{"id":654,"date":"2022-05-10T12:31:40","date_gmt":"2022-05-10T10:31:40","guid":{"rendered":"https:\/\/e-biostat.uniag.sk\/?p=654"},"modified":"2022-05-10T13:58:21","modified_gmt":"2022-05-10T11:58:21","slug":"analyza-rozptylu-anova","status":"publish","type":"post","link":"https:\/\/e-biostat.uniag.sk\/?p=654","title":{"rendered":"Anal\u00fdza rozptylu (ANOVA)"},"content":{"rendered":"\n<p class=\"has-small-font-size\">Anal\u00fdza rozptylu je parametrick\u00e1 \u0161tatistick\u00e1 met\u00f3da vytvoren\u00e1 na vz\u00e1jomn\u00e9 porovn\u00e1vanie znakov viacer\u00fdch skup\u00edn (faktorov, \u010dinite\u013eov), ktor\u00fdch po\u010det je v\u00e4\u010d\u0161\u00ed ako dve. Ve\u013emi zjednodu\u0161ene sa m\u00f4\u017ee poveda\u0165, \u017ee je to v skuto\u010dnosti akoby T-test pre viac ako dve skupiny v\u00fdberov\u00fdch \u00fadajov. Anal\u00fdza rozptylu patr\u00ed medzi z\u00e1kladn\u00e9 met\u00f3dy \u0161tatistickej anal\u00fdzy \u00fadajov. ANOVA nach\u00e1dza ve\u013emi \u0161irok\u00e9 uplatnenie prakticky vo v\u0161etk\u00fdch oblastiach aplikovanej \u0161tatistiky.<br>V oblasti biologick\u00e9ho v\u00fdskumu a anal\u00fdzy \u00fadajov m\u00e1 nezastupite\u013en\u00e9 miesto prakticky vo v\u0161etk\u00fdch komplexnej\u0161\u00edch anal\u00fdzach ch\u00e1pania samotn\u00fdch biologick\u00fdch probl\u00e9mov a javov. Je neodmyslite\u013en\u00e1 pri r\u00f4znych typoch genetick\u00fdch hodnoten\u00ed zvierat. Princ\u00edp odhadu plemenn\u00fdch hodn\u00f4t (odhad genetickej kvality zvierat) je vo svojej podstate zalo\u017een\u00fd na vyu\u017e\u00edvan\u00ed r\u00f4znych typov a modifik\u00e1ci\u00ed anal\u00fdzy rozptylu.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Existuje viacero typov anal\u00fdzy rozptylu. Najjednoduch\u0161\u00edm typom anal\u00fdzy rozptylu je jednofaktorov\u00e1 anal\u00fdza rozptylu (One-Way ANOVA). Anal\u00fdza rozptylu, ktor\u00e1 obsahuje viac ako jeden faktor sa naz\u00fdva viacfaktorov\u00e1 anal\u00fdza rozptylu.<br>Jednofaktorov\u00e1 anal\u00fdza rozptylu n\u00e1m umo\u017e\u0148uje testova\u0165 hypot\u00e9zy o rovnostiach stredn\u00fdch hodn\u00f4t viacer\u00fdch skup\u00edn. Cie\u013eom anal\u00fdzy rozptylu je zisti\u0165, \u010di rozdiely, ktor\u00e9 sme vo viacer\u00fdch skupin\u00e1ch zistili, s\u00fa, alebo nie s\u00fa \u0161tatisticky v\u00fdznamn\u00e9. Ak nie s\u00fa \u0161tatisticky v\u00fdznamn\u00e9 tak s\u00fa iba iba v\u00fdsledkom n\u00e1hody.