29020},[1299],[1301,29022,29023],{"xmlns":1303},[1305,29024,29025,29033],{},[1308,29026,29027],{},[1311,29028,29029,29031],{},[1314,29030,6887],{},[1562,29032,1564],{},[1319,29034,27565],{"encoding":1321}," (obvykle 0) a ",[1296,29037,29039],{"className":29038},[1299],[1301,29040,29041],{"xmlns":1303},[1305,29042,29043,29051],{},[1308,29044,29045],{},[1311,29046,29047,29049],{},[1314,29048,6887],{},[1314,29050,1209],{},[1319,29052,29053],{"encoding":1321},"\\mu_D",[1296,29055,29057],{"className":29056},[1299],[1301,29058,29059],{"xmlns":1303,"display":1962},[1305,29060,29061,29111],{},[1308,29062,29063,29065,29067,29091,29095,29097,29109],{},[1314,29064,7098],{},[1685,29066,1980],{},[2738,29068,29069,29085],{},[1308,29070,29071,29077,29079],{},[2722,29072,29073,29075],{"accent":1530},[1314,29074,7792],{},[1685,29076,11454],{},[1685,29078,3062],{},[1311,29080,29081,29083],{},[1314,29082,6887],{},[1562,29084,1564],{},[1311,29086,29087,29089],{},[1314,29088,1852],{},[1314,29090,7792],{},[4452,29092,29093],{},[1314,29094,1683],{},[1685,29096,9178],{},[1311,29098,29099,29101],{},[1314,29100,7140],{},[1308,29102,29103,29105,29107],{},[1314,29104,1683],{},[1685,29106,3062],{},[1562,29108,1792],{},[1314,29110,1395],{"mathvariant":2119},[1319,29112,29113],{"encoding":1321},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1162,29115,29116,29173],{},[1165,29117,29118],{},[1168,29119,29120,29139,29158],{},[1171,29121,29122],{},[1296,29123,29125],{"className":29124},[1299],[1301,29126,29127],{"xmlns":1303},[1305,29128,29129,29137],{},[1308,29130,29131],{},[1311,29132,29133,29135],{},[1314,29134,1560],{},[1562,29136,1564],{},[1319,29138,1567],{"encoding":1321},[1171,29140,29141],{},[1296,29142,29144],{"className":29143},[1299],[1301,29145,29146],{"xmlns":1303},[1305,29147,29148,29156],{},[1308,29149,29150],{},[1311,29151,29152,29154],{},[1314,29153,1560],{},[1562,29155,1792],{},[1319,29157,2994],{"encoding":1321},[1171,29159,27703,29160],{},[1296,29161,29163],{"className":29162},[1299],[1301,29164,29165],{"xmlns":1303},[1305,29166,29167,29171],{},[1308,29168,29169],{},[1314,29170,1602],{},[1319,29172,1602],{"encoding":1321},[1178,29174,29175,29272,29377],{},[1168,29176,29177,29205,29233],{},[1183,29178,29179],{},[1296,29180,29182],{"className":29181},[1299],[1301,29183,29184],{"xmlns":1303},[1305,29185,29186,29202],{},[1308,29187,29188,29194,29196],{},[1311,29189,29190,29192],{},[1314,29191,6887],{},[1314,29193,1209],{},[1685,29195,6731],{},[1311,29197,29198,29200],{},[1314,29199,6887],{},[1562,29201,1564],{},[1319,29203,29204],{"encoding":1321},"\\mu_D \\le \\mu_0",[1183,29206,29207],{},[1296,29208,29210],{"className":29209},[1299],[1301,29211,29212],{"xmlns":1303},[1305,29213,29214,29230],{},[1308,29215,29216,29222,29224],{},[1311,29217,29218,29220],{},[1314,29219,6887],{},[1314,29221,1209],{},[1685,29223,1687],{},[1311,29225,29226,29228],{},[1314,29227,6887],{},[1562,29229,1564],{},[1319,29231,29232],{"encoding":1321},"\\mu_D > \\mu_0",[1183,29234,29235],{},[1296,29236,29238],{"className":29237},[1299],[1301,29239,29240],{"xmlns":1303},[1305,29241,29242,29270],{},[1308,29243,29244,29246,29248,29260,29262,29264,29266,29268],{},[1314,29245,7140],{},[1685,29247,3349],{},[1311,29249,29250,29252],{},[1314,29251,7140],{},[1308,29253,29254,29256,29258],{},[1562,29255,1792],{},[1685,29257,3062],{},[1314,29259,3363],{},[1685,29261,1873],{"stretchy":1872},[1314,29263,1683],{},[1685,29265,3062],{},[1562,29267,1792],{},[1685,29269,1884],{"stretchy":1872},[1319,29271,27808],{"encoding":1321},[1168,29273,29274,29302,29330],{},[1183,29275,29276],{},[1296,29277,29279],{"className":29278},[1299],[1301,29280,29281],{"xmlns":1303},[1305,29282,29283,29299],{},[1308,29284,29285,29291,29293],{},[1311,29286,29287,29289],{},[1314,29288,6887],{},[1314,29290,1209],{},[1685,29292,1980],{},[1311,29294,29295,29297],{},[1314,29296,6887],{},[1562,29298,1564],{},[1319,29300,29301],{"encoding":1321},"\\mu_D = \\mu_0",[1183,29303,29304],{},[1296,29305,29307],{"className":29306},[1299],[1301,29308,29309],{"xmlns":1303},[1305,29310,29311,29327],{},[1308,29312,29313,29319,29321],{},[1311,29314,29315,29317],{},[1314,29316,6887],{},[1314,29318,1209],{},[1685,29320,10951],{"mathvariant":2119},[1311,29322,29323,29325],{},[1314,29324,6887],{},[1562,29326,1564],{},[1319,29328,29329],{"encoding":1321},"\\mu_D \\neq \\mu_0",[1183,29331,29332],{},[1296,29333,29335],{"className":29334},[1299],[1301,29336,29337],{"xmlns":1303},[1305,29338,29339,29375],{},[1308,29340,29341,29343,29345,29347,29349,29365,29367,29369,29371,29373],{},[1685,29342,23016],{"stretchy":1872},[1314,29344,7140],{},[1685,29346,23016],{"stretchy":1872},[1685,29348,3349],{},[1311,29350,29351,29353],{},[1314,29352,7140],{},[1308,29354,29355,29357,29359,29361,29363],{},[1562,29356,1792],{},[1685,29358,3062],{},[1314,29360,3363],{},[1314,29362,1502],{"mathvariant":2119},[1562,29364,1586],{},[1685,29366,1873],{"stretchy":1872},[1314,29368,1683],{},[1685,29370,3062],{},[1562,29372,1792],{},[1685,29374,1884],{"stretchy":1872},[1319,29376,27906],{"encoding":1321},[1168,29378,29379,29407,29435],{},[1183,29380,29381],{},[1296,29382,29384],{"className":29383},[1299],[1301,29385,29386],{"xmlns":1303},[1305,29387,29388,29404],{},[1308,29389,29390,29396,29398],{},[1311,29391,29392,29394],{},[1314,29393,6887],{},[1314,29395,1209],{},[1685,29397,3349],{},[1311,29399,29400,29402],{},[1314,29401,6887],{},[1562,29403,1564],{},[1319,29405,29406],{"encoding":1321},"\\mu_D \\ge \\mu_0",[1183,29408,29409],{},[1296,29410,29412],{"className":29411},[1299],[1301,29413,29414],{"xmlns":1303},[1305,29415,29416,29432],{},[1308,29417,29418,29424,29426],{},[1311,29419,29420,29422],{},[1314,29421,6887],{},[1314,29423,1209],{},[1685,29425,4331],{},[1311,29427,29428,29430],{},[1314,29429,6887],{},[1562,29431,1564],{},[1319,29433,29434],{"encoding":1321},"\\mu_D \u003C \\mu_0",[1183,29436,29437],{},[1296,29438,29440],{"className":29439},[1299],[1301,29441,29442],{"xmlns":1303},[1305,29443,29444,29474],{},[1308,29445,29446,29448,29450,29452,29464,29466,29468,29470,29472],{},[1314,29447,7140],{},[1685,29449,6731],{},[1685,29451,3062],{},[1311,29453,29454,29456],{},[1314,29455,7140],{},[1308,29457,29458,29460,29462],{},[1562,29459,1792],{},[1685,29461,3062],{},[1314,29463,3363],{},[1685,29465,1873],{"stretchy":1872},[1314,29467,1683],{},[1685,29469,3062],{},[1562,29471,1792],{},[1685,29473,1884],{"stretchy":1872},[1319,29475,27998],{"encoding":1321},[1514,29477,29479,29486,29628,29692,29778],{"className":29478,"dataCallout":3475},[1517,3474],[1148,29480,29482,29485],{"className":29481},[1523],[1296,29483],{"className":29484,"ariaHidden":1530},[1527,3482,1529],"Příklad: Snížení spotřeby paliva aditivem",[1148,29487,29488,29489,29507,29508,29526,29527,29545,29546,29579,29580,29603,29604,29627],{},"U ",[1296,29490,29492],{"className":29491},[1299],[1301,29493,29494],{"xmlns":1303},[1305,29495,29496,29504],{},[1308,29497,29498,29500,29502],{},[1314,29499,1683],{},[1685,29501,1980],{},[1562,29503,9028],{},[1319,29505,29506],{"encoding":1321},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1296,29509,29511],{"className":29510},[1299],[1301,29512,29513],{"xmlns":1303},[1305,29514,29515,29523],{},[1308,29516,29517],{},[1311,29518,29519,29521],{},[1314,29520,6728],{},[1314,29522,1876],{},[1319,29524,29525],{"encoding":1321},"X_i",") a po něm (",[1296,29528,29530],{"className":29529},[1299],[1301,29531,29532],{"xmlns":1303},[1305,29533,29534,29542],{},[1308,29535,29536],{},[1311,29537,29538,29540],{},[1314,29539,7084],{},[1314,29541,1876],{},[1319,29543,29544],{"encoding":1321},"Y_i","), diference ",[1296,29547,29549],{"className":29548},[1299],[1301,29550,29551],{"xmlns":1303},[1305,29552,29553,29577],{},[1308,29554,29555,29561,29563,29569,29571],{},[1311,29556,29557,29559],{},[1314,29558,1209],{},[1314,29560,1876],{},[1685,29562,1980],{},[1311,29564,29565,29567],{},[1314,29566,6728],{},[1314,29568,1876],{},[1685,29570,3062],{},[1311,29572,29573,29575],{},[1314,29574,7084],{},[1314,29576,1876],{},[1319,29578,28925],{"encoding":1321}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1296,29581,29583],{"className":29582},[1299],[1301,29584,29585],{"xmlns":1303},[1305,29586,29587,29600],{},[1308,29588,29589,29595,29597],{},[2722,29590,29591,29593],{"accent":1530},[1314,29592,7792],{},[1685,29594,11454],{},[1685,29596,1980],{},[1562,29598,29599],{},"0,4",[1319,29601,29602],{"encoding":1321},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1296,29605,29607],{"className":29606},[1299],[1301,29608,29609],{"xmlns":1303},[1305,29610,29611,29624],{},[1308,29612,29613,29619,29621],{},[1311,29614,29615,29617],{},[1314,29616,1852],{},[1314,29618,7792],{},[1685,29620,1980],{},[1562,29622,29623],{},"0,35",[1319,29625,29626],{"encoding":1321},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1148,29629,29630,29660,29661,29691],{},[1296,29631,29633],{"className":29632},[1299],[1301,29634,29635],{"xmlns":1303},[1305,29636,29637,29657],{},[1308,29638,29639,29645,29647,29653,29655],{},[1311,29640,29641,29643],{},[1314,29642,1560],{},[1562,29644,1564],{},[1685,29646,1956],{},[1311,29648,29649,29651],{},[1314,29650,6887],{},[1314,29652,1209],{},[1685,29654,6731],{},[1562,29656,1564],{},[1319,29658,29659],{"encoding":1321},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1296,29662,29664],{"className":29663},[1299],[1301,29665,29666],{"xmlns":1303},[1305,29667,29668,29688],{},[1308,29669,29670,29676,29678,29684,29686],{},[1311,29671,29672,29674],{},[1314,29673,1560],{},[1562,29675,1792],{},[1685,29677,1956],{},[1311,29679,29680,29682],{},[1314,29681,6887],{},[1314,29683,1209],{},[1685,29685,1687],{},[1562,29687,1564],{},[1319,29689,29690],{"encoding":1321},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1148,29693,29694],{},[1296,29695,29697],{"className":29696},[1299],[1301,29698,29699],{"xmlns":1303},[1305,29700,29701,29775],{},[1308,29702,29703,29705,29707,29719,29723,29725,29728,29730,29732,29734,29736,29738,29740,29742,29754,29756,29758,29760,29762,29764,29766,29768,29770,29773],{},[1314,29704,7140],{},[1685,29706,1980],{},[2738,29708,29709,29717],{},[1308,29710,29711,29713,29715],{},[1562,29712,29599],{},[1685,29714,3062],{},[1562,29716,1564],{},[1562,29718,29623],{},[4452,29720,29721],{},[1562,29722,9028],{},[1685,29724,1980],{},[1562,29726,29727],{},"3,614",[1685,29729,1795],{"separator":1530},[2010,29731],{"width":2012},[1314,29733,1602],{},[1685,29735,1980],{},[1685,29737,3332],{"stretchy":1872},[1314,29739,7140],{},[1685,29741,3349],{},[1311,29743,29744,29746],{},[1314,29745,7140],{},[1308,29747,29748,29750,29752],{},[1562,29749,1564],{},[1685,29751,1795],{"separator":1530},[1562,29753,21790],{},[1685,29755,1873],{"stretchy":1872},[1562,29757,3593],{},[1685,29759,1884],{"stretchy":1872},[1685,29761,3392],{"stretchy":1872},[1685,29763,1980],{},[1685,29765,3332],{"stretchy":1872},[1314,29767,7140],{},[1685,29769,3349],{},[1562,29771,29772],{},"1,833",[1685,29774,3392],{"stretchy":1872},[1319,29776,29777],{"encoding":1321},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1148,29779,28389,29780,6003,29797,29814],{},[1296,29781,29783],{"className":29782},[1299],[1301,29784,29785],{"xmlns":1303},[1305,29786,29787,29795],{},[1308,29788,29789,29791,29793],{},[1314,29790,7140],{},[1685,29792,7015],{},[1314,29794,1602],{},[1319,29796,28407],{"encoding":1321},[1296,29798,29800],{"className":29799},[1299],[1301,29801,29802],{"xmlns":1303},[1305,29803,29804,29812],{},[1308,29805,29806],{},[1311,29807,29808,29810],{},[1314,29809,1560],{},[1562,29811,1564],{},[1319,29813,1567],{"encoding":1321},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3692,29816,29818],{"className":3694,"code":29817,"language":71,"meta":1452,"style":1452},"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",[3468,29819,29820,29849,29880,29906,29910],{"__ignoreMap":1452},[1296,29821,29822,29825,29827,29830,29832,29835,29837,29840,29842,29844,29846],{"class":3700,"line":10},[1296,29823,29824],{"class":3703},"dbar",[1296,29826,3708],{"class":3707},[1296,29828,29829],{"class":3723}," 0.4",[1296,29831,25176],{"class":3715},[1296,29833,29834],{"class":3703},"sd_d",[1296,29836,3708],{"class":3707},[1296,29838,29839],{"class":3723}," 0.35",[1296,29841,25176],{"class":3715},[1296,29843,1683],{"class":3703},[1296,29845,3708],{"class":3707},[1296,29847,29848],{"class":3723}," 10\n",[1296,29850,29851,29853,29855,29857,29859,29861,29863,29865,29867,29870,29872,29874,29876,29878],{"class":3700,"line":27},[1296,29852,7140],{"class":3703},[1296,29854,3708],{"class":3707},[1296,29856,4604],{"class":3715},[1296,29858,29824],{"class":3703},[1296,29860,25513],{"class":3707},[1296,29862,9965],{"class":3723},[1296,29864,4599],{"class":3715},[1296,29866,1502],{"class":3707},[1296,29868,29869],{"class":3703}," sd_d",[1296,29871,18636],{"class":3707},[1296,29873,4576],{"class":3711},[1296,29875,1873],{"class":3715},[1296,29877,1683],{"class":3703},[1296,29879,3900],{"class":3715},[1296,29881,29882,29884,29886,29888,29890,29892,29894,29896,29898,29900,29902,29904],{"class":3700,"line":148},[1296,29883,28514],{"class":3703},[1296,29885,3708],{"class":3707},[1296,29887,28519],{"class":3711},[1296,29889,1873],{"class":3715},[1296,29891,10821],{"class":3723},[1296,29893,1795],{"class":3707},[1296,29895,10804],{"class":3703},[1296,29897,3796],{"class":3707},[1296,29899,28533],{"class":3703},[1296,29901,25513],{"class":3707},[1296,29903,4638],{"class":3723},[1296,29905,3900],{"class":3715},[1296,29907,29908],{"class":3700,"line":111},[1296,29909,28544],{"class":3703},[1296,29911,29912],{"class":3700,"line":96},[1296,29913,28549],{"class":3703},[3692,29915,29918],{"className":29916,"code":29917,"language":3922,"meta":1452},[3920],"[1] 3.614032\n[1] 1.833113\n",[3468,29919,29917],{"__ignoreMap":1452},[1514,29921,29923,29930,29933,30078,30084],{"className":29922,"dataCallout":6409},[1517,6408],[1148,29924,29926,29929],{"className":29925},[1523],[1296,29927],{"className":29928,"ariaHidden":1530},[1527,6416,1529],"Ověřte normalitu diferencí, ne jen výsledek