{"id":263,"date":"2020-01-29T09:58:23","date_gmt":"2020-01-29T08:58:23","guid":{"rendered":"http:\/\/estatistika.ku.sk\/?page_id=263"},"modified":"2022-01-11T15:09:58","modified_gmt":"2022-01-11T14:09:58","slug":"testovanie-normality-rozdelenia-dat","status":"publish","type":"page","link":"https:\/\/estatistika.ku.sk\/index.php\/testovanie-normality-rozdelenia-dat\/","title":{"rendered":"Testovanie normality rozdelenia d\u00e1t"},"content":{"rendered":"<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Norm\u00e1lne rozdelenie je jednou z d\u00f4le\u017eit\u00fdch podmienok realiz\u00e1cie viacer\u00fdch \u0161tatistick\u00fdch proced\u00far s kardin\u00e1lnou\/kardin\u00e1lnymi premenn\u00fdmi (napr. parametrick\u00fdch testov, regresnej anal\u00fdzy a i.).\u00a0<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Premenn\u00e1 je norm\u00e1lne rozdelen\u00e1 v pr\u00edpade, ak m\u00e1 podobu zvonovej (Gaussovej) krivky, ktor\u00e1 je symetrick\u00e1 okolo strednej osy (vi\u010f graf). Najvhodnej\u0161\u00edm sp\u00f4sobom vizualiz\u00e1cie je histogram.<\/span><\/p>\n<p style=\"text-align: justify;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/estatistika.ku.sk\/wp-content\/uploads\/2020\/01\/Sn\u00edmka1266.jpg\" alt=\"\" width=\"590\" height=\"427\" \/><\/p>\n<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Norm\u00e1lne rozdelenie je charakteristick\u00e9 nasleduj\u00facimi znakmi (Rabu\u0161ic, Soukup, Mare\u0161, 2019):<\/span><\/p>\n<ul style=\"text-align: left;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">v\u00e4\u010d\u0161ina hodn\u00f4t sa s\u00fastred\u00ed okolo priemeru a ich distrib\u00facia je symetrick\u00e1 &#8211; polovica hodn\u00f4t je v\u00e4\u010d\u0161ia ako priemer a polovica hodn\u00f4t je men\u0161ia ako priemer;<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">norm\u00e1lne rozdelenie m\u00e1 jeden vrchol, m\u00e1 tvar zvonu, jeho \u013eav\u00e1 strana je zrkadlov\u00fdm obrazom pravej strany a naopak;<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">plat\u00ed, \u017ee do jednej \u0161tandardnej odch\u00fdlky na ka\u017ed\u00fa stranu spadne 68,26 % pr\u00edpadov, do dvoch \u0161tandardn\u00fdch odch\u00fdlok na ka\u017ed\u00fa stranu spadne 95,34 % pr\u00edpadov &#8211; to znamen\u00e1, \u017ee je 95 % pravdepodobnos\u0165, \u017ee pr\u00edpad bude le\u017ea\u0165 v intervale \u00b1 2 \u0161tandardn\u00e9 odch\u00fdlky (\u01a1) okolo priemeru. Do troch \u0161tandardn\u00fdch odch\u00fdlok na ka\u017ed\u00fa stranu spadne 99,7 % pr\u00edpadov.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Na testovanie norm\u00e1lneho rozdelenia pou\u017e\u00edvame v programe SPSS dva druhy testov:<\/span><\/p>\n<ul style=\"text-align: left;\">\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Kolmogorov-Smirnov test<\/strong> (pou\u017e\u00edvame, ak je v s\u00fabore viac ako 50 respondentov),<\/span><\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\"><strong>Shapiro-Wilkov test<\/strong> (pou\u017e\u00edvame, ak je v s\u00fabore menej ako 50 respondentov ).<\/span><br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">V\u00fdsledkom testu je p hodnota. Ak ide o v\u00fdsledok p &lt; 0,05, tak d\u00e1ta nevykazuj\u00fa norm\u00e1lne rozdelenie. V pr\u00edpade, ak je <strong>p \u02c3 0,05<\/strong>, d\u00e1ta s\u00fa norm\u00e1lne rozdelen\u00e9. K t\u00fdmto testom je ni\u017e\u0161ie na str\u00e1nke vytvoren\u00fd videon\u00e1vod realiz\u00e1cie v programe SPSS i Excel.<\/span><\/li>\n<\/ul>\n<blockquote>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Ako upozor\u0148uje Rimar\u010d\u00edk (2007) \u201etesty normality je potrebn\u00e9 pou\u017e\u00edva\u0165 opatrne, preto\u017ee pri mal\u00fdch vzork\u00e1ch, ktor\u00e9 sa aj vizu\u00e1lne odli\u0161uj\u00fa od norm\u00e1lneho rozdelenia, sa hypot\u00e9za o\u00a0normalite, d\u00f4sledkom n\u00edzkej sily, nezamietne. Naopak, pri ve\u013ek\u00fdch vzork\u00e1ch d\u00f4sledkom prive\u013ekej sily testov sa normalita \u010dasto zamietne, aj ke\u010f m\u00e1 premenn\u00e1 rozdelenie ve\u013emi bl\u00edzke norm\u00e1lnemu.