<br>Jednofaktorov\u00e1 je vo svojej podstate najjednoduch\u0161ou formou ANOVA, ktor\u00e1 sk\u00fama vz\u0165ah medzi intervalovou a nomin\u00e1lnou premennou. Prakticky testuje nulov\u00fa hypot\u00e9zu o zhode stredn\u00fdch hodn\u00f4t, pri\u010dom predpoklad\u00e1, \u017ee v\u00fdbery maj\u00fa rovnak\u00fd rozptyl. Nulov\u00e1 hypot\u00e9za vyjadruje, \u017ee medzi intervalovou a nomin\u00e1lnou premennou nie je vz\u0165ah. V pr\u00edpade, \u017ee nulov\u00fa hypot\u00e9zu mus\u00edme odmietnu\u0165 plat\u00ed hypot\u00e9za jednotkov\u00e1, \u017ee medzi intervalovou a nomin\u00e1lnou premennou je \u0161tatisticky v\u00fdznamn\u00fd, alebo dokonca vysoko \u0161tatisticky v\u00fdznamn\u00fd vz\u0165ah.<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>Anal\u00fdzy rozptylu, tak ako aj in\u00e9 \u0161tatistick\u00e9 anal\u00fdzy, je zalo\u017een\u00e1 na splnen\u00ed viac<\/strong>e<strong>r\u00fdch predpokladov:<\/strong><\/p>\n\n\n\n<ol class=\"has-small-font-size\"><li>Skupiny \u00fadajov musia by\u0165 n\u00e1hodn\u00e9 a nez\u00e1visl\u00e9.<\/li><li>\u00dadaje neobsahuj\u00fa \u017eiadne mimoriadne extr\u00e9mne hodnoty.<\/li><li>Skupiny \u00fadajov maj\u00fa pribli\u017ene rovnak\u00fd rozptyl (homoskedascitita).<br>Naru\u0161enie rovnak\u00e9ho rozptylu nevad\u00ed ak s\u00fa skupiny vyv\u00e1\u017een\u00e9 (rovnako ve\u013ek\u00e9), alebo pou\u017eijeme Welchov F-test<\/li><li>Analyzovan\u00e9 pozorovania poch\u00e1dzaj\u00face v r\u00e1mci skup\u00edn z norm\u00e1lneho rozlo\u017eenia po\u010detnosti (pri pou\u017eit\u00ed anal\u00fdzy rozptylu sk\u00famame v r\u00e1mci v\u00fdsledkov normalitu rezidu\u00e1lnej zlo\u017eky variability).<br>Naru\u0161enie normality nevad\u00ed, ak s\u00fa skupiny rovnako ve\u013ek\u00e9 a maj\u00fa minim\u00e1lnu ve\u013ekos\u0165 30 pozorovan\u00ed, neparametrick\u00e1 mo\u017enos\u0165 \u2013 pou\u017eitie Kruskal-Wallisovho testu.<\/li><\/ol>\n\n\n\n<p class=\"has-small-font-size\">Splnenie predpokladov anal\u00fdzy rozptylu sa mus\u00ed overi\u0165 e\u0161te pred samotn\u00fdm pou\u017eit\u00edm met\u00f3dy.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Zostavenie grafov a z\u00e1kladn\u00e1 popisn\u00e1 \u0161tatistika \u00fadajov n\u00e1m m\u00f4\u017ee pom\u00f4c\u0165 overi\u0165 predpoklad pribli\u017ene rovnak\u00fdch rozptylov pre ka\u017ed\u00fa skupinu. Pokia\u013e chceme exaktne upresni\u0165 tento predpoklad mus\u00edme by pou\u017ei\u0165 test homogenity rozptylov. Naj\u010dastej\u0161ie sa pou\u017e\u00edvaj\u00fa Leveneov, Brown-Forsytheov test, alebo Bartlettov test na zistenie homogenyty rozptylov.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Testy s\u00fa ale pomerne rozdielne a ich v\u00fdsledky a pou\u017eitie m\u00f4\u017ee by\u0165 pri rovnak\u00fdch \u00fadajoch zna\u010dne odli\u0161n\u00e9. V\u00fdsledok ich interpret\u00e1cie m\u00f4\u017ee vies\u0165 k \u00faplne opa\u010dn\u00e9mu z\u00e1veru. Bartlettov test je mimoriadne citliv\u00fd na dodr\u017eanie normality \u00fadajov, \u010do nie je tak pr\u00edsne definovan\u00e9 pre pou\u017eitie Leveneovho testu. Predpoklad zhodn\u00fdch rozptylov ale nie je \u00faplne