testu",[1148,29931,29932],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3692,29934,29936],{"className":3694,"code":29935,"language":71,"meta":1452,"style":1452},"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",[3468,29937,29938,29989,30040,30064],{"__ignoreMap":1452},[1296,29939,29940,29943,29945,29947,29949,29952,29954,29957,29959,29962,29964,29967,29969,29972,29974,29977,29979,29982,29984,29987],{"class":3700,"line":10},[1296,29941,29942],{"class":3703},"estA",[1296,29944,3708],{"class":3707},[1296,29946,3834],{"class":3711},[1296,29948,1873],{"class":3715},[1296,29950,29951],{"class":3723},"3282",[1296,29953,1795],{"class":3707},[1296,29955,29956],{"class":3723}," 2506",[1296,29958,1795],{"class":3707},[1296,29960,29961],{"class":3723}," 2812",[1296,29963,1795],{"class":3707},[1296,29965,29966],{"class":3723}," 5453",[1296,29968,1795],{"class":3707},[1296,29970,29971],{"class":3723}," 3263",[1296,29973,1795],{"class":3707},[1296,29975,29976],{"class":3723}," 4571",[1296,29978,1795],{"class":3707},[1296,29980,29981],{"class":3723}," 3121",[1296,29983,1795],{"class":3707},[1296,29985,29986],{"class":3723}," 2963",[1296,29988,3900],{"class":3715},[1296,29990,29991,29994,29996,29998,30000,30003,30005,30008,30010,30013,30015,30018,30020,30023,30025,30028,30030,30033,30035,30038],{"class":3700,"line":27},[1296,29992,29993],{"class":3703},"estB",[1296,29995,3708],{"class":3707},[1296,29997,3834],{"class":3711},[1296,29999,1873],{"class":3715},[1296,30001,30002],{"class":3723},"3271",[1296,30004,1795],{"class":3707},[1296,30006,30007],{"class":3723}," 2531",[1296,30009,1795],{"class":3707},[1296,30011,30012],{"class":3723}," 2799",[1296,30014,1795],{"class":3707},[1296,30016,30017],{"class":3723}," 5471",[1296,30019,1795],{"class":3707},[1296,30021,30022],{"class":3723}," 3285",[1296,30024,1795],{"class":3707},[1296,30026,30027],{"class":3723}," 4557",[1296,30029,1795],{"class":3707},[1296,30031,30032],{"class":3723}," 3139",[1296,30034,1795],{"class":3707},[1296,30036,30037],{"class":3723}," 2976",[1296,30039,3900],{"class":3715},[1296,30041,30042,30044,30046,30048,30050,30053,30055,30058,30060,30062],{"class":3700,"line":148},[1296,30043,28069],{"class":3711},[1296,30045,1873],{"class":3715},[1296,30047,29942],{"class":3703},[1296,30049,1795],{"class":3707},[1296,30051,30052],{"class":3703}," estB",[1296,30054,1795],{"class":3707},[1296,30056,30057],{"class":3703}," paired",[1296,30059,3796],{"class":3707},[1296,30061,3809],{"class":3723},[1296,30063,3900],{"class":3715},[1296,30065,30066,30068,30070,30072,30074,30076],{"class":3700,"line":111},[1296,30067,17572],{"class":3711},[1296,30069,1873],{"class":3715},[1296,30071,29942],{"class":3703},[1296,30073,25513],{"class":3707},[1296,30075,30052],{"class":3703},[1296,30077,3900],{"class":3715},[3692,30079,30082],{"className":30080,"code":30081,"language":3922,"meta":1452},[3920],"    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",[3468,30083,30081],{"__ignoreMap":1452},[1148,30085,30086,30087,4604,30104,30123,30124,30147],{},"Párový t-test sám nezamítá ",[1296,30088,30090],{"className":30089},[1299],[1301,30091,30092],{"xmlns":1303},[1305,30093,30094,30102],{},[1308,30095,30096],{},[1311,30097,30098,30100],{},[1314,30099,1560],{},[1562,30101,1564],{},[1319,30103,1567],{"encoding":1321},[1296,30105,30107],{"className":30106},[1299],[1301,30108,30109],{"xmlns":1303},[1305,30110,30111,30120],{},[1308,30112,30113,30115,30117],{},[1314,30114,1148],{},[1685,30116,1980],{},[1562,30118,30119],{},"0,2635",[1319,30121,30122],{"encoding":1321},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1296,30125,30127],{"className":30126},[1299],[1301,30128,30129],{"xmlns":1303},[1305,30130,30131,30144],{},[1308,30132,30133,30135,30137,30140,30142],{},[1314,30134,1148],{},[1685,30136,1980],{},[1562,30138,30139],{},"0,03203",[1685,30141,4331],{},[1562,30143,3983],{},[1319,30145,30146],{"encoding":1321},"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).",[1143,30149,30151],{"id":30150},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1148,30153,30154,30155,30181,30182,30220,30221,1370,30239,30220,30277,30295,30296,1370,30328,30360,30361,30387,30388,1395],{},"Uvažují se dva nezávislé základní soubory ",[1296,30156,30158],{"className":30157},[1299],[1301,30159,30160],{"xmlns":1303},[1305,30161,30162,30178],{},[1308,30163,30164,30170,30172],{},[1311,30165,30166,30168],{},[1314,30167,8920],{},[1562,30169,1792],{},[1685,30171,1795],{"separator":1530},[1311,30173,30174,30176],{},[1314,30175,8920],{},[1562,30177,1586],{},[1319,30179,30180],{"encoding":1321},"Z_1, Z_2"," se znakem ",[1296,30183,30185],{"className":30184},[1299],[1301,30186,30187],{"xmlns":1303},[1305,30188,30189,30217],{},[1308,30190,30191,30193,30195,30197,30199,30205,30207,30215],{},[1314,30192,6728],{},[1685,30194,9178],{},[1314,30196,6882],{},[1685,30198,1873],{"stretchy":1872},[1311,30200,30201,30203],{},[1314,30202,6887],{},[1562,30204,1792],{},[1685,30206,1795],{"separator":1530},[3351,30208,30209,30211,30213],{},[1314,30210,6895],{},[1562,30212,1792],{},[1562,30214,1586],{},[1685,30216,1884],{"stretchy":1872},[1319,30218,30219],{"encoding":1321},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1296,30222,30224],{"className":30223},[1299],[1301,30225,30226],{"xmlns":1303},[1305,30227,30228,30236],{},[1308,30229,30230],{},[1311,30231,30232,30234],{},[1314,30233,8920],{},[1562,30235,1792],{},[1319,30237,30238],{"encoding":1321},"Z_1",[1296,30240,30242],{"className":30241},[1299],[1301,30243,30244],{"xmlns":1303},[1305,30245,30246,30274],{},[1308,30247,30248,30250,30252,30254,30256,30262,30264,30272],{},[1314,30249,6728],{},[1685,30251,9178],{},[1314,30253,6882],{},[1685,30255,1873],{"stretchy":1872},[1311,30257,30258,30260],{},[1314,30259,6887],{},[1562,30261,1586],{},[1685,30263,1795],{"separator":1530},[3351,30265,30266,30268,30270],{},[1314,30267,6895],{},[1562,30269,1586],{},[1562,30271,1586],{},[1685,30273,1884],{"stretchy":1872},[1319,30275,30276],{"encoding":1321},"X \\sim N(\\mu_2, \\sigma_2^2)",[1296,30278,30280],{"className":30279},[1299],[1301,30281,30282],{"xmlns":1303},[1305,30283,30284,30292],{},[1308,30285,30286],{},[1311,30287,30288,30290],{},[1314,30289,8920],{},[1562,30291,1586],{},[1319,30293,30294],{"encoding":1321},"Z_2",". Z výběrů se určí ",[1296,30297,30299],{"className":30298},[1299],[1301,30300,30301],{"xmlns":1303},[1305,30302,30303,30325],{},[1308,30304,30305,30315,30317],{},[1311,30306,30307,30313],{},[2722,30308,30309,30311],{"accent":1530},[1314,30310,6716],{},[1685,30312,11454],{},[1562,30314,1792],{},[1685,30316,1795],{"separator":1530},[3351,30318,30319,30321,30323],{},[1314,30320,1852],{},[1562,30322,1792],{},[1562,30324,1586],{},[1319,30326,30327],{"encoding":1321},"\\bar{x}_1, s_1^2",[1296,30329,30331],{"className":30330},[1299],[1301,30332,30333],{"xmlns":1303},[1305,30334,30335,30357],{},[1308,30336,30337,30347,30349],{},[1311,30338,30339,30345],{},[2722,30340,30341,30343],{"accent":1530},[1314,30342,6716],{},[1685,30344,11454],{},[1562,30346,1586],{},[1685,30348,1795],{"separator":1530},[3351,30350,30351,30353,30355],{},[1314,30352,1852],{},[1562,30354,1586],{},[1562,30356,1586],{},[1319,30358,30359],{"encoding":1321},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1296,30362,30364],{"className":30363},[1299],[1301,30365,30366],{"xmlns":1303},[1305,30367,30368,30384],{},[1308,30369,30370,30376,30378],{},[1311,30371,30372,30374],{},[1314,30373,6887],{},[1562,30375,1792],{},[1685,30377,1795],{"separator":1530},[1311,30379,30380,30382],{},[1314,30381,6887],{},[1562,30383,1586],{},[1319,30385,30386],{"encoding":1321},"\\mu_1, \\mu_2",", resp. mezi ",[1296,30389,30391],{"className":30390},[1299],[1301,30392,30393],{"xmlns":1303},[1305,30394,30395,30415],{},[1308,30396,30397,30405,30407],{},[3351,30398,30399,30401,30403],{},[1314,30400,6895],{},[1562,30402,1792],{},[1562,30404,1586],{},[1685,30406,1795],{"separator":1530},[3351,30408,30409,30411,30413],{},[1314,30410,6895],{},[1562,30412,1586],{},[1562,30414,1586],{},[1319,30416,30417],{"encoding":1321},"\\sigma_1^2, \\sigma_2^2",[16742,30419,30421],{"id":30420},"f-test-o-rozptylech","F-test o rozptylech",[1148,30423,30424],{},"Statistika",[1296,30426,30428],{"className":30427},[1299],[1301,30429,30430],{"xmlns":1303,"display":1962},[1305,30431,30432,30488],{},[1308,30433,30434,30436,30438,30456,30458],{},[1314,30435,1225],{},[1685,30437,1980],{},[2738,30439,30440,30448],{},[3351,30441,30442,30444,30446],{},[1314,30443,1852],{},[1562,30445,1792],{},[1562,30447,1586],{},[3351,30449,30450,30452,30454],{},[1314,30451,1852],{},[1562,30453,1586],{},[1562,30455,1586],{},[1685,30457,9178],{},[1311,30459,30460,30462],{},[1314,30461,1225],{},[1308,30463,30464,30470,30472,30474,30476,30478,30484,30486],{},[1311,30465,30466,30468],{},[1314,30467,1683],{},[1562,30469,1792],{},[1685,30471,3062],{},[1562,30473,1792],{},[1685,30475,1795],{"separator":1530},[2907,30477,2909],{},[1311,30479,30480,30482],{},[1314,30481,1683],{},[1562,30483,1586],{},[1685,30485,3062],{},[1562,30487,1792],{},[1319,30489,30490],{"encoding":1321},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1148,30492,30493,30494,1370,30516,27656],{},"má Fisherovo-Snedecorovo rozdělení o ",[1296,30495,30497],{"className":30496},[1299],[1301,30498,30499],{"xmlns":1303},[1305,30500,30501,30513],{},[1308,30502,30503,30509,30511],{},[1311,30504,30505,30507],{},[1314,30506,1683],{},[1562,30508,1792],{},[1685,30510,3062],{},[1562,30512,1792],{},[1319,30514,30515],{"encoding":1321},"n_1-1",[1296,30517,30519],{"className":30518},[1299],[1301,30520,30521],{"xmlns":1303},[1305,30522,30523,30535],{},[1308,30524,30525,30531,30533],{},[1311,30526,30527,30529],{},[1314,30528,1683],{},[1562,30530,1586],{},[1685,30532,3062],{},[1562,30534,1792],{},[1319,30536,30537],{"encoding":1321},"n_2-1",[1162,30539,30540,30597],{},[1165,30541,30542],{},[1168,30543,30544,30563,30582],{},[1171,30545,30546],{},[1296,30547,30549],{"className":30548},[1299],[1301,30550,30551],{"xmlns":1303},[1305,30552,30553,30561],{},[1308,30554,30555],{},[1311,30556,30557,30559],{},[1314,30558,1560],{},[1562,30560,1564],{},[1319,30562,1567],{"encoding":1321},[1171,30564,30565],{},[1296,30566,30568],{"className":30567},[1299],[1301,30569,30570],{"xmlns":1303},[1305,30571,30572,30580],{},[1308,30573,30574],{},[1311,30575,30576,30578],{},[1314,30577,1560],{},[1562,30579,1792],{},[1319,30581,2994],{"encoding":1321},[1171,30583,27703,30584],{},[1296,30585,30587],{"className":30586},[1299],[1301,30588,30589],{"xmlns":1303},[1305,30590,30591,30595],{},[1308,30592,30593],{},[1314,30594,1602],{},[1319,30596,1602],{"encoding":1321},[1178,30598,30599,30713,30886],{},[1168,30600,30601,30629,30657],{},[1183,30602,30603],{},[1296,30604,30606],{"className":30605},[1299],[1301,30607,30608],{"xmlns":1303},[1305,30609,30610,30626],{},[1308,30611,30612,30618,30620],{},[1311,30613,30614,30616],{},[1314,30615,6895],{},[1562,30617,1792],{},[1685,30619,6731],{},[1311,30621,30622,30624],{},[1314,30623,6895],{},[1562,30625,1586],{},[1319,30627,30628],{"encoding":1321},"\\sigma_1 \\le \\sigma_2",[1183,30630,30631],{},[1296,30632,30634],{"className":30633},[1299],[1301,30635,30636],{"xmlns":1303},[1305,30637,30638,30654],{},[1308,30639,30640,30646,30648],{},[1311,30641,30642,30644],{},[1314,30643,6895],{},[1562,30645,1792],{},[1685,30647,1687],{},[1311,30649,30650,30652],{},[1314,30651,6895],{},[1562,30653,1586],{},[1319,30655,30656],{"encoding":1321},"\\sigma_1 > \\sigma_2",[1183,30658,30659],{},[1296,30660,30662],{"className":30661},[1299],[1301,30663,30664],{"xmlns":1303},[1305,30665,30666,30710],{},[1308,30667,30668,30670,30672,30684,30686,30692,30694,30696,30698,30704,30706,30708],{},[1314,30669,1225],{},[1685,30671,3349],{},[1311,30673,30674,30676],{},[1314,30675,1225],{},[1308,30677,30678,30680,30682],{},[1562,30679,1792],{},[1685,30681,3062],{},[1314,30683,3363],{},[1685,30685,1873],{"stretchy":1872},[1311,30687,30688,30690],{},[1314,30689,1683],{},[1562,30691,1792],{},[1685,30693,3062],{},[1562,30695,1792],{},[1685,30697,1795],{"separator":1530},[1311,30699,30700,30702],{},[1314,30701,1683],{},[1562,30703,1586],{},[1685,30705,3062],{},[1562,30707,1792],{},[1685,30709,1884],{"stretchy":1872},[1319,30711,30712],{"encoding":1321},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1168,30714,30715,30743,30771],{},[1183,30716,30717],{},[1296,30718,30720],{"className":30719},[1299],[1301,30721,30722],{"xmlns":1303},[1305,30723,30724,30740],{},[1308,30725,30726,30732,30734],{},[1311,30727,30728,30730],{},[1314,30729,6895],{},[1562,30731,1792],{},[1685,30733,1980],{},[1311,30735,30736,30738],{},[1314,30737,6895],{},[1562,30739,1586],{},[1319,30741,30742],{"encoding":1321},"\\sigma_1 = \\sigma_2",[1183,30744,30745],{},[1296,30746,30748],{"className":30747},[1299],[1301,30749,30750],{"xmlns":1303},[1305,30751,30752,30768],{},[1308,30753,30754,30760,30762],{},[1311,30755,30756,30758],{},[1314,30757,6895],{},[1562,30759,1792],{},[1685,30761,10951],{"mathvariant":2119},[1311,30763,30764,30766],{},[1314,30765,6895],{},[1562,30767,1586],{},[1319,30769,30770],{"encoding":1321},"\\sigma_1 \\neq \\sigma_2",[1183,30772,30773,30827,30828],{},[1296,30774,30776],{"className":30775},[1299],[1301,30777,30778],{"xmlns":1303},[1305,30779,30780,30824],{},[1308,30781,30782,30784,30786,30798,30800,30806,30808,30810,30812,30818,30820,30822],{},[1314,30783,1225],{},[1685,30785,6731],{},[1311,30787,30788,30790],{},[1314,30789,1225],{},[1308,30791,30792,30794,30796],{},[1314,30793,3363],{},[1314,30795,1502],{"mathvariant":2119},[1562,30797,1586],{},[1685,30799,1873],{"stretchy":1872},[1311,30801,30802,30804],{},[1314,30803,1683],{},[1562,30805,1792],{},[1685,30807,3062],{},[1562,30809,1792],{},[1685,30811,1795],{"separator":1530},[1311,30813,30814,30816],{},[1314,30815,1683],{},[1562,30817,1586],{},[1685,30819,3062],{},[1562,30821,1792],{},[1685,30823,1884],{"stretchy":1872},[1319,30825,30826],{"encoding":1321},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1296,30829,30831],{"className":30830},[1299],[1301,30832,30833],{"xmlns":1303},[1305,30834,30835,30883],{},[1308,30836,30837,30839,30841,30857,30859,30865,30867,30869,30871,30877,30879,30881],{},[1314,30838,1225],{},[1685,30840,3349],{},[1311,30842,30843,30845],{},[1314,30844,1225],{},[1308,30846,30847,30849,30851,30853,30855],{},[1562,30848,1792],{},[1685,30850,3062],{},[1314,30852,3363],{},[1314,30854,1502],{"mathvariant":2119},[1562,30856,1586],{},[1685,30858,1873],{"stretchy":1872},[1311,30860,30861,30863],{},[1314,30862,1683],{},[1562,30864,1792],{},[1685,30866,3062],{},[1562,30868,1792],{},[1685,30870,1795],{"separator":1530},[1311,30872,30873,30875],{},[1314,30874,1683],{},[1562,30876,1586],{},[1685,30878,3062],{},[1562,30880,1792],{},[1685,30882,1884],{"stretchy":1872},[1319,30884,30885],{"encoding":1321},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1168,30887,30888,30916,30944],{},[1183,30889,30890],{},[1296,30891,30893],{"className":30892},[1299],[1301,30894,30895],{"xmlns":1303},[1305,30896,30897,30913],{},[1308,30898,30899,30905,30907],{},[1311,30900,30901,30903],{},[1314,30902,6895],{},[1562,30904,1792],{},[1685,30906,3349],{},[1311,30908,30909,30911],{},[1314,30910,6895],{},[1562,30912,1586],{},[1319,30914,30915],{"encoding":1321},"\\sigma_1 \\ge \\sigma_2",[1183,30917,30918],{},[1296,30919,30921],{"className":30920},[1299],[1301,30922,30923],{"xmlns":1303},[1305,30924,30925,30941],{},[1308,30926,30927,30933,30935],{},[1311,30928,30929,30931],{},[1314,30930,6895],{},[1562,30932,1792],{},[1685,30934,4331],{},[1311,30936,30937,30939],{},[1314,30938,6895],{},[1562,30940,1586],{},[1319,30942,30943],{"encoding":1321},"\\sigma_1 \u003C \\sigma_2",[1183,30945,30946],{},[1296,30947,30949],{"className":30948},[1299],[1301,30950,30951],{"xmlns":1303},[1305,30952,30953,30991],{},[1308,30954,30955,30957,30959,30965,30967,30973,30975,30977,30979,30985,30987,30989],{},[1314,30956,1225],{},[1685,30958,6731],{},[1311,30960,30961,30963],{},[1314,30962,1225],{},[1314,30964,3363],{},[1685,30966,1873],{"stretchy":1872},[1311,30968,30969,30971],{},[1314,30970,1683],{},[1562,30972,1792],{},[1685,30974,3062],{},[1562,30976,1792],{},[1685,30978,1795],{"separator":1530},[1311,30980,30981,30983],{},[1314,30982,1683],{},[1562,30984,1586],{},[1685,30986,3062],{},[1562,30988,1792],{},[1685,30990,1884],{"stretchy":1872},[1319,30992,30993],{"encoding":1321},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[16742,30995,30997],{"id":30996},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1148,30999,31000],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1296,31002,31004],{"className":31003},[1299],[1301,31005,31006],{"xmlns":1303,"display":1962},[1305,31007,31008,31185],{},[1308,31009,31010,31016,31018,31094,31142,31144,31146,31155,31157,31163,31165,31171,31173,31179,31181,31183],{},[1311,31011,31012,31014],{},[1314,31013,7098],{},[1562,31015,1792],{},[1685,31017,1980],{},[2738,31019,31020,31044],{},[1308,31021,31022,31032,31034],{},[1311,31023,31024,31030],{},[2722,31025,31026,31028],{"accent":1530},[1314,31027,6716],{},[1685,31029,11454],{},[1562,31031,1792],{},[1685,31033,3062],{},[1311,31035,31036,31042],{},[2722,31037,31038,31040],{"accent":1530},[1314,31039,6716],{},[1685,31041,11454],{},[1562,31043,1586],{},[4452,31045,31046],{},[1308,31047,31048,31050,31056,31058,31060,31062,31070,31072,31074,31080,31082,31084,31086],{},[1685,31049,1873],{"stretchy":1872},[1311,31051,31052,31054],{},[1314,31053,1683],{},[1562,31055,1792],{},[1685,31057,3062],{},[1562,31059,1792],{},[1685,31061,1884],{"stretchy":1872},[3351,31063,31064,31066,31068],{},[1314,31065,1852],{},[1562,31067,1792],{},[1562,31069,1586],{},[1685,31071,5474],{},[1685,31073,1873],{"stretchy":1872},[1311,31075,31076,31078],{},[1314,31077,1683],{},[1562,31079,1586],{},[1685,31081,3062],{},[1562,31083,1792],{},[1685,31085,1884],{"stretchy":1872},[3351,31087,31088,31090,31092],{},[1314,31089,1852],{},[1562,31091,1586],{},[1562,31093,1586],{},[4452,31095,31096],{},[2738,31097,31098,31118],{},[1308,31099,31100,31106,31108,31114,31116],{},[1311,31101,31102,31104],{},[1314,31103,1683],{},[1562,31105,1792],{},[1685,31107,5474],{},[1311,31109,31110,31112],{},[1314,31111,1683],{},[1562,31113,1586],{},[1685,31115,3062],{},[1562,31117,1586],{},[1308,31119,31120,31130,31132],{},[2738,31121,31122,31124],{},[1562,31123,1792],{},[1311,31125,31126,31128],{},[1314,31127,1683],{},[1562,31129,1792],{},[1685,31131,5474],{},[2738,31133,31134,31136],{},[1562,31135,1792],{},[1311,31137,31138,31140],{},[1314,31139,1683],{},[1562,31141,1586],{},[1685,31143,1795],{"separator":1530},[2010,31145],{"width":2012},[3351,31147,31148,31150,31152],{},[1314,31149,7140],{},[1314,31151,1148],{},[1685,31153,31154],{},"∗",[1685,31156,1980],{},[1311,31158,31159,31161],{},[1314,31160,7140],{},[1314,31162,1148],{},[1685,31164,1873],{"stretchy":1872},[1311,31166,31167,31169],{},[1314,31168,1683],{},[1562,31170,1792],{},[1685,31172,5474],{},[1311,31174,31175,31177],{},[1314,31176,1683],{},[1562,31178,1586],{},[1685,31180,3062],{},[1562,31182,1586],{},[1685,31184,1884],{"stretchy":1872},[1319,31186,31187],{"encoding":1321},"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)",[1148,31189,31190,31191,31220],{},"se použije, pokud jsou rozptyly ",[1296,31192,31194],{"className":31193},[1299],[1301,31195,31196],{"xmlns":1303},[1305,31197,31198,31218],{},[1308,31199,31200,31208,31210],{},[3351,31201,31202,31204,31206],{},[1314,31203,6895],{},[1562,31205,1792],{},[1562,31207,1586],{},[1685,31209,1795],{"separator":1530},[3351,31211,31212,31214,31216],{},[1314,31213,6895],{},[1562,31215,1586],{},[1562,31217,1586],{},[1319,31219,30417],{"encoding":1321}," alespoň přibližně shodné; při rozdílných rozptylech",[1296,31222,31224],{"className":31223},[1299],[1301,31225,31226],{"xmlns":1303,"display":1962},[1305,31227,31228,31440],{},[1308,31229,31230,31236,31238,31302,31304,31306,31314,31316,31438],{},[1311,31231,31232,31234],{},[1314,31233,7098],{},[1562,31235,1586],{},[1685,31237,1980],{},[2738,31239,31240,31264],{},[1308,31241,31242,31252,31254],{},[1311,31243,31244,31250],{},[2722,31245,31246,31248],{"accent":1530},[1314,31247,6716],{},[1685,31249,11454],{},[1562,31251,1792],{},[1685,31253,3062],{},[1311,31255,31256,31262],{},[2722,31257,31258,31260],{"accent":1530},[1314,31259,6716],{},[1685,31261,11454],{},[1562,31263,1586],{},[4452,31265,31266],{},[1308,31267,31268,31276,31278,31284,31286,31294,31296],{},[3351,31269,31270,31272,31274],{},[1314,31271,1852],{},[1562,31273,1792],{},[1562,31275,1586],{},[1314,31277,1502],{"mathvariant":2119},[1311,31279,31280,31282],{},[1314,31281,1683],{},[1562,31283,1792],{},[1685,31285,5474],{},[3351,31287,31288,31290,31292],{},[1314,31289,1852],{},[1562,31291,1586],{},[1562,31293,1586],{},[1314,31295,1502],{"mathvariant":2119},[1311,31297,31298,31300],{},[1314,31299,1683],{},[1562,31301,1586],{},[1685,31303,1795],{"separator":1530},[2010,31305],{"width":2012},[3351,31307,31308,31310,31312],{},[1314,31309,7140],{},[1314,31311,1148],{},[1685,31313,31154],{},[1685,31315,1980],{},[2738,31317,31318,31398],{},[1308,31319,31320,31338,31344,31346,31352,31354,31356,31358,31360,31378,31384,31386,31392,31394,31396],{},[3239,31321,31322],{"scriptlevel":1564,"displaystyle":1530},[2738,31323,31324,31332],{},[3351,31325,31326,31328,31330],{},[1314,31327,1852],{},[1562,31329,1792],{},[1562,31331,1586],{},[1311,31333,31334,31336],{},[1314,31335,1683],{},[1562,31337,1792],{},[1311,31339,31340,31342],{},[1314,31341,7140],{},[1314,31343,1148],{},[1685,31345,1873],{"stretchy":1872},[1311,31347,31348,31350],{},[1314,31349,1683],{},[1562,31351,1792],{},[1685,31353,3062],{},[1562,31355,1792],{},[1685,31357,1884],{"stretchy":1872},[1685,31359,5474],{},[3239,31361,31362],{"scriptlevel":1564,"displaystyle":1530},[2738,31363,31364,31372],{},[3351,31365,31366,31368,31370],{},[1314,31367,1852],{},[1562,31369,1586],{},[1562,31371,1586],{},[1311,31373,31374,31376],{},[1314,31375,1683],{},[1562,31377,1586],{},[1311,31379,31380,31382],{},[1314,31381,7140],{},[1314,31383,1148],{},[1685,31385,1873],{"stretchy":1872},[1311,31387,31388,31390],{},[1314,31389,1683],{},[1562,31391,1586],{},[1685,31393,3062],{},[1562,31395,1792],{},[1685,31397,1884],{"stretchy":1872},[1308,31399,31400,31418,31420],{},[3239,31401,31402],{"scriptlevel":1564,"displaystyle":1530},[2738,31403,31404,31412],{},[3351,31405,31406,31408,31410],{},[1314,31407,1852],{},[1562,31409,1792],{},[1562,31411,1586],{},[1311,31413,31414,31416],{},[1314,31415,1683],{},[1562,31417,1792],{},[1685,31419,5474],{},[3239,31421,31422],{"scriptlevel":1564,"displaystyle":1530},[2738,31423,31424,31432],{},[3351,31425,31426,31428,31430],{},[1314,31427,1852],{},[1562,31429,1586],{},[1562,31431,1586],{},[1311,31433,31434,31436],{},[1314,31435,1683],{},[1562,31437,1586],{},[1314,31439,1395],{"mathvariant":2119},[1319,31441,31442],{"encoding":1321},"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}}.",[1162,31444,31445,31502],{},[1165,31446,31447],{},[1168,31448,31449,31468,31487],{},[1171,31450,31451],{},[1296,31452,31454],{"className":31453},[1299],[1301,31455,31456],{"xmlns":1303},[1305,31457,31458,31466],{},[1308,31459,31460],{},[1311,31461,31462,31464],{},[1314,31463,1560],{},[1562,31465,1564],{},[1319,31467,1567],{"encoding":1321},[1171,31469,31470],{},[1296,31471,31473],{"className":31472},[1299],[1301,31474,31475],{"xmlns":1303},[1305,31476,31477,31485],{},[1308,31478,31479],{},[1311,31480,31481,31483],{},[1314,31482,1560],{},[1562,31484,1792],{},[1319,31486,2994],{"encoding":1321},[1171,31488,27703,31489],{},[1296,31490,31492],{"className":31491},[1299],[1301,31493,31494],{"xmlns":1303},[1305,31495,31496,31500],{},[1308,31497,31498],{},[1314,31499,1602],{},[1319,31501,1602],{"encoding":1321},[1178,31503,31504,31588,31676],{},[1168,31505,31506,31534,31562],{},[1183,31507,31508],{},[1296,31509,31511],{"className":31510},[1299],[1301,31512,31513],{"xmlns":1303},[1305,31514,31515,31531],{},[1308,31516,31517,31523,31525],{},[1311,31518,31519,31521],{},[1314,31520,6887],{},[1562,31522,1792],{},[1685,31524,6731],{},[1311,31526,31527,31529],{},[1314,31528,6887],{},[1562,31530,1586],{},[1319,31532,31533],{"encoding":1321},"\\mu_1 \\le \\mu_2",[1183,31535,31536],{},[1296,31537,31539],{"className":31538},[1299],[1301,31540,31541],{"xmlns":1303},[1305,31542,31543,31559],{},[1308,31544,31545,31551,31553],{},[1311,31546,31547,31549],{},[1314,31548,6887],{},[1562,31550,1792],{},[1685,31552,1687],{},[1311,31554,31555,31557],{},[1314,31556,6887],{},[1562,31558,1586],{},[1319,31560,31561],{"encoding":1321},"\\mu_1 > \\mu_2",[1183,31563,31564],{},[1296,31565,31567],{"className":31566},[1299],[1301,31568,31569],{"xmlns":1303},[1305,31570,31571,31585],{},[1308,31572,31573,31575,31577],{},[1314,31574,7140],{},[1685,31576,3349],{},[3351,31578,31579,31581,31583],{},[1314,31580,7140],{},[1314,31582,1148],{},[1685,31584,31154],{},[1319,31586,31587],{"encoding":1321},"t \\ge t_p^*",[1168,31589,31590,31618,31646],{},[1183,31591,31592],{},[1296,31593,31595],{"className":31594},[1299],[1301,31596,31597],{"xmlns":1303},[1305,31598,31599,31615],{},[1308,31600,31601,31607,31609],{},[1311,31602,31603,31605],{},[1314,31604,6887],{},[1562,31606,1792],{},[1685,31608,1980],{},[1311,31610,31611,31613],{},[1314,31612,6887],{},[1562,31614,1586],{},[1319,31616,31617],{"encoding":1321},"\\mu_1 = \\mu_2",[1183,31619,31620],{},[1296,31621,31623],{"className":31622},[1299],[1301,31624,31625],{"xmlns":1303},[1305,31626,31627,31643],{},[1308,31628,31629,31635,31637],{},[1311,31630,31631,31633],{},[1314,31632,6887],{},[1562,31634,1792],{},[1685,31636,10951],{"mathvariant":2119},[1311,31638,31639,31641],{},[1314,31640,6887],{},[1562,31642,1586],{},[1319,31644,31645],{"encoding":1321},"\\mu_1 \\neq \\mu_2",[1183,31647,31648],{},[1296,31649,31651],{"className":31650},[1299],[1301,31652,31653],{"xmlns":1303},[1305,31654,31655,31673],{},[1308,31656,31657,31659,31661,31663,31665],{},[1685,31658,23016],{"stretchy":1872},[1314,31660,7140],{},[1685,31662,23016],{"stretchy":1872},[1685,31664,3349],{},[3351,31666,31667,31669,31671],{},[1314,31668,7140],{},[1314,31670,1148],{},[1685,31672,31154],{},[1319,31674,31675],{"encoding":1321},"\\lvert t \\rvert \\ge t_p^*",[1168,31677,31678,31706,31734],{},[1183,31679,31680],{},[1296,31681,31683],{"className":31682},[1299],[1301,31684,31685],{"xmlns":1303},[1305,31686,31687,31703],{},[1308,31688,31689,31695,31697],{},[1311,31690,31691,31693],{},[1314,31692,6887],{},[1562,31694,1792],{},[1685,31696,3349],{},[1311,31698,31699,31701],{},[1314,31700,6887],{},[1562,31702,1586],{},[1319,31704,31705],{"encoding":1321},"\\mu_1 \\ge \\mu_2",[1183,31707,31708],{},[1296,31709,31711],{"className":31710},[1299],[1301,31712,31713],{"xmlns":1303},[1305,31714,31715,31731],{},[1308,31716,31717,31723,31725],{},[1311,31718,31719,31721],{},[1314,31720,6887],{},[1562,31722,1792],{},[1685,31724,4331],{},[1311,31726,31727,31729],{},[1314,31728,6887],{},[1562,31730,1586],{},[1319,31732,31733],{"encoding":1321},"\\mu_1 \u003C \\mu_2",[1183,31735,31736],{},[1296,31737,31739],{"className":31738},[1299],[1301,31740,31741],{"xmlns":1303},[1305,31742,31743,31759],{},[1308,31744,31745,31747,31749,31751],{},[1314,31746,7140],{},[1685,31748,6731],{},[1685,31750,3062],{},[3351,31752,31753,31755,31757],{},[1314,31754,7140],{},[1314,31756,1148],{},[1685,31758,31154],{},[1319,31760,31761],{"encoding":1321},"t \\le -t_p^*",[1148,31763,31764,31765,30827,31783,1395],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1296,31766,31768],{"className":31767},[1299],[1301,31769,31770],{"xmlns":1303},[1305,31771,31772,31780],{},[1308,31773,31774],{},[1311,31775,31776,31778],{},[1314,31777,7098],{},[1562,31779,1792],{},[1319,31781,31782],{"encoding":1321},"T_1",[1296,31784,31786],{"className":31785},[1299],[1301,31787,31788],{"xmlns":1303},[1305,31789,31790,31798],{},[1308,31791,31792],{},[1311,31793,31794,31796],{},[1314,31795,7098],{},[1562,31797,1586],{},[1319,31799,31800],{"encoding":1321},"T_2",[1148,31802,31803],{},[4382,31804],{"alt":31805,"className":31806,"src":31807},"mask-th-f-kriticky-obor",[1245,4386],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1514,31809,31811,31818,31968,32049,32178,32216,32289,32428],{"className":31810,"dataCallout":3475},[1517,3474],[1148,31812,31814,31817],{"className":31813},[1523],[1296,31815],{"className":31816,"ariaHidden":1530},[1527,3482,1529],"Příklad: Porovnání dvou dodavatelů součástek",[1148,31819,31820,31821,1323,31843,31869,31870,31894,31895,1323,31917,31869,31943,31967],{},"Pevnost plastových dílů: dodavatel A (",[1296,31822,31824],{"className":31823},[1299],[1301,31825,31826],{"xmlns":1303},[1305,31827,31828,31840],{},[1308,31829,31830,31836,31838],{},[1311,31831,31832,31834],{},[1314,31833,1683],{},[1562,31835,1792],{},[1685,31837,1980],{},[1562,31839,9028],{},[1319,31841,31842],{"encoding":1321},"n_1 = 10",[1296,31844,31846],{"className":31845},[1299],[1301,31847,31848],{"xmlns":1303},[1305,31849,31850,31866],{},[1308,31851,31852,31862,31864],{},[1311,31853,31854,31860],{},[2722,31855,31856,31858],{"accent":1530},[1314,31857,6716],{},[1685,31859,11454],{},[1562,31861,1792],{},[1685,31863,1980],{},[1562,31865,3626],{},[1319,31867,31868],{"encoding":1321},"\\bar{x}_1 = 82"," MPa, ",[1296,31871,31873],{"className":31872},[1299],[1301,31874,31875],{"xmlns":1303},[1305,31876,31877,31891],{},[1308,31878,31879,31887,31889],{},[3351,31880,31881,31883,31885],{},[1314,31882,1852],{},[1562,31884,1792],{},[1562,31886,1586],{},[1685,31888,1980],{},[1562,31890,4057],{},[1319,31892,31893],{"encoding":1321},"s_1^2 = 25","), dodavatel B (",[1296,31896,31898],{"className":31897},[1299],[1301,31899,31900],{"xmlns":1303},[1305,31901,31902,31914],{},[1308,31903,31904,31910,31912],{},[1311,31905,31906,31908],{},[1314,31907,1683],{},[1562,31909,1586],{},[1685,31911,1980],{},[1562,31913,2274],{},[1319,31915,31916],{"encoding":1321},"n_2 = 12",[1296,31918,31920],{"className":31919},[1299],[1301,31921,31922],{"xmlns":1303},[1305,31923,31924,31940],{},[1308,31925,31926,31936,31938],{},[1311,31927,31928,31934],{},[2722,31929,31930,31932],{"accent":1530},[1314,31931,6716],{},[1685,31933,11454],{},[1562,31935,1586],{},[1685,31937,1980],{},[1562,31939,14727],{},[1319,31941,31942],{"encoding":1321},"\\bar{x}_2 = 75",[1296,31944,31946],{"className":31945},[1299],[1301,31947,31948],{"xmlns":1303},[1305,31949,31950,31964],{},[1308,31951,31952,31960,31962],{},[3351,31953,31954,31956,31958],{},[1314,31955,1852],{},[1562,31957,1586],{},[1562,31959,1586],{},[1685,31961,1980],{},[1562,31963,22018],{},[1319,31965,31966],{"encoding":1321},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1148,31969,31970,1651,31973,1323,32011,1395],{},[1108,31971,31972],{},"Krok 1 — F-test rozptylů.",[1296,31974,31976],{"className":31975},[1299],[1301,31977,31978],{"xmlns":1303},[1305,31979,31980,32008],{},[1308,31981,31982,31988,31990,31998,32000],{},[1311,31983,31984,31986],{},[1314,31985,1560],{},[1562,31987,1564],{},[1685,31989,1956],{},[3351,31991,31992,31994,31996],{},[1314,31993,6895],{},[1562,31995,1792],{},[1562,31997,1586],{},[1685,31999,1980],{},[3351,32001,32002,32004,32006],{},[1314,32003,6895],{},[1562,32005,1586],{},[1562,32007,1586],{},[1319,32009,32010],{"encoding":1321},"H_0: \\sigma_1^2 = \\sigma_2^2",[1296,32012,32014],{"className":32013},[1299],[1301,32015,32016],{"xmlns":1303},[1305,32017,32018,32046],{},[1308,32019,32020,32026,32028,32036,32038],{},[1311,32021,32022,32024],{},[1314,32023,1560],{},[1562,32025,1792],{},[1685,32027,1956],{},[3351,32029,32030,32032,32034],{},[1314,32031,6895],{},[1562,32033,1792],{},[1562,32035,1586],{},[1685,32037,10951],{"mathvariant":2119},[3351,32039,32040,32042,32044],{},[1314,32041,6895],{},[1562,32043,1586],{},[1562,32045,1586],{},[1319,32047,32048],{"encoding":1321},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1148,32050,32051],{},[1296,32052,32054],{"className":32053},[1299],[1301,32055,32056],{"xmlns":1303},[1305,32057,32058,32175],{},[1308,32059,32060,32062,32064,32070,32072,32075,32077,32079,32081,32083,32085,32087,32089,32102,32104,32106,32108,32110,32112,32115,32118,32120,32122,32124,32137,32139,32141,32143,32145,32147,32149,32151,32153,32155,32157,32160,32162,32164,32166,32168,32170,32173],{},[1314,32061,1225],{},[1685,32063,1980],{},[2738,32065,32066,32068],{},[1562,32067,4057],{},[1562,32069,22018],{},[1685,32071,1980],{},[1562,32073,32074],{},"1,5625",[1685,32076,1795],{"separator":1530},[2010,32078],{"width":2012},[1314,32080,1602],{},[1685,32082,1980],{},[1685,32084,3332],{"stretchy":1872},[1314,32086,1225],{},[1685,32088,6731],{},[1311,32090,32091,32093],{},[1314,32092,1225],{},[1308,32094,32095,32097,32099],{},[1562,32096,1564],{},[1685,32098,1795],{"separator":1530},[1562,32100,32101],{},"025",[1685,32103,1873],{"stretchy":1872},[1562,32105,3593],{},[1685,32107,1795],{"separator":1530},[1562,32109,2253],{},[1685,32111,1884],{"stretchy":1872},[2907,32113,32114],{},"  ",[2907,32116,32117],{},"nebo",[2907,32119,32114],{},[1314,32121,1225],{},[1685,32123,3349],{},[1311,32125,32126,32128],{},[1314,32127,1225],{},[1308,32129,32130,32132,32134],{},[1562,32131,1564],{},[1685,32133,1795],{"separator":1530},[1562,32135,32136],{},"975",[1685,32138,1873],{"stretchy":1872},[1562,32140,3593],{},[1685,32142,1795],{"separator":1530},[1562,32144,2253],{},[1685,32146,1884],{"stretchy":1872},[1685,32148,3392],{"stretchy":1872},[1685,32150,1980],{},[1685,32152,3332],{"stretchy":1872},[1314,32154,1225],{},[1685,32156,6731],{},[1562,32158,32159],{},"0,256",[2907,32161,32114],{},[2907,32163,32117],{},[2907,32165,32114],{},[1314,32167,1225],{},[1685,32169,3349],{},[1562,32171,32172],{},"3,588",[1685,32174,3392],{"stretchy":1872},[1319,32176,32177],{"encoding":1321},"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\\}",[1148,32179,32180,32198,32199,1395],{},[1296,32181,32183],{"className":32182},[1299],[1301,32184,32185],{"xmlns":1303},[1305,32186,32187,32195],{},[1308,32188,32189,32191,32193],{},[1314,32190,1225],{},[1685,32192,27264],{"mathvariant":2119},[1314,32194,1602],{},[1319,32196,32197],{"encoding":1321},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1296,32200,32202],{"className":32201},[1299],[1301,32203,32204],{"xmlns":1303},[1305,32205,32206,32214],{},[1308,32207,32208],{},[1311,32209,32210,32212],{},[1314,32211,7098],{},[1562,32213,1792],{},[1319,32215,31782],{"encoding":1321},[1148,32217,32218,1651,32221,1323,32255,1395],{},[1108,32219,32220],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1296,32222,32224],{"className":32223},[1299],[1301,32225,32226],{"xmlns":1303},[1305,32227,32228,32252],{},[1308,32229,32230,32236,32238,32244,32246],{},[1311,32231,32232,32234],{},[1314,32233,1560],{},[1562,32235,1564],{},[1685,32237,1956],{},[1311,32239,32240,32242],{},[1314,32241,6887],{},[1562,32243,1792],{},[1685,32245,1980],{},[1311,32247,32248,32250],{},[1314,32249,6887],{},[1562,32251,1586],{},[1319,32253,32254],{"encoding":1321},"H_0: \\mu_1 = \\mu_2",[1296,32256,32258],{"className":32257},[1299],[1301,32259,32260],{"xmlns":1303},[1305,32261,32262,32286],{},[1308,32263,32264,32270,32272,32278,32280],{},[1311,32265,32266,32268],{},[1314,32267,1560],{},[1562,32269,1792],{},[1685,32271,1956],{},[1311,32273,32274,32276],{},[1314,32275,6887],{},[1562,32277,1792],{},[1685,32279,10951],{"mathvariant":2119},[1311,32281,32282,32284],{},[1314,32283,6887],{},[1562,32285,1586],{},[1319,32287,32288],{"encoding":1321},"H_1: \\mu_1 \\neq \\mu_2",[1148,32290,32291],{},[1296,32292,32294],{"className":32293},[1299],[1301,32295,32296],{"xmlns":1303},[1305,32297,32298,32425],{},[1308,32299,32300,32308,32310,32330,32332,32335,32337,32339,32341,32343,32357,32365,32367,32370,32372,32374,32376,32378,32380,32382,32384,32386,32388,32400,32402,32404,32406,32408,32410,32412,32414,32416,32418,32420,32423],{},[3351,32301,32302,32304,32306],{},[1314,32303,1852],{},[1314,32305,1148],{},[1562,32307,1586],{},[1685,32309,1980],{},[2738,32311,32312,32328],{},[1308,32313,32314,32316,32318,32320,32322,32324,32326],{},[1562,32315,3593],{},[1685,32317,8106],{},[1562,32319,4057],{},[1685,32321,5474],{},[1562,32323,2253],{},[1685,32325,8106],{},[1562,32327,22018],{},[1562,32329,4044],{},[1685,32331,1980],{},[1562,32333,32334],{},"20,05",[1685,32336,1795],{"separator":1530},[2010,32338],{"width":2012},[1314,32340,7140],{},[1685,32342,1980],{},[2738,32344,32345,32353],{},[1308,32346,32347,32349,32351],{},[1562,32348,3626],{},[1685,32350,3062],{},[1562,32352,14727],{},[4452,32354,32355],{},[1562,32356,32334],{},[4452,32358,32359],{},[2738,32360,32361,32363],{},[1562,32362,21878],{},[1562,32364,2388],{},[1685,32366,9435],{},[1562,32368,32369],{},"3,651",[1685,32371,1795],{"separator":1530},[2010,32373],{"width":2012},[1314,32375,1602],{},[1685,32377,1980],{},[1685,32379,3332],{"stretchy":1872},[1685,32381,23016],{"stretchy":1872},[1314,32383,7140],{},[1685,32385,23016],{"stretchy":1872},[1685,32387,3349],{},[1311,32389,32390,32392],{},[1314,32391,7140],{},[1308,32393,32394,32396,32398],{},[1562,32395,1564],{},[1685,32397,1795],{"separator":1530},[1562,32399,32136],{},[1685,32401,1873],{"stretchy":1872},[1562,32403,4044],{},[1685,32405,1884],{"stretchy":1872},[1685,32407,3392],{"stretchy":1872},[1685,32409,1980],{},[1685,32411,3332],{"stretchy":1872},[1685,32413,23016],{"stretchy":1872},[1314,32415,7140],{},[1685,32417,23016],{"stretchy":1872},[1685,32419,3349],{},[1562,32421,32422],{},"2,086",[1685,32424,3392],{"stretchy":1872},[1319,32426,32427],{"encoding":1321},"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\\}",[1148,32429,32430,6003,32447,32464],{},[1296,32431,32433],{"className":32432},[1299],[1301,32434,32435],{"xmlns":1303},[1305,32436,32437,32445],{},[1308,32438,32439,32441,32443],{},[1314,32440,7140],{},[1685,32442,7015],{},[1314,32444,1602],{},[1319,32446,28407],{"encoding":1321},[1296,32448,32450],{"className":32449},[1299],[1301,32451,32452],{"xmlns":1303},[1305,32453,32454,32462],{},[1308,32455,32456],{},[1311,32457,32458,32460],{},[1314,32459,1560],{},[1562,32461,1564],{},[1319,32463,1567],{"encoding":1321},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3692,32466,32468],{"className":3694,"code":32467,"language":71,"meta":1452,"style":1452},"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",[3468,32469,32470,32488,32508,32523,32558,32589,32594,32599],{"__ignoreMap":1452},[1296,32471,32472,32475,32477,32479,32481,32484,32486],{"class":3700,"line":10},[1296,32473,32474],{"class":3703},"s1",[1296,32476,3708],{"class":3707},[1296,32478,14397],{"class":3723},[1296,32480,25176],{"class":3715},[1296,32482,32483],{"class":3703},"n1",[1296,32485,3708],{"class":3707},[1296,32487,29848],{"class":3723},[1296,32489,32490,32493,32495,32498,32500,32503,32505],{"class":3700,"line":27},[1296,32491,32492],{"class":3703},"s2",[1296,32494,3708],{"class":3707},[1296,32496,32497],{"class":3723}," 16",[1296,32499,25176],{"class":3715},[1296,32501,32502],{"class":3703},"n2",[1296,32504,3708],{"class":3707},[1296,32506,32507],{"class":3723}," 12\n",[1296,32509,32510,32513,32515,32518,32520],{"class":3700,"line":148},[1296,32511,32512],{"class":3703},"Fstat",[1296,32514,3708],{"class":3707},[1296,32516,32517],{"class":3703}," s1",[1296,32519,10070],{"class":3707},[1296,32521,32522],{"class":3703}," s2\n",[1296,32524,32525,32528,32530,32533,32535,32538,32540,32543,32545,32547,32549,32552,32554,32556],{"class":3700,"line":111},[1296,32526,32527],{"class":3703},"F_dolni",[1296,32529,3708],{"class":3707},[1296,32531,32532],{"class":3711}," qf",[1296,32534,1873],{"class":3715},[1296,32536,32537],{"class":3723},"0.025",[1296,32539,1795],{"class":3707},[1296,32541,32542],{"class":3703}," n1",[1296,32544,25513],{"class":3707},[1296,32546,4638],{"class":3723},[1296,32548,1795],{"class":3707},[1296,32550,32551],{"class":3703}," n2",[1296,32553,25513],{"class":3707},[1296,32555,4638],{"class":3723},[1296,32557,3900],{"class":3715},[1296,32559,32560,32563,32565,32567,32569,32571,32573,32575,32577,32579,32581,32583,32585,32587],{"class":3700,"line":96},[1296,32561,32562],{"class":3703},"F_horni",[1296,32564,3708],{"class":3707},[1296,32566,32532],{"class":3711},[1296,32568,1873],{"class":3715},[1296,32570,9084],{"class":3723},[1296,32572,1795],{"class":3707},[1296,32574,32542],{"class":3703},[1296,32576,25513],{"class":3707},[1296,32578,4638],{"class":3723},[1296,32580,1795],{"class":3707},[1296,32582,32551],{"class":3703},[1296,32584,25513],{"class":3707},[1296,32586,4638],{"class":3723},[1296,32588,3900],{"class":3715},[1296,32590,32591],{"class":3700,"line":89},[1296,32592,32593],{"class":3703},"Fstat\n",[1296,32595,32596],{"class":3700,"line":82},[1296,32597,32598],{"class":3703},"F_dolni\n",[1296,32600,32601],{"class":3700,"line":75},[1296,32602,32603],{"class":3703},"F_horni\n",[3692,32605,32608],{"className":32606,"code":32607,"language":3922,"meta":1452},[3920],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3468,32609,32607],{"__ignoreMap":1452},[3692,32611,32613],{"className":3694,"code":32612,"language":71,"meta":1452,"style":1452},"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",[3468,32614,32615,32672,32723,32753,32758,32762],{"__ignoreMap":1452},[1296,32616,32617,32620,32622,32625,32627,32629,32631,32633,32635,32637,32639,32641,32643,32645,32647,32649,32651,32654,32656,32658,32660,32662,32664,32666,32668,32670],{"class":3700,"line":10},[1296,32618,32619],{"class":3703},"sp2",[1296,32621,3708],{"class":3707},[1296,32623,32624],{"class":3715}," ((",[1296,32626,32483],{"class":3703},[1296,32628,25513],{"class":3707},[1296,32630,4638],{"class":3723},[1296,32632,4599],{"class":3715},[1296,32634,4616],{"class":3707},[1296,32636,32517],{"class":3703},[1296,32638,18511],{"class":3707},[1296,32640,4604],{"class":3715},[1296,32642,32502],{"class":3703},[1296,32644,25513],{"class":3707},[1296,32646,4638],{"class":3723},[1296,32648,4599],{"class":3715},[1296,32650,4616],{"class":3707},[1296,32652,32653],{"class":3703}," s2",[1296,32655,4599],{"class":3715},[1296,32657,1502],{"class":3707},[1296,32659,4604],{"class":3715},[1296,32661,32483],{"class":3703},[1296,32663,18511],{"class":3707},[1296,32665,32551],{"class":3703},[1296,32667,25513],{"class":3707},[1296,32669,4179],{"class":3723},[1296,32671,3900],{"class":3715},[1296,32673,32674,32676,32678,32680,32682,32684,32687,32689,32691,32693,32695,32697,32699,32701,32703,32705,32707,32709,32711,32713,32715,32717,32719,32721],{"class":3700,"line":27},[1296,32675,7140],{"class":3703},[1296,32677,3708],{"class":3707},[1296,32679,4604],{"class":3715},[1296,32681,3626],{"class":3723},[1296,32683,25513],{"class":3707},[1296,32685,32686],{"class":3723}," 