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Testy normality <strong>nie je vhodn\u00e9 pou\u017e\u00edva\u0165 na slep\u00e9 rozhodnutie,<\/strong> \u010di pou\u017ei\u0165 parametrick\u00fa, alebo neparametrick\u00fa met\u00f3du, o tom treba rozhodn\u00fa\u0165 na z\u00e1klade poznania z\u00e1kladn\u00e9ho s\u00faboru a kontroly histogramu vytvoren\u00e9ho zo vzorky.\u201c<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">Okrem pou\u017eitia testov normality je vhodn\u00e9 pozna\u0165 <a style=\"color: #000000;\" href=\"http:\/\/estatistika.ku.sk\/index.php\/deskriptivna-statistika\/54-2\/\">\u0161tatistick\u00e9 ukazovatele<\/a> (priemer, medi\u00e1n, modus, \u0161tandardn\u00fa odch\u00fdlku, \u0161ikmos\u0165, strmos\u0165) a pos\u00fadi\u0165 tvar Gaussovej krivky v histograme (tvorba histogramu v SPSS).<\/span><\/p>\n<\/blockquote>\n<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">D\u00f4le\u017eit\u00fdm pojmom v s\u00favislosti s normalitou rozlo\u017eenia je tzv. <strong>centr\u00e1lna limitn\u00e1 veta<\/strong>, ktor\u00fa ako prv\u00fd sformuloval Pierre Simon Laplace v roku 1810. T\u00e1to veta hovor\u00ed o tom, \u017ee s\u00fa\u010det (a teda aj priemer) ve\u013ek\u00e9ho po\u010dtu nez\u00e1visl\u00fdch n\u00e1hodn\u00fdch premenn\u00fdch s rovnak\u00fdm rozdelen\u00edm m\u00e1 norm\u00e1lne rozdelenie. T\u00e1to veta vysvet\u013euje, pre\u010do sa s norm\u00e1lnym rozdelen\u00edm tak \u010dasto stret\u00e1vame takmer v\u0161ade okolo n\u00e1s \u2013 v pr\u00edrode, ale aj u \u013eud\u00ed (napr. v\u00fd\u0161ka IQ, hmotnos\u0165, \u2026).<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif; font-size: 14pt;\">D\u00f4sledkom platnosti centr\u00e1lnej limitnej vety m\u00e1 norm\u00e1lne rozdelenie v indukt\u00edvnej \u0161tatistike dominantn\u00e9 postavenie. <strong>Ak zo z\u00e1kladn\u00e9ho s\u00faboru s \u013eubovo\u013en\u00fdm rozdelen\u00edm budeme vybera\u0165 dostato\u010dne ve\u013ek\u00e9 n\u00e1hodn\u00e9 vzorky, v\u00fdberov\u00e9 rozdelenie priemeru bude norm\u00e1lne.<\/strong><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 80px;\">\n<tbody>\n<tr style=\"height: 40px;\">\n<td style=\"width: 50%; height: 40px; text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>Videon\u00e1vod: SPSS<\/strong><\/span><\/td>\n<td style=\"width: 50%; height: 40px; text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">Videon\u00e1vod: EXCEL<\/span><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"width: 50%; height: 40px;\"><iframe title=\"Testovanie normality rozdelenia d\u00e1t - SPSS\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/VUeAU1O8JXE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/td>\n<td style=\"width: 50%; height: 40px;\"><iframe title=\"Testovanie normality d\u00e1t - Excel\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/_ifd00uv14c?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Norm\u00e1lne rozdelenie je jednou z d\u00f4le\u017eit\u00fdch podmienok realiz\u00e1cie viacer\u00fdch \u0161tatistick\u00fdch proced\u00far s kardin\u00e1lnou\/kardin\u00e1lnymi premenn\u00fdmi (napr. parametrick\u00fdch testov, regresnej anal\u00fdzy a i.).\u00a0 Premenn\u00e1 je norm\u00e1lne rozdelen\u00e1 v pr\u00edpade, ak m\u00e1 podobu zvonovej (Gaussovej) krivky, ktor\u00e1 je symetrick\u00e1 okolo strednej osy (vi\u010f graf). Najvhodnej\u0161\u00edm sp\u00f4sobom vizualiz\u00e1cie je histogram. Norm\u00e1lne rozdelenie je charakteristick\u00e9 nasleduj\u00facimi znakmi (Rabu\u0161ic, Soukup, Mare\u0161, [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"footnotes":""},"class_list":["post-263","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/263","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/comments?post=263"}],"version-history":[{"count":35,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/263\/revisions"}],"predecessor-version":[{"id":2255,"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/pages\/263\/revisions\/2255"}],"wp:attachment":[{"href":"https:\/\/estatistika.ku.sk\/index.php\/wp-json\/wp\/v2\/media?parent=263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}