75",[1296,32688,4599],{"class":3715},[1296,32690,1502],{"class":3707},[1296,32692,4576],{"class":3711},[1296,32694,1873],{"class":3715},[1296,32696,32619],{"class":3703},[1296,32698,4599],{"class":3715},[1296,32700,4616],{"class":3707},[1296,32702,4576],{"class":3711},[1296,32704,1873],{"class":3715},[1296,32706,32483],{"class":3703},[1296,32708,18636],{"class":3707},[1296,32710,32551],{"class":3703},[1296,32712,10070],{"class":3707},[1296,32714,4604],{"class":3715},[1296,32716,32483],{"class":3703},[1296,32718,18511],{"class":3707},[1296,32720,32551],{"class":3703},[1296,32722,9488],{"class":3715},[1296,32724,32725,32727,32729,32731,32733,32735,32737,32739,32741,32743,32745,32747,32749,32751],{"class":3700,"line":148},[1296,32726,28514],{"class":3703},[1296,32728,3708],{"class":3707},[1296,32730,28519],{"class":3711},[1296,32732,1873],{"class":3715},[1296,32734,9084],{"class":3723},[1296,32736,1795],{"class":3707},[1296,32738,10804],{"class":3703},[1296,32740,3796],{"class":3707},[1296,32742,32542],{"class":3703},[1296,32744,18511],{"class":3707},[1296,32746,32551],{"class":3703},[1296,32748,25513],{"class":3707},[1296,32750,4179],{"class":3723},[1296,32752,3900],{"class":3715},[1296,32754,32755],{"class":3700,"line":111},[1296,32756,32757],{"class":3703},"sp2\n",[1296,32759,32760],{"class":3700,"line":96},[1296,32761,28544],{"class":3703},[1296,32763,32764],{"class":3700,"line":89},[1296,32765,28549],{"class":3703},[3692,32767,32770],{"className":32768,"code":32769,"language":3922,"meta":1452},[3920],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3468,32771,32769],{"__ignoreMap":1452},[1148,32773,32774],{},[4382,32775],{"alt":32776,"className":32777,"src":32778},"mask-th-t-dvoustranny",[1245,4386],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1148,32780,32781,32782,1370,32785,32787,32788,32791,32792,1370,32809,3987,32826,32828,32829,32831],{},"V R provede obě kroky ",[3468,32783,32784],{},"var.test()",[3468,32786,28004],{},". Parametr ",[3468,32789,32790],{},"var.equal"," nastavuje volbu mezi ",[1296,32793,32795],{"className":32794},[1299],[1301,32796,32797],{"xmlns":1303},[1305,32798,32799,32807],{},[1308,32800,32801],{},[1311,32802,32803,32805],{},[1314,32804,7098],{},[1562,32806,1792],{},[1319,32808,31782],{"encoding":1321},[1296,32810,32812],{"className":32811},[1299],[1301,32813,32814],{"xmlns":1303},[1305,32815,32816,32824],{},[1308,32817,32818],{},[1311,32819,32820,32822],{},[1314,32821,7098],{},[1562,32823,1586],{},[1319,32825,31800],{"encoding":1321},[3468,32827,9519],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3468,32830,9522],{}," předpoklad rozdílných rozptylů.",[1148,32833,32834,32837],{},[1108,32835,32836],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3692,32839,32841],{"className":3694,"code":32840,"language":71,"meta":1452,"style":1452},"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",[3468,32842,32843,32909,32972,32988],{"__ignoreMap":1452},[1296,32844,32845,32847,32849,32851,32853,32856,32858,32861,32863,32866,32868,32871,32873,32875,32877,32880,32882,32885,32887,32889,32891,32894,32896,32898,32900,32903,32905,32907],{"class":3700,"line":10},[1296,32846,1185],{"class":3703},[1296,32848,3708],{"class":3707},[1296,32850,3834],{"class":3711},[1296,32852,1873],{"class":3715},[1296,32854,32855],{"class":3723},"313",[1296,32857,1795],{"class":3707},[1296,32859,32860],{"class":3723}," 299",[1296,32862,1795],{"class":3707},[1296,32864,32865],{"class":3723}," 315",[1296,32867,1795],{"class":3707},[1296,32869,32870],{"class":3723}," 312",[1296,32872,1795],{"class":3707},[1296,32874,15365],{"class":3723},[1296,32876,1795],{"class":3707},[1296,32878,32879],{"class":3723}," 308",[1296,32881,1795],{"class":3707},[1296,32883,32884],{"class":3723}," 314",[1296,32886,1795],{"class":3707},[1296,32888,14157],{"class":3723},[1296,32890,1795],{"class":3707},[1296,32892,32893],{"class":3723}," 305",[1296,32895,1795],{"class":3707},[1296,32897,15365],{"class":3723},[1296,32899,1795],{"class":3707},[1296,32901,32902],{"class":3723}," 309",[1296,32904,1795],{"class":3707},[1296,32906,32884],{"class":3723},[1296,32908,3900],{"class":3715},[1296,32910,32911,32913,32915,32917,32919,32922,32924,32927,32929,32931,32933,32935,32937,32940,32942,32945,32947,32949,32951,32953,32955,32957,32959,32962,32964,32966,32968,32970],{"class":3700,"line":27},[1296,32912,1193],{"class":3703},[1296,32914,3708],{"class":3707},[1296,32916,3834],{"class":3711},[1296,32918,1873],{"class":3715},[1296,32920,32921],{"class":3723},"307",[1296,32923,1795],{"class":3707},[1296,32925,32926],{"class":3723}," 322",[1296,32928,1795],{"class":3707},[1296,32930,14157],{"class":3723},[1296,32932,1795],{"class":3707},[1296,32934,14157],{"class":3723},[1296,32936,1795],{"class":3707},[1296,32938,32939],{"class":3723}," 311",[1296,32941,1795],{"class":3707},[1296,32943,32944],{"class":3723}," 316",[1296,32946,1795],{"class":3707},[1296,32948,32865],{"class":3723},[1296,32950,1795],{"class":3707},[1296,32952,32884],{"class":3723},[1296,32954,1795],{"class":3707},[1296,32956,32879],{"class":3723},[1296,32958,1795],{"class":3707},[1296,32960,32961],{"class":3723}," 319",[1296,32963,1795],{"class":3707},[1296,32965,14157],{"class":3723},[1296,32967,1795],{"class":3707},[1296,32969,32870],{"class":3723},[1296,32971,3900],{"class":3715},[1296,32973,32974,32977,32979,32981,32983,32986],{"class":3700,"line":148},[1296,32975,32976],{"class":3711},"var.test",[1296,32978,1873],{"class":3715},[1296,32980,1185],{"class":3703},[1296,32982,1795],{"class":3707},[1296,32984,32985],{"class":3703}," B",[1296,32987,3900],{"class":3715},[1296,32989,32990,32992,32994,32996,32998,33000,33002,33005,33007,33009],{"class":3700,"line":111},[1296,32991,28069],{"class":3711},[1296,32993,1873],{"class":3715},[1296,32995,1185],{"class":3703},[1296,32997,1795],{"class":3707},[1296,32999,32985],{"class":3703},[1296,33001,1795],{"class":3707},[1296,33003,33004],{"class":3703}," var.equal",[1296,33006,3796],{"class":3707},[1296,33008,3809],{"class":3723},[1296,33010,3900],{"class":3715},[3692,33012,33015],{"className":33013,"code":33014,"language":3922,"meta":1452},[3920],"    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",[3468,33016,33014],{"__ignoreMap":1452},[1148,33018,33019,33020,12049,33039,33042,33043,33062,33063,33080],{},"F-test shodu rozptylů nezamítá (",[1296,33021,33023],{"className":33022},[1299],[1301,33024,33025],{"xmlns":1303},[1305,33026,33027,33036],{},[1308,33028,33029,33031,33033],{},[1314,33030,1148],{},[1685,33032,1980],{},[1562,33034,33035],{},"0,7776",[1319,33037,33038],{"encoding":1321},"p = 0{,}7776",[3468,33040,33041],{},"var.equal = TRUE",". Výsledný t-test dává ",[1296,33044,33046],{"className":33045},[1299],[1301,33047,33048],{"xmlns":1303},[1305,33049,33050,33059],{},[1308,33051,33052,33054,33056],{},[1314,33053,1148],{},[1685,33055,1980],{},[1562,33057,33058],{},"0,06932",[1319,33060,33061],{"encoding":1321},"p = 0{,}06932"," — na hladině 5 % se ",[1296,33064,33066],{"className":33065},[1299],[1301,33067,33068],{"xmlns":1303},[1305,33069,33070,33078],{},[1308,33071,33072],{},[1311,33073,33074,33076],{},[1314,33075,1560],{},[1562,33077,1564],{},[1319,33079,1567],{"encoding":1321}," nezamítá, ale hodnota je těsně nad hranicí.",[1148,33082,33083],{},[1108,33084,33085],{},"Výšky chlapců a dívek v páté třídě:",[3692,33087,33089],{"className":3694,"code":33088,"language":71,"meta":1452,"style":1452},"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",[3468,33090,33091,33171,33234,33249],{"__ignoreMap":1452},[1296,33092,33093,33096,33098,33100,33102,33105,33107,33109,33111,33114,33116,33119,33121,33124,33126,33129,33131,33133,33135,33137,33139,33141,33143,33145,33147,33150,33152,33155,33157,33160,33162,33164,33166,33169],{"class":3700,"line":10},[1296,33094,33095],{"class":3703},"boys",[1296,33097,3708],{"class":3707},[1296,33099,3834],{"class":3711},[1296,33101,1873],{"class":3715},[1296,33103,33104],{"class":3723},"130",[1296,33106,1795],{"class":3707},[1296,33108,15314],{"class":3723},[1296,33110,1795],{"class":3707},[1296,33112,33113],{"class":3723}," 136",[1296,33115,1795],{"class":3707},[1296,33117,33118],{"class":3723}," 141",[1296,33120,1795],{"class":3707},[1296,33122,33123],{"class":3723}," 139",[1296,33125,1795],{"class":3707},[1296,33127,33128],{"class":3723}," 133",[1296,33130,1795],{"class":3707},[1296,33132,18468],{"class":3723},[1296,33134,1795],{"class":3707},[1296,33136,14172],{"class":3723},[1296,33138,1795],{"class":3707},[1296,33140,33123],{"class":3723},[1296,33142,1795],{"class":3707},[1296,33144,33113],{"class":3723},[1296,33146,1795],{"class":3707},[1296,33148,33149],{"class":3723}," 138",[1296,33151,1795],{"class":3707},[1296,33153,33154],{"class":3723}," 142",[1296,33156,1795],{"class":3707},[1296,33158,33159],{"class":3723}," 127",[1296,33161,1795],{"class":3707},[1296,33163,33123],{"class":3723},[1296,33165,1795],{"class":3707},[1296,33167,33168],{"class":3723}," 147",[1296,33170,3900],{"class":3715},[1296,33172,33173,33176,33178,33180,33182,33184,33186,33188,33190,33193,33195,33198,33200,33203,33205,33207,33209,33211,33213,33215,33217,33219,33221,33224,33226,33228,33230,33232],{"class":3700,"line":27},[1296,33174,33175],{"class":3703},"girls",[1296,33177,3708],{"class":3707},[1296,33179,3834],{"class":3711},[1296,33181,1873],{"class":3715},[1296,33183,21829],{"class":3723},[1296,33185,1795],{"class":3707},[1296,33187,33118],{"class":3723},[1296,33189,1795],{"class":3707},[1296,33191,33192],{"class":3723}," 143",[1296,33194,1795],{"class":3707},[1296,33196,33197],{"class":3723}," 132",[1296,33199,1795],{"class":3707},[1296,33201,33202],{"class":3723}," 146",[1296,33204,1795],{"class":3707},[1296,33206,33202],{"class":3723},[1296,33208,1795],{"class":3707},[1296,33210,14172],{"class":3723},[1296,33212,1795],{"class":3707},[1296,33214,33118],{"class":3723},[1296,33216,1795],{"class":3707},[1296,33218,33118],{"class":3723},[1296,33220,1795],{"class":3707},[1296,33222,33223],{"class":3723}," 131",[1296,33225,1795],{"class":3707},[1296,33227,33154],{"class":3723},[1296,33229,1795],{"class":3707},[1296,33231,33118],{"class":3723},[1296,33233,3900],{"class":3715},[1296,33235,33236,33238,33240,33242,33244,33247],{"class":3700,"line":148},[1296,33237,32976],{"class":3711},[1296,33239,1873],{"class":3715},[1296,33241,33095],{"class":3703},[1296,33243,1795],{"class":3707},[1296,33245,33246],{"class":3703}," girls",[1296,33248,3900],{"class":3715},[1296,33250,33251,33253,33255,33257,33259,33261,33263,33265,33267,33269],{"class":3700,"line":111},[1296,33252,28069],{"class":3711},[1296,33254,1873],{"class":3715},[1296,33256,33095],{"class":3703},[1296,33258,1795],{"class":3707},[1296,33260,33246],{"class":3703},[1296,33262,1795],{"class":3707},[1296,33264,33004],{"class":3703},[1296,33266,3796],{"class":3707},[1296,33268,3809],{"class":3723},[1296,33270,3900],{"class":3715},[3692,33272,33275],{"className":33273,"code":33274,"language":3922,"meta":1452},[3920],"    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",[3468,33276,33274],{"__ignoreMap":1452},[1148,33278,33019,33279,33298,33299,33301,33302,33321],{},[1296,33280,33282],{"className":33281},[1299],[1301,33283,33284],{"xmlns":1303},[1305,33285,33286,33295],{},[1308,33287,33288,33290,33292],{},[1314,33289,1148],{},[1685,33291,1980],{},[1562,33293,33294],{},"0,6977",[1319,33296,33297],{"encoding":1321},"p = 0{,}6977","), t-test s ",[3468,33300,33041],{}," dává ",[1296,33303,33305],{"className":33304},[1299],[1301,33306,33307],{"xmlns":1303},[1305,33308,33309,33318],{},[1308,33310,33311,33313,33315],{},[1314,33312,1148],{},[1685,33314,1980],{},[1562,33316,33317],{},"0,4883",[1319,33319,33320],{"encoding":1321},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1143,33323,33325],{"id":33324},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1148,33327,33328],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[16742,33330,33332],{"id":33331},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1148,33334,33335,33336,33359,33360,33379],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1296,33337,33339],{"className":33338},[1299],[1301,33340,33341],{"xmlns":1303},[1305,33342,33343,33357],{},[1308,33344,33345,33351,33353,33355],{},[1311,33346,33347,33349],{},[1314,33348,1225],{},[1314,33350,1683],{},[1685,33352,1873],{"stretchy":1872},[1314,33354,6716],{},[1685,33356,1884],{"stretchy":1872},[1319,33358,11178],{"encoding":1321}," s teoretickou distribuční funkcí ",[1296,33361,33363],{"className":33362},[1299],[1301,33364,33365],{"xmlns":1303},[1305,33366,33367,33377],{},[1308,33368,33369,33371,33373,33375],{},[1314,33370,1225],{},[1685,33372,1873],{"stretchy":1872},[1314,33374,6716],{},[1685,33376,1884],{"stretchy":1872},[1319,33378,7331],{"encoding":1321}," testovaného rozdělení.",[1102,33381,33382,33445,33465,33521],{},[1105,33383,33384,33401,33402,1370,33425,33444],{},[1296,33385,33387],{"className":33386},[1299],[1301,33388,33389],{"xmlns":1303},[1305,33390,33391,33399],{},[1308,33392,33393],{},[1311,33394,33395,33397],{},[1314,33396,1560],{},[1562,33398,1564],{},[1319,33400,1567],{"encoding":1321},": odchylky mezi ",[1296,33403,33405],{"className":33404},[1299],[1301,33406,33407],{"xmlns":1303},[1305,33408,33409,33423],{},[1308,33410,33411,33417,33419,33421],{},[1311,33412,33413,33415],{},[1314,33414,1225],{},[1314,33416,1683],{},[1685,33418,1873],{"stretchy":1872},[1314,33420,6716],{},[1685,33422,1884],{"stretchy":1872},[1319,33424,11178],{"encoding":1321},[1296,33426,33428],{"className":33427},[1299],[1301,33429,33430],{"xmlns":1303},[1305,33431,33432,33442],{},[1308,33433,33434,33436,33438,33440],{},[1314,33435,1225],{},[1685,33437,1873],{"stretchy":1872},[1314,33439,6716],{},[1685,33441,1884],{"stretchy":1872},[1319,33443,7331],{"encoding":1321}," jsou náhodné (data mají dané rozdělení).",[1105,33446,33447,33464],{},[1296,33448,33450],{"className":33449},[1299],[1301,33451,33452],{"xmlns":1303},[1305,33453,33454,33462],{},[1308,33455,33456],{},[1311,33457,33458,33460],{},[1314,33459,1560],{},[1562,33461,1792],{},[1319,33463,2994],{"encoding":1321},": data nemají dané rozdělení.",[1105,33466,33467,33468,1395],{},"Testové kritérium: ",[1296,33469,33471],{"className":33470},[1299],[1301,33472,33473],{"xmlns":1303},[1305,33474,33475,33518],{},[1308,33476,33477,33479,33481,33492,33494,33500,33502,33504,33506,33508,33510,33512,33514,33516],{},[1314,33478,1209],{},[1685,33480,1980],{},[1311,33482,33483,33490],{},[1308,33484,33485,33488],{},[1314,33486,33487],{},"sup",[1685,33489,4489],{},[1314,33491,6716],{},[1685,33493,23016],{"stretchy":1872},[1311,33495,33496,33498],{},[1314,33497,1225],{},[1314,33499,1683],{},[1685,33501,1873],{"stretchy":1872},[1314,33503,6716],{},[1685,33505,1884],{"stretchy":1872},[1685,33507,3062],{},[1314,33509,1225],{},[1685,33511,1873],{"stretchy":1872},[1314,33513,6716],{},[1685,33515,1884],{"stretchy":1872},[1685,33517,23016],{"stretchy":1872},[1319,33519,33520],{"encoding":1321},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1105,33522,3316,33523,33567,33568,33586,33587,1395],{},[1296,33524,33526],{"className":33525},[1299],[1301,33527,33528],{"xmlns":1303},[1305,33529,33530,33564],{},[1308,33531,33532,33538,33540,33542,33544,33546,33548,33550,33556,33558,33560,33562],{},[1311,33533,33534,33536],{},[1314,33535,1602],{},[1314,33537,3363],{},[1685,33539,1980],{},[1685,33541,3332],{"stretchy":1872},[1314,33543,7792],{},[1685,33545,1956],{},[1314,33547,7792],{},[1685,33549,1687],{},[1311,33551,33552,33554],{},[1314,33553,1209],{},[1314,33555,3363],{},[1685,33557,1873],{"stretchy":1872},[1314,33559,1683],{},[1685,33561,1884],{"stretchy":1872},[1685,33563,3392],{"stretchy":1872},[1319,33565,33566],{"encoding":1321},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1296,33569,33571],{"className":33570},[1299],[1301,33572,33573],{"xmlns":1303},[1305,33574,33575,33583],{},[1308,33576,33577,33579,33581],{},[1314,33578,1683],{},[1685,33580,1687],{},[1562,33582,22028],{},[1319,33584,33585],{"encoding":1321},"n>30"," se kritická hodnota aproximuje zlomkem ",[1296,33588,33590],{"className":33589},[1299],[1301,33591,33592],{"xmlns":1303},[1305,33593,33594,33605],{},[1308,33595,33596,33599,33601],{},[1562,33597,33598],{},"1,36",[1314,33600,1502],{"mathvariant":2119},[4452,33602,33603],{},[1314,33604,1683],{},[1319,33606,33607],{"encoding":1321},"1{,}36\u002F\\sqrt{n}",[1148,33609,28001,33610,33613,33614,33616,33617,1323,33620,33623],{},[3468,33611,33612],{},"ks.test()",", kde se za ",[3468,33615,7331],{}," dosadí příslušná distribuční funkce (",[3468,33618,33619],{},"\"pnorm\"",[3468,33621,33622],{},"\"pexp\"",", …) s jejími parametry:",[3692,33625,33627],{"className":3694,"code":33626,"language":71,"meta":1452,"style":1452},"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",[3468,33628,33629,33679],{"__ignoreMap":1452},[1296,33630,33631,33633,33635,33637,33639,33641,33643,33645,33647,33649,33651,33653,33655,33657,33659,33661,33663,33665,33667,33669,33671,33673,33675,33677],{"class":3700,"line":10},[1296,33632,28715],{"class":3703},[1296,33634,3708],{"class":3707},[1296,33636,3834],{"class":3711},[1296,33638,1873],{"class":3715},[1296,33640,11981],{"class":3723},[1296,33642,1795],{"class":3707},[1296,33644,11986],{"class":3723},[1296,33646,1795],{"class":3707},[1296,33648,11991],{"class":3723},[1296,33650,1795],{"class":3707},[1296,33652,11996],{"class":3723},[1296,33654,1795],{"class":3707},[1296,33656,11991],{"class":3723},[1296,33658,1795],{"class":3707},[1296,33660,11991],{"class":3723},[1296,33662,1795],{"class":3707},[1296,33664,12009],{"class":3723},[1296,33666,1795],{"class":3707},[1296,33668,12014],{"class":3723},[1296,33670,1795],{"class":3707},[1296,33672,11986],{"class":3723},[1296,33674,1795],{"class":3707},[1296,33676,11986],{"class":3723},[1296,33678,3900],{"class":3715},[1296,33680,33681,33684,33686,33688,33690,33693,33695,33697,33699,33701,33703,33705,33707,33709,33711],{"class":3700,"line":27},[1296,33682,33683],{"class":3711},"ks.test",[1296,33685,1873],{"class":3715},[1296,33687,28715],{"class":3703},[1296,33689,1795],{"class":3707},[1296,33691,33692],{"class":3839}," \"pnorm\"",[1296,33694,1795],{"class":3707},[1296,33696,9226],{"class":3711},[1296,33698,1873],{"class":3715},[1296,33700,28715],{"class":3703},[1296,33702,1884],{"class":3715},[1296,33704,1795],{"class":3707},[1296,33706,9236],{"class":3711},[1296,33708,1873],{"class":3715},[1296,33710,28715],{"class":3703},[1296,33712,9488],{"class":3715},[3692,33714,33717],{"className":33715,"code":33716,"language":3922,"meta":1452},[3920],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3468,33718,33716],{"__ignoreMap":1452},[1148,33720,33721,33744],{},[1296,33722,33724],{"className":33723},[1299],[1301,33725,33726],{"xmlns":1303},[1305,33727,33728,33741],{},[1308,33729,33730,33732,33734,33737,33739],{},[1314,33731,1148],{},[1685,33733,1980],{},[1562,33735,33736],{},"0,8847",[1685,33738,1687],{},[1562,33740,3983],{},[1319,33742,33743],{"encoding":1321},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[16742,33746,33748],{"id":33747},"shapiro-wilkův-test","Shapiro-Wilkův test",[1148,33750,33751],{},"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.",[1102,33753,33754,33774,33794],{},[1105,33755,33756,33773],{},[1296,33757,33759],{"className":33758},[1299],[1301,33760,33761],{"xmlns":1303},[1305,33762,33763,33771],{},[1308,33764,33765],{},[1311,33766,33767,33769],{},[1314,33768,1560],{},[1562,33770,1564],{},[1319,33772,1567],{"encoding":1321},": data mají normální rozdělení.",[1105,33775,33776,33793],{},[1296,33777,33779],{"className":33778},[1299],[1301,33780,33781],{"xmlns":1303},[1305,33782,33783,33791],{},[1308,33784,33785],{},[1311,33786,33787,33789],{},[1314,33788,1560],{},[1562,33790,1792],{},[1319,33792,2994],{"encoding":1321},": data nemají normální rozdělení.",[1105,33795,33796,33797,33823],{},"Testová statistika ",[1296,33798,33800],{"className":33799},[1299],[1301,33801,33802],{"xmlns":1303},[1305,33803,33804,33820],{},[1308,33805,33806,33808,33810,33812,33814,33816,33818],{},[1314,33807,1602],{},[1685,33809,7015],{},[1685,33811,8420],{"stretchy":1872},[1562,33813,1564],{},[1685,33815,1795],{"separator":1530},[1562,33817,1792],{},[1685,33819,7439],{"stretchy":1872},[1319,33821,33822],{"encoding":1321},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1148,33825,33826,33827,33840,33841,1651,33861,33878,33879,1651,33899,33916],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1296,33828,33830],{"className":33829},[1299],[1301,33831,33832],{"xmlns":1303},[1305,33833,33834,33838],{},[1308,33835,33836],{},[1314,33837,1602],{},[1319,33839,1602],{"encoding":1321}," se běžně neudává): ",[1296,33842,33844],{"className":33843},[1299],[1301,33845,33846],{"xmlns":1303},[1305,33847,33848,33858],{},[1308,33849,33850,33852,33854,33856],{},[1314,33851,1148],{},[1685,33853,3349],{},[1314,33855,3363],{},[1685,33857,7545],{},[1319,33859,33860],{"encoding":1321},"p \\ge \\alpha \\Rightarrow",[1296,33862,33864],{"className":33863},[1299],[1301,33865,33866],{"xmlns":1303},[1305,33867,33868,33876],{},[1308,33869,33870],{},[1311,33871,33872,33874],{},[1314,33873,1560],{},[1562,33875,1564],{},[1319,33877,1567],{"encoding":1321}," nezamítáme (normalitu lze předpokládat); ",[1296,33880,33882],{"className":33881},[1299],[1301,33883,33884],{"xmlns":1303},[1305,33885,33886,33896],{},[1308,33887,33888,33890,33892,33894],{},[1314,33889,1148],{},[1685,33891,4331],{},[1314,33893,3363],{},[1685,33895,7545],{},[1319,33897,33898],{"encoding":1321},"p \u003C \\alpha \\Rightarrow",[1296,33900,33902],{"className":33901},[1299],[1301,33903,33904],{"xmlns":1303},[1305,33905,33906,33914],{},[1308,33907,33908],{},[1311,33909,33910,33912],{},[1314,33911,1560],{},[1562,33913,1564],{},[1319,33915,1567],{"encoding":1321}," zamítáme (předpoklad normality je porušen).",[3692,33918,33920],{"className":3694,"code":33919,"language":71,"meta":1452,"style":1452},"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",[3468,33921,33922,33976],{"__ignoreMap":1452},[1296,33923,33924,33926,33928,33930,33932,33934,33936,33938,33940,33942,33944,33946,33948,33950,33952,33954,33956,33958,33960,33962,33964,33966,33968,33970,33972,33974],{"class":3700,"line":10},[1296,33925,28583],{"class":3703},[1296,33927,3708],{"class":3707},[1296,33929,3834],{"class":3711},[1296,33931,1873],{"class":3715},[1296,33933,28592],{"class":3723},[1296,33935,1795],{"class":3707},[1296,33937,28597],{"class":3723},[1296,33939,1795],{"class":3707},[1296,33941,28602],{"class":3723},[1296,33943,1795],{"class":3707},[1296,33945,28607],{"class":3723},[1296,33947,1795],{"class":3707},[1296,33949,28612],{"class":3723},[1296,33951,1795],{"class":3707},[1296,33953,28617],{"class":3723},[1296,33955,1795],{"class":3707},[1296,33957,28607],{"class":3723},[1296,33959,1795],{"class":3707},[1296,33961,28626],{"class":3723},[1296,33963,1795],{"class":3707},[1296,33965,28612],{"class":3723},[1296,33967,1795],{"class":3707},[1296,33969,28635],{"class":3723},[1296,33971,1795],{"class":3707},[1296,33973,28607],{"class":3723},[1296,33975,3900],{"class":3715},[1296,33977,33978,33980,33982,33984],{"class":3700,"line":27},[1296,33979,17572],{"class":3711},[1296,33981,1873],{"class":3715},[1296,33983,28583],{"class":3703},[1296,33985,3900],{"class":3715},[3692,33987,33990],{"className":33988,"code":33989,"language":3922,"meta":1452},[3920],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3468,33991,33989],{"__ignoreMap":1452},[1148,33993,33994,33995,34014],{},"U dat o životnosti baterií se normalita nezamítá (",[1296,33996,33998],{"className":33997},[1299],[1301,33999,34000],{"xmlns":1303},[1305,34001,34002,34011],{},[1308,34003,34004,34006,34008],{},[1314,34005,1148],{},[1685,34007,1980],{},[1562,34009,34010],{},"0,7744",[1319,34012,34013],{"encoding":1321},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1514,34016,34018,34025,34028,34395,34401],{"className":34017,"dataCallout":3475},[1517,3474],[1148,34019,34021,34024],{"className":34020},[1523],[1296,34022],{"className":34023,"ariaHidden":1530},[1527,3482,1529],"Příklad: Doba do poruchy výrobku",[1148,34026,34027],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3692,34029,34031],{"className":3694,"code":34030,"language":71,"meta":1452,"style":1452},"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",[3468,34032,34033,34124,34202,34290,34324,34334,34344,34354,34364],{"__ignoreMap":1452},[1296,34034,34035,34037,34039,34041,34043,34045,34047,34049,34051,34053,34055,34057,34059,34061,34063,34065,34067,34069,34071,34073,34075,34077,34079,34081,34083,34086,34088,34090,34092,34094,34096,34098,34100,34102,34104,34106,34108,34110,34112,34114,34116,34118,34120,34122],{"class":3700,"line":10},[1296,34036,14071],{"class":3703},[1296,34038,3708],{"class":3707},[1296,34040,3834],{"class":3711},[1296,34042,1873],{"class":3715},[1296,34044,14080],{"class":3723},[1296,34046,1795],{"class":3707},[1296,34048,14085],{"class":3723},[1296,34050,1795],{"class":3707},[1296,34052,14090],{"class":3723},[1296,34054,1795],{"class":3707},[1296,34056,14095],{"class":3723},[1296,34058,1795],{"class":3707},[1296,34060,9472],{"class":3723},[1296,34062,1795],{"class":3707},[1296,34064,4179],{"class":3723},[1296,34066,1795],{"class":3707},[1296,34068,3733],{"class":3723},[1296,34070,1795],{"class":3707},[1296,34072,14112],{"class":3723},[1296,34074,1795],{"class":3707},[1296,34076,9989],{"class":3723},[1296,34078,1795],{"class":3707},[1296,34080,14121],{"class":3723},[1296,34082,1795],{"class":3707},[1296,34084,34085],{"class":3723}," 367",[1296,34087,1795],{"class":3707},[1296,34089,14133],{"class":3723},[1296,34091,1795],{"class":3707},[1296,34093,14138],{"class":3723},[1296,34095,1795],{"class":3707},[1296,34097,14143],{"class":3723},[1296,34099,1795],{"class":3707},[1296,34101,3751],{"class":3723},[1296,34103,1795],{"class":3707},[1296,34105,14152],{"class":3723},[1296,34107,1795],{"class":3707},[1296,34109,14157],{"class":3723},[1296,34111,1795],{"class":3707},[1296,34113,14162],{"class":3723},[1296,34115,1795],{"class":3707},[1296,34117,14167],{"class":3723},[1296,34119,1795],{"class":3707},[1296,34121,14172],{"class":3723},[1296,34123,3736],{"class":3707},[1296,34125,34126,34128,34130,34132,34134,34136,34138,34140,34142,34144,34146,34148,34150,34152,34154,34156,34158,34160,34162,34164,34166,34168,34170,34172,34174,34176,34178,34180,34182,34184,34186,34188,34190,34192,34194,34196,34198,34200],{"class":3700,"line":27},[1296,34127,14179],{"class":3723},[1296,34129,1795],{"class":3707},[1296,34131,14184],{"class":3723},[1296,34133,1795],{"class":3707},[1296,34135,14189],{"class":3723},[1296,34137,1795],{"class":3707},[1296,34139,14194],{"class":3723},[1296,34141,1795],{"class":3707},[1296,34143,14199],{"class":3723},[1296,34145,1795],{"class":3707},[1296,34147,3751],{"class":3723},[1296,34149,1795],{"class":3707},[1296,34151,14208],{"class":3723},[1296,34153,1795],{"class":3707},[1296,34155,3733],{"class":3723},[1296,34157,1795],{"class":3707},[1296,34159,14217],{"class":3723},[1296,34161,1795],{"class":3707},[1296,34163,14222],{"class":3723},[1296,34165,1795],{"class":3707},[1296,34167,15314],{"class":3723},[1296,34169,1795],{"class":3707},[1296,34171,14234],{"class":3723},[1296,34173,1795],{"class":3707},[1296,34175,14239],{"class":3723},[1296,34177,1795],{"class":3707},[1296,34179,14133],{"class":3723},[1296,34181,1795],{"class":3707},[1296,34183,14248],{"class":3723},[1296,34185,1795],{"class":3707},[1296,34187,14253],{"class":3723},[1296,34189,1795],{"class":3707},[1296,34191,14258],{"class":3723},[1296,34193,1795],{"class":3707},[1296,34195,14263],{"class":3723},[1296,34197,1795],{"class":3707},[1296,34199,14268],{"class":3723},[1296,34201,3736],{"class":3707},[1296,34203,34204,34206,34208,34211,34213,34215,34217,34219,34221,34223,34225,34227,34229,34231,34233,34235,34237,34239,34241,34243,34245,34247,34249,34252,34254,34256,34258,34260,34262,34264,34266,34268,34270,34272,34274,34276,34278,34280,34282,34284,34286,34288],{"class":3700,"line":148},[1296,34205,14378],{"class":3723},[1296,34207,1795],{"class":3707},[1296,34209,34210],{"class":3723}," 74",[1296,34212,1795],{"class":3707},[1296,34214,14285],{"class":3723},[1296,34216,1795],{"class":3707},[1296,34218,14290],{"class":3723},[1296,34220,1795],{"class":3707},[1296,34222,14295],{"class":3723},[1296,34224,1795],{"class":3707},[1296,34226,14300],{"class":3723},[1296,34228,1795],{"class":3707},[1296,34230,14217],{"class":3723},[1296,34232,1795],{"class":3707},[1296,34234,14309],{"class":3723},[1296,34236,1795],{"class":3707},[1296,34238,10850],{"class":3723},[1296,34240,1795],{"class":3707},[1296,34242,14318],{"class":3723},[1296,34244,1795],{"class":3707},[1296,34246,14323],{"class":3723},[1296,34248,1795],{"class":3707},[1296,34250,34251],{"class":3723}," 194",[1296,34253,1795],{"class":3707},[1296,34255,4144],{"class":3723},[1296,34257,1795],{"class":3707},[1296,34259,14339],{"class":3723},[1296,34261,1795],{"class":3707},[1296,34263,14344],{"class":3723},[1296,34265,1795],{"class":3707},[1296,34267,14349],{"class":3723},[1296,34269,1795],{"class":3707},[1296,34271,14300],{"class":3723},[1296,34273,1795],{"class":3707},[1296,34275,9989],{"class":3723},[1296,34277,1795],{"class":3707},[1296,34279,4179],{"class":3723},[1296,34281,1795],{"class":3707},[1296,34283,14366],{"class":3723},[1296,34285,1795],{"class":3707},[1296,34287,14371],{"class":3723},[1296,34289,3736],{"class":3707},[1296,34291,34292,34294,34296,34298,34300,34302,34304,34306,34308,34310,34312,34314,34316,34318,34320,34322],{"class":3700,"line":111},[1296,34293,14378],{"class":3723},[1296,34295,1795],{"class":3707},[1296,34297,3728],{"class":3723},[1296,34299,1795],{"class":3707},[1296,34301,14387],{"class":3723},[1296,34303,1795],{"class":3707},[1296,34305,14392],{"class":3723},[1296,34307,1795],{"class":3707},[1296,34309,14397],{"class":3723},[1296,34311,1795],{"class":3707},[1296,34313,14402],{"class":3723},[1296,34315,1795],{"class":3707},[1296,34317,14133],{"class":3723},[1296,34319,1795],{"class":3707},[1296,34321,14411],{"class":3723},[1296,34323,3900],{"class":3715},[1296,34325,34326,34328,34330,34332],{"class":3700,"line":96},[1296,34327,12133],{"class":3711},[1296,34329,1873],{"class":3715},[1296,34331,14071],{"class":3703},[1296,34333,3900],{"class":3715},[1296,34335,34336,34338,34340,34342],{"class":3700,"line":89},[1296,34337,12155],{"class":3711},[1296,34339,1873],{"class":3715},[1296,34341,14071],{"class":3703},[1296,34343,3900],{"class":3715},[1296,34345,34346,34348,34350,34352],{"class":3700,"line":82},[1296,34347,12855],{"class":3711},[1296,34349,1873],{"class":3715},[1296,34351,14071],{"class":3703},[1296,34353,3900],{"class":3715},[1296,34355,34356,34358,34360,34362],{"class":3700,"line":75},[1296,34357,17572],{"class":3711},[1296,34359,1873],{"class":3715},[1296,34361,14071],{"class":3703},[1296,34363,3900],{"class":3715},[1296,34365,34366,34368,34370,34372,34374,34377,34379,34381,34383,34385,34387,34389,34391,34393],{"class":3700,"line":3890},[1296,34367,33683],{"class":3711},[1296,34369,1873],{"class":3715},[1296,34371,14071],{"class":3703},[1296,34373,1795],{"class":3707},[1296,34375,34376],{"class":3839}," \"pexp\"",[1296,34378,1795],{"class":3707},[1296,34380,10063],{"class":3703},[1296,34382,3796],{"class":3707},[1296,34384,4638],{"class":3723},[1296,34386,10070],{"class":3707},[1296,34388,9226],{"class":3711},[1296,34390,1873],{"class":3715},[1296,34392,14071],{"class":3703},[1296,34394,9488],{"class":3715},[3692,34396,34399],{"className":34397,"code":34398,"language":3922,"meta":1452},[3920],"[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",[3468,34400,34398],{"__ignoreMap":1452},[1148,34402,34403,34404,34423,34424,34441,34442,34461],{},"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 (",[1296,34405,34407],{"className":34406},[1299],[1301,34408,34409],{"xmlns":1303},[1305,34410,34411,34420],{},[1308,34412,34413,34415,34417],{},[1314,34414,1148],{},[1685,34416,4331],{},[1562,34418,34419],{},"0,0001",[1319,34421,34422],{"encoding":1321},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1296,34425,34427],{"className":34426},[1299],[1301,34428,34429],{"xmlns":1303},[1305,34430,34431,34439],{},[1308,34432,34433],{},[2722,34434,34435,34437],{"accent":1530},[1314,34436,6716],{},[1685,34438,11454],{},[1319,34440,21557],{"encoding":1321}," shodu nezamítá (",[1296,34443,34445],{"className":34444},[1299],[1301,34446,34447],{"xmlns":1303},[1305,34448,34449,34458],{},[1308,34450,34451,34453,34455],{},[1314,34452,1148],{},[1685,34454,1980],{},[1562,34456,34457],{},"0,8421",[1319,34459,34460],{"encoding":1321},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1148,34463,34464],{},[4382,34465],{"alt":34466,"className":34467,"src":34468},"mask-th-exponencialni-shoda",[1245,4386],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1143,34470,34472],{"id":34471},"neparametrické-testy","Neparametrické testy",[1148,34474,34475,34476,4604,34478,34502],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1108,34477,11546],{},[1296,34479,34481],{"className":34480},[1299],[1301,34482,34483],{"xmlns":1303},[1305,34484,34485,34499],{},[1308,34486,34487],{},[1311,34488,34489,34491],{},[1314,34490,6716],{},[1308,34492,34493,34495,34497],{},[1562,34494,1564],{},[1685,34496,1795],{"separator":1530},[1562,34498,9921],{},[1319,34500,34501],{"encoding":1321},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[16742,34504,34506],{"id":34505},"wilcoxonovy-testy","Wilcoxonovy testy",[1162,34508,34509,34554],{},[1165,34510,34511],{},[1168,34512,34513,34532,34551],{},[1171,34514,34515],{},[1296,34516,34518],{"className":34517},[1299],[1301,34519,34520],{"xmlns":1303},[1305,34521,34522,34530],{},[1308,34523,34524],{},[1311,34525,34526,34528],{},[1314,34527,1560],{},[1562,34529,1564],{},[1319,34531,1567],{"encoding":1321},[1171,34533,34534],{},[1296,34535,34537],{"className":34536},[1299],[1301,34538,34539],{"xmlns":1303},[1305,34540,34541,34549],{},[1308,34542,34543],{},[1311,34544,34545,34547],{},[1314,34546,1560],{},[1562,34548,1792],{},[1319,34550,2994],{"encoding":1321},[1171,34552,34553],{},"Příkaz v R",[1178,34555,34556,34623,34690],{},[1168,34557,34558,34588,34618],{},[1183,34559,34560],{},[1296,34561,34563],{"className":34562},[1299],[1301,34564,34565],{"xmlns":1303},[1305,34566,34567,34585],{},[1308,34568,34569,34581,34583],{},[1311,34570,34571,34573],{},[1314,34572,6716],{},[1308,34574,34575,34577,34579],{},[1562,34576,1564],{},[1685,34578,1795],{"separator":1530},[1562,34580,9921],{},[1685,34582,6731],{},[1314,34584,3718],{},[1319,34586,34587],{"encoding":1321},"x_{0,5} \\le c",[1183,34589,34590],{},[1296,34591,34593],{"className":34592},[1299],[1301,34594,34595],{"xmlns":1303},[1305,34596,34597,34615],{},[1308,34598,34599,34611,34613],{},[1311,34600,34601,34603],{},[1314,34602,6716],{},[1308,34604,34605,34607,34609],{},[1562,34606,1564],{},[1685,34608,1795],{"separator":1530},[1562,34610,9921],{},[1685,34612,1687],{},[1314,34614,3718],{},[1319,34616,34617],{"encoding":1321},"x_{0,5} > c",[1183,34619,34620],{},[3468,34621,34622],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1168,34624,34625,34655,34685],{},[1183,34626,34627],{},[1296,34628,34630],{"className":34629},[1299],[1301,34631,34632],{"xmlns":1303},[1305,34633,34634,34652],{},[1308,34635,34636,34648,34650],{},[1311,34637,34638,34640],{},[1314,34639,6716],{},[1308,34641,34642,34644,34646],{},[1562,34643,1564],{},[1685,34645,1795],{"separator":1530},[1562,34647,9921],{},[1685,34649,1980],{},[1314,34651,3718],{},[1319,34653,34654],{"encoding":1321},"x_{0,5} = c",[1183,34656,34657],{},[1296,34658,34660],{"className":34659},[1299],[1301,34661,34662],{"xmlns":1303},[1305,34663,34664,34682],{},[1308,34665,34666,34678,34680],{},[1311,34667,34668,34670],{},[1314,34669,6716],{},[1308,34671,34672,34674,34676],{},[1562,34673,1564],{},[1685,34675,1795],{"separator":1530},[1562,34677,9921],{},[1685,34679,10951],{"mathvariant":2119},[1314,34681,3718],{},[1319,34683,34684],{"encoding":1321},"x_{0,5} \\neq c",[1183,34686,34687],{},[3468,34688,34689],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1168,34691,34692,34722,34752],{},[1183,34693,34694],{},[1296,34695,34697],{"className":34696},[1299],[1301,34698,34699],{"xmlns":1303},[1305,34700,34701,34719],{},[1308,34702,34703,34715,34717],{},[1311,34704,34705,34707],{},[1314,34706,6716],{},[1308,34708,34709,34711,34713],{},[1562,34710,1564],{},[1685,34712,1795],{"separator":1530},[1562,34714,9921],{},[1685,34716,3349],{},[1314,34718,3718],{},[1319,34720,34721],{"encoding":1321},"x_{0,5} \\ge c",[1183,34723,34724],{},[1296,34725,34727],{"className":34726},[1299],[1301,34728,34729],{"xmlns":1303},[1305,34730,34731,34749],{},[1308,34732,34733,34745,34747],{},[1311,34734,34735,34737],{},[1314,34736,6716],{},[1308,34738,34739,34741,34743],{},[1562,34740,1564],{},[1685,34742,1795],{"separator":1530},[1562,34744,9921],{},[1685,34746,4331],{},[1314,34748,3718],{},[1319,34750,34751],{"encoding":1321},"x_{0,5} \u003C c",[1183,34753,34754],{},[3468,34755,34756],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1148,34758,34759,34762,34763,1395],{},[6638,34760,34761],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1296,34764,34766],{"className":34765},[1299],[1301,34767,34768],{"xmlns":1303},[1305,34769,34770,34774],{},[1308,34771,34772],{},[1314,34773,3718],{},[1319,34775,3718],{"encoding":1321},[1148,34777,34778,34781,34782,8829,34820,34833,34834,1395],{},[6638,34779,34780],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1296,34783,34785],{"className":34784},[1299],[1301,34786,34787],{"xmlns":1303},[1305,34788,34789,34817],{},[1308,34790,34791,34803,34805],{},[1311,34792,34793,34795],{},[1314,34794,6716],{},[1308,34796,34797,34799,34801],{},[1562,34798,1564],{},[1685,34800,1795],{"separator":1530},[1562,34802,9921],{},[1685,34804,3062],{},[1311,34806,34807,34809],{},[1314,34808,7126],{},[1308,34810,34811,34813,34815],{},[1562,34812,1564],{},[1685,34814,1795],{"separator":1530},[1562,34816,9921],{},[1319,34818,34819],{"encoding":1321},"x_{0,5}-y_{0,5}",[1296,34821,34823],{"className":34822},[1299],[1301,34824,34825],{"xmlns":1303},[1305,34826,34827,34831],{},[1308,34828,34829],{},[1314,34830,3718],{},[1319,34832,3718],{"encoding":1321},"; v R se volá se stejnými argumenty jako výše a navíc ",[3468,34835,34836],{},"paired = TRUE",[1148,34838,34839,34842,34843,34845],{},[6638,34840,34841],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3468,34844,25440],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3692,34847,34849],{"className":3694,"code":34848,"language":71,"meta":1452,"style":1452},"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",[3468,34850,34851,34921,34979],{"__ignoreMap":1452},[1296,34852,34853,34855,34857,34859,34861,34863,34865,34867,34869,34871,34873,34875,34877,34879,34881,34883,34885,34887,34889,34891,34893,34895,34897,34899,34901,34903,34905,34907,34909,34911,34913,34915,34917,34919],{"class":3700,"line":10},[1296,34854,33095],{"class":3703},[1296,34856,3708],{"class":3707},[1296,34858,3834],{"class":3711},[1296,34860,1873],{"class":3715},[1296,34862,33104],{"class":3723},[1296,34864,1795],{"class":3707},[1296,34866,15314],{"class":3723},[1296,34868,1795],{"class":3707},[1296,34870,33113],{"class":3723},[1296,34872,1795],{"class":3707},[1296,34874,33118],{"class":3723},[1296,34876,1795],{"class":3707},[1296,34878,33123],{"class":3723},[1296,34880,1795],{"class":3707},[1296,34882,33128],{"class":3723},[1296,34884,1795],{"class":3707},[1296,34886,18468],{"class":3723},[1296,34888,1795],{"class":3707},[1296,34890,14172],{"class":3723},[1296,34892,1795],{"class":3707},[1296,34894,33123],{"class":3723},[1296,34896,1795],{"class":3707},[1296,34898,33113],{"class":3723},[1296,34900,1795],{"class":3707},[1296,34902,33149],{"class":3723},[1296,34904,1795],{"class":3707},[1296,34906,33154],{"class":3723},[1296,34908,1795],{"class":3707},[1296,34910,33159],{"class":3723},[1296,34912,1795],{"class":3707},[1296,34914,33123],{"class":3723},[1296,34916,1795],{"class":3707},[1296,34918,33168],{"class":3723},[1296,34920,3900],{"class":3715},[1296,34922,34923,34925,34927,34929,34931,34933,34935,34937,34939,34941,34943,34945,34947,34949,34951,34953,34955,34957,34959,34961,34963,34965,34967,34969,34971,34973,34975,34977],{"class":3700,"line":27},[1296,34924,33175],{"class":3703},[1296,34926,3708],{"class":3707},[1296,34928,3834],{"class":3711},[1296,34930,1873],{"class":3715},[1296,34932,21829],{"class":3723},[1296,34934,1795],{"class":3707},[1296,34936,33118],{"class":3723},[1296,34938,1795],{"class":3707},[1296,34940,33192],{"class":3723},[1296,34942,1795],{"class":3707},[1296,34944,33197],{"class":3723},[1296,34946,1795],{"class":3707},[1296,34948,33202],{"class":3723},[1296,34950,1795],{"class":3707},[1296,34952,33202],{"class":3723},[1296,34954,1795],{"class":3707},[1296,34956,14172],{"class":3723},[1296,34958,1795],{"class":3707},[1296,34960,33118],{"class":3723},[1296,34962,1795],{"class":3707},[1296,34964,33118],{"class":3723},[1296,34966,1795],{"class":3707},[1296,34968,33223],{"class":3723},[1296,34970,1795],{"class":3707},[1296,34972,33154],{"class":3723},[1296,34974,1795],{"class":3707},[1296,34976,33118],{"class":3723},[1296,34978,3900],{"class":3715},[1296,34980,34981,34984,34986,34988,34990,34992,34994,34996,34998,35000],{"class":3700,"line":148},[1296,34982,34983],{"class":3711},"wilcox.test",[1296,34985,1873],{"class":3715},[1296,34987,33095],{"class":3703},[1296,34989,1795],{"class":3707},[1296,34991,33246],{"class":3703},[1296,34993,1795],{"class":3707},[1296,34995,28086],{"class":3703},[1296,34997,3796],{"class":3707},[1296,34999,28091],{"class":3839},[1296,35001,3900],{"class":3715},[3692,35003,35006],{"className":35004,"code":35005,"language":3922,"meta":1452},[3920],"    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",[3468,35007,35005],{"__ignoreMap":1452},[1148,35009,35010,35033],{},[1296,35011,35013],{"className":35012},[1299],[1301,35014,35015],{"xmlns":1303},[1305,35016,35017,35030],{},[1308,35018,35019,35021,35023,35026,35028],{},[1314,35020,1148],{},[1685,35022,1980],{},[1562,35024,35025],{},"0,315",[1685,35027,1687],{},[1562,35029,3983],{},[1319,35031,35032],{"encoding":1321},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1514,35035,35037,35044,35066,35177,35183],{"className":35036,"dataCallout":3475},[1517,3474],[1148,35038,35040,35043],{"className":35039},[1523],[1296,35041],{"className":35042,"ariaHidden":1530},[1527,3482,1529],"Příklad: Realitní odhadci — neparametrická alternativa",[1148,35045,35046,35047,35065],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1296,35048,35050],{"className":35049},[1299],[1301,35051,35052],{"xmlns":1303},[1305,35053,35054,35062],{},[1308,35055,35056,35058,35060],{},[1314,35057,1148],{},[1685,35059,1980],{},[1562,35061,30139],{},[1319,35063,35064],{"encoding":1321},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3692,35067,35069],{"className":3694,"code":35068,"language":71,"meta":1452,"style":1452},"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",[3468,35070,35071,35113,35155],{"__ignoreMap":1452},[1296,35072,35073,35075,35077,35079,35081,35083,35085,35087,35089,35091,35093,35095,35097,35099,35101,35103,35105,35107,35109,35111],{"class":3700,"line":10},[1296,35074,29942],{"class":3703},[1296,35076,3708],{"class":3707},[1296,35078,3834],{"class":3711},[1296,35080,1873],{"class":3715},[1296,35082,29951],{"class":3723},[1296,35084,1795],{"class":3707},[1296,35086,29956],{"class":3723},[1296,35088,1795],{"class":3707},[1296,35090,29961],{"class":3723},[1296,35092,1795],{"class":3707},[1296,35094,29966],{"class":3723},[1296,35096,1795],{"class":3707},[1296,35098,29971],{"class":3723},[1296,35100,1795],{"class":3707},[1296,35102,29976],{"class":3723},[1296,35104,1795],{"class":3707},[1296,35106,29981],{"class":3723},[1296,35108,1795],{"class":3707},[1296,35110,29986],{"class":3723},[1296,35112,3900],{"class":3715},[1296,35114,35115,35117,35119,35121,35123,35125,35127,35129,35131,35133,35135,35137,35139,35141,35143,35145,35147,35149,35151,35153],{"class":3700,"line":27},[1296,35116,29993],{"class":3703},[1296,35118,3708],{"class":3707},[1296,35120,3834],{"class":3711},[1296,35122,1873],{"class":3715},[1296,35124,30002],{"class":3723},[1296,35126,1795],{"class":3707},[1296,35128,30007],{"class":3723},[1296,35130,1795],{"class":3707},[1296,35132,30012],{"class":3723},[1296,35134,1795],{"class":3707},[1296,35136,30017],{"class":3723},[1296,35138,1795],{"class":3707},[1296,35140,30022],{"class":3723},[1296,35142,1795],{"class":3707},[1296,35144,30027],{"class":3723},[1296,35146,1795],{"class":3707},[1296,35148,30032],{"class":3723},[1296,35150,1795],{"class":3707},[1296,35152,30037],{"class":3723},[1296,35154,3900],{"class":3715},[1296,35156,35157,35159,35161,35163,35165,35167,35169,35171,35173,35175],{"class":3700,"line":148},[1296,35158,34983],{"class":3711},[1296,35160,1873],{"class":3715},[1296,35162,29942],{"class":3703},[1296,35164,1795],{"class":3707},[1296,35166,30052],{"class":3703},[1296,35168,1795],{"class":3707},[1296,35170,30057],{"class":3703},[1296,35172,3796],{"class":3707},[1296,35174,3809],{"class":3723},[1296,35176,3900],{"class":3715},[3692,35178,35181],{"className":35179,"code":35180,"language":3922,"meta":1452},[3920],"    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",[3468,35182,35180],{"__ignoreMap":1452},[1148,35184,35185,35208],{},[1296,35186,35188],{"className":35187},[1299],[1301,35189,35190],{"xmlns":1303},[1305,35191,35192,35205],{},[1308,35193,35194,35196,35198,35201,35203],{},[1314,35195,1148],{},[1685,35197,1980],{},[1562,35199,35200],{},"0,1484",[1685,35202,1687],{},[1562,35204,3983],{},[1319,35206,35207],{"encoding":1321},"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.",[16742,35210,35212],{"id":35211},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1148,35214,35215,35216,35233],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1296,35217,35219],{"className":35218},[1299],[1301,35220,35221],{"xmlns":1303},[1305,35222,35223,35231],{},[1308,35224,35225],{},[1311,35226,35227,35229],{},[1314,35228,1560],{},[1562,35230,1564],{},[1319,35232,1567],{"encoding":1321},": všechny výběry pocházejí ze stejného rozdělení.",[3692,35235,35237],{"className":3694,"code":35236,"language":71,"meta":1452,"style":1452},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3468,35238,35239],{"__ignoreMap":1452},[1296,35240,35241,35244,35246,35249,35251,35254,35256,35258,35260,35263],{"class":3700,"line":10},[1296,35242,35243],{"class":3711},"kruskal.test",[1296,35245,1873],{"class":3715},[1296,35247,35248],{"class":3703},"kvantitativní_proměnná",[1296,35250,16853],{"class":3707},[1296,35252,35253],{"class":3703}," faktor",[1296,35255,1795],{"class":3707},[1296,35257,20162],{"class":3703},[1296,35259,3796],{"class":3707},[1296,35261,35262],{"class":3703}," soubor",[1296,35264,3900],{"class":3715},[16742,35266,35268],{"id":35267},"mediánový-test","Mediánový test",[1148,35270,35271,35272,35289,35290,1956],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1296,35273,35275],{"className":35274},[1299],[1301,35276,35277],{"xmlns":1303},[1305,35278,35279,35287],{},[1308,35280,35281],{},[1311,35282,35283,35285],{},[1314,35284,1560],{},[1562,35286,1564],{},[1319,35288,1567],{"encoding":1321},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3468,35291,35292],{},"agricolae",[3692,35294,35296],{"className":3694,"code":35295,"language":71,"meta":1452,"style":1452},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3468,35297,35298,35308],{"__ignoreMap":1452},[1296,35299,35300,35302,35304,35306],{"class":3700,"line":10},[1296,35301,17392],{"class":3707},[1296,35303,1873],{"class":3715},[1296,35305,35292],{"class":3703},[1296,35307,3900],{"class":3715},[1296,35309,35310,35313,35315,35317,35319,35321],{"class":3700,"line":27},[1296,35311,35312],{"class":3711},"Median.test",[1296,35314,1873],{"class":3715},[1296,35316,35248],{"class":3703},[1296,35318,1795],{"class":3707},[1296,35320,35253],{"class":3703},[1296,35322,3900],{"class":3715},[16742,35324,35326],{"id":35325},"friedmanův-test","Friedmanův test",[1148,35328,35329,35330,35347,35348,35386],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1296,35331,35333],{"className":35332},[1299],[1301,35334,35335],{"xmlns":1303},[1305,35336,35337,35345],{},[1308,35338,35339],{},[1311,35340,35341,35343],{},[1314,35342,1560],{},[1562,35344,1564],{},[1319,35346,1567],{"encoding":1321},": distribuční funkce veličin ",[1296,35349,35351],{"className":35350},[1299],[1301,35352,35353],{"xmlns":1303},[1305,35354,35355,35383],{},[1308,35356,35357,35367,35369,35371,35373],{},[1311,35358,35359,35361],{},[1314,35360,6728],{},[1308,35362,35363,35365],{},[1314,35364,1876],{},[1562,35366,1792],{},[1685,35368,1795],{"separator":1530},[1685,35370,1798],{},[1685,35372,1795],{"separator":1530},[1311,35374,35375,35377],{},[1314,35376,6728],{},[1308,35378,35379,35381],{},[1314,35380,1876],{},[1314,35382,1343],{},[1319,35384,35385],{"encoding":1321},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3692,35388,35390],{"className":3694,"code":35389,"language":71,"meta":1452,"style":1452},"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",[3468,35391,35392,35422,35427],{"__ignoreMap":1452},[1296,35393,35394,35397,35399,35401,35403,35406,35409,35412,35414,35416,35418,35420],{"class":3700,"line":10},[1296,35395,35396],{"class":3711},"friedman.test",[1296,35398,1873],{"class":3715},[1296,35400,35248],{"class":3703},[1296,35402,16853],{"class":3707},[1296,35404,35405],{"class":3703}," faktor_A",[1296,35407,35408],{"class":3707}," |",[1296,35410,35411],{"class":3703}," faktor_B",[1296,35413,1795],{"class":3707},[1296,35415,20162],{"class":3703},[1296,35417,3796],{"class":3707},[1296,35419,35262],{"class":3703},[1296,35421,3900],{"class":3715},[1296,35423,35424],{"class":3700,"line":27},[1296,35425,35426],{"class":12028},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1296,35428,35429,35431,35433,35435,35437,35439,35441,35443],{"class":3700,"line":148},[1296,35430,35396],{"class":3711},[1296,35432,1873],{"class":3715},[1296,35434,35248],{"class":3703},[1296,35436,1795],{"class":3707},[1296,35438,35405],{"class":3703},[1296,35440,1795],{"class":3707},[1296,35442,35411],{"class":3703},[1296,35444,3900],{"class":3715},[1143,35446,35448],{"id":35447},"přehled-testů","Přehled testů",[1148,35450,35451],{},[4382,35452],{"alt":35453,"className":35454,"src":35455},"mask-ilu-volba-testu",[1245,4386],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1162,35457,35458,35471],{},[1165,35459,35460],{},[1168,35461,35462,35465,35468],{},[1171,35463,35464],{},"Situace",[1171,35466,35467],{},"Test",[1171,35469,35470],{},"R funkce",[1178,35472,35473,35486,35499,35511,35524,35539,35551,35564,35577,35590,35602,35617],{},[1168,35474,35475,35478,35481],{},[1183,35476,35477],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1183,35479,35480],{},"jednovýběrový t-test",[1183,35482,35483],{},[3468,35484,35485],{},"t.test(x, mu = ..., alternative = ...)",[1168,35487,35488,35491,35494],{},[1183,35489,35490],{},"Rozdíl dvou závislých měření, diference normální",[1183,35492,35493],{},"párový t-test",[1183,35495,35496],{},[3468,35497,35498],{},"t.test(x, y, paired = TRUE)",[1168,35500,35501,35504,35506],{},[1183,35502,35503],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1183,35505,20070],{},[1183,35507,35508],{},[3468,35509,35510],{},"var.test(x, y)",[1168,35512,35513,35516,35519],{},[1183,35514,35515],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1183,35517,35518],{},"dvouvýběrový t-test",[1183,35520,35521],{},[3468,35522,35523],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1168,35525,35526,35529,35531],{},[1183,35527,35528],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1183,35530,33332],{},[1183,35532,35533,1323,35536],{},[3468,35534,35535],{},"ks.test(x, \"pnorm\", mu, sigma)",[3468,35537,35538],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1168,35540,35541,35544,35546],{},[1183,35542,35543],{},"Normalita dat",[1183,35545,33748],{},[1183,35547,35548],{},[3468,35549,35550],{},"shapiro.test(x)",[1168,35552,35553,35556,35559],{},[1183,35554,35555],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1183,35557,35558],{},"jednovýběrový Wilcoxonův test",[1183,35560,35561],{},[3468,35562,35563],{},"wilcox.test(x, mu = c, alternative = ...)",[1168,35565,35566,35569,35572],{},[1183,35567,35568],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1183,35570,35571],{},"párový Wilcoxonův test",[1183,35573,35574],{},[3468,35575,35576],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1168,35578,35579,35582,35585],{},[1183,35580,35581],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1183,35583,35584],{},"dvouvýběrový Wilcoxonův test",[1183,35586,35587],{},[3468,35588,35589],{},"wilcox.test(x, y)",[1168,35591,35592,35595,35597],{},[1183,35593,35594],{},"Více než dva nezávislé výběry, data nejsou normální",[1183,35596,35212],{},[1183,35598,35599],{},[3468,35600,35601],{},"kruskal.test(y ~ faktor, data)",[1168,35603,35604,35607,35610],{},[1183,35605,35606],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1183,35608,35609],{},"mediánový test",[1183,35611,35612,22657,35615],{},[3468,35613,35614],{},"Median.test(y, faktor)",[3468,35616,35292],{},[1168,35618,35619,35622,35624],{},[1183,35620,35621],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1183,35623,35326],{},[1183,35625,35626],{},[3468,35627,35628],{},"friedman.test(y ~ A | B, data)",[1143,35630,6404],{"id":6403},[1102,35632,35633,35710,35716,35733,35764],{},[1105,35634,35635,35674,35675,33062,35692,35709],{},[1108,35636,35637,35638,35655,35656,35673],{},"Nezamítnutí ",[1296,35639,35641],{"className":35640},[1299],[1301,35642,35643],{"xmlns":1303},[1305,35644,35645,35653],{},[1308,35646,35647],{},[1311,35648,35649,35651],{},[1314,35650,1560],{},[1562,35652,1564],{},[1319,35654,1567],{"encoding":1321}," není důkaz, že ",[1296,35657,35659],{"className":35658},[1299],[1301,35660,35661],{"xmlns":1303},[1305,35662,35663,35671],{},[1308,35664,35665],{},[1311,35666,35667,35669],{},[1314,35668,1560],{},[1562,35670,1564],{},[1319,35672,1567],{"encoding":1321}," platí."," U kabelů A\u002FB vyšlo ",[1296,35676,35678],{"className":35677},[1299],[1301,35679,35680],{"xmlns":1303},[1305,35681,35682,35690],{},[1308,35683,35684,35686,35688],{},[1314,35685,1148],{},[1685,35687,1980],{},[1562,35689,33058],{},[1319,35691,33061],{"encoding":1321},[1296,35693,35695],{"className":35694},[1299],[1301,35696,35697],{"xmlns":1303},[1305,35698,35699,35707],{},[1308,35700,35701],{},[1311,35702,35703,35705],{},[1314,35704,1560],{},[1562,35706,1564],{},[1319,35708,1567],{"encoding":1321}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1105,35711,35712,35715],{},[1108,35713,35714],{},"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.",[1105,35717,35718,35725,35726,35729,35730,35732],{},[1108,35719,35720,30220,35722,35724],{},[3468,35721,32790],{},[3468,35723,28004],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3468,35727,35728],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3468,35731,33041],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1105,35734,35735,35738,35739,35742,35743,35760,35761,1395],{},[1108,35736,35737],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3468,35740,35741],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1296,35744,35746],{"className":35745},[1299],[1301,35747,35748],{"xmlns":1303},[1305,35749,35750,35758],{},[1308,35751,35752],{},[1311,35753,35754,35756],{},[1314,35755,1560],{},[1562,35757,1792],{},[1319,35759,2994],{"encoding":1321}," v zadání, ne být ponechána na výchozí hodnotě ",[3468,35762,35763],{},"\"two.sided\"",[1105,35765,35766,35769,35770,35783],{},[1108,35767,35768],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1296,35771,35773],{"className":35772},[1299],[1301,35774,35775],{"xmlns":1303},[1305,35776,35777,35781],{},[1308,35778,35779],{},[1314,35780,1602],{},[1319,35782,1602],{"encoding":1321}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1143,35785,6592],{"id":6591},[1102,35787,35788,35793,35798,35803,35808,35813,35818],{},[1105,35789,35790],{},[1242,35791,1717],{"className":35792,"dataFsResolvedFilePath":1715,"href":1716},[1245],[1105,35794,35795],{},[1242,35796,1248],{"className":35797,"dataFsResolvedFilePath":1246,"href":1247},[1245],[1105,35799,35800],{},[1242,35801,1257],{"className":35802,"dataFsResolvedFilePath":1255,"href":1256},[1245],[1105,35804,35805],{},[1242,35806,1275],{"className":35807,"dataFsResolvedFilePath":1273,"href":1274},[1245],[1105,35809,35810],{},[1242,35811,1284],{"className":35812,"dataFsResolvedFilePath":1282,"href":1283},[1245],[1105,35814,35815],{},[1242,35816,1293],{"className":35817,"dataFsResolvedFilePath":1291,"href":1292},[1245],[1105,35819,35820],{},[1242,35821,6630],{"className":35822,"dataFsResolvedFilePath":1447,"href":1448},[1245],[1143,35824,6633],{"id":934},[1148,35826,6636,35827,6641],{},[6638,35828,6640],{},[6643,35830,35831],{},"html pre.shiki code .sP4rz, html 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