nevyhnutn\u00fd a v skuto\u010dnosti existuje modifik\u00e1cia anal\u00fdzy rozptylu, ktor\u00e1 sa m\u00f4\u017ee pou\u017ei\u0165 aj bez dodr\u017eania predpokladu rovnak\u00fdch rozptylov. Bartlettov test je modifik\u00e1ciou testu pomeru norm\u00e1lnej te\u00f3rie. Tento test vypo\u010d\u00edta presn\u00fa chybovos\u0165 typu I, ke\u010f je distrib\u00facia \u00fadajov norm\u00e1lna. Brown-Forsytheov test je vari\u00e1ciou Leveneovho testu. Rovnak\u00e9 rozptyly sa ur\u010duj\u00fa pomocou absol\u00fatnych odch\u00fdlok od stredov\u00fdch hodn\u00f4t skupiny. Hoci je to dobr\u00fd test na ur\u010denie rozdielov rozptylu, m\u00f4\u017ee by\u0165 n\u00e1ro\u010dn\u00fd na zdroje, ak va\u0161e \u00fadaje obsahuj\u00fa nieko\u013eko r\u00f4znych ve\u013ek\u00fdch skup\u00edn. Leveneov test sa pova\u017euje za \u0161tandardn\u00fd test homogenity rozptylu. Tento test po\u010d\u00edta druh\u00fa mocninu rez\u00eddu\u00ed, aby sa ur\u010dil rovnak\u00fd rozptyl.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Ostatn\u00e9 predpoklady anal\u00fdzy rozptylu, n\u00e1hodn\u00e9, nez\u00e1visl\u00e9 pozorovania a norm\u00e1lne rozlo\u017een\u00e9 po\u010detnosti \u00fadajov mo\u017eno tie\u017e overi\u0165 zostaven\u00edm grafov rezidu\u00ed spolu s&nbsp;odhadnut\u00fdmi&nbsp; hodnotami.<\/p>\n\n\n\n<p class=\"has-small-font-size\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V&nbsp;tabu\u013eke 6.1 uv\u00e1dzame z\u00e1kladn\u00e9 \u010d\u00edseln\u00e9 inform\u00e1cie, parametre a&nbsp;hodnoty s&nbsp;ktor\u00fdmi sa stret\u00e1vame pri &nbsp;anal\u00fdze rozptylu.<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"546\" height=\"150\" src=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok.png\" alt=\"\" class=\"wp-image-662\" srcset=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok.png 546w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-300x82.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-small-font-size\">Variabilita medzi skupinami (Model) je vyjadren\u00e1 ako suma \u0161tvorcov rozdielov medzi priemerom pre ka\u017ed\u00fa skupinu a celkov\u00fdm priemerom (SS, variabilita ktor\u00e1 je vysvetlen\u00e1 nez\u00e1visle premennou). Variabilita vo vn\u00fatri skup\u00edn (chyba) je vyjadren\u00e1 ako suma \u0161tvorcov rozdielov medzi ka\u017edou pozorovanou hodnotou a priemerom pre pr\u00edslu\u0161n\u00fa skupinu (variabilita, ktor\u00e1 je nevysvetlen\u00e1). Tieto rozdiely sa ozna\u010duj\u00fa ako rez\u00eddu\u00e1. Celkov\u00e1 variabilita (spolu) je suma \u0161tvorcov rozdielov medzi ka\u017edou pozorovanou hodnotou a celkov\u00fdm priemerom.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Stupne vo\u013enosti (df) s\u00fa dan\u00e9 rozdielom po\u010dtu pozorovan\u00ed v&nbsp;analyzovanom s\u00fabore a po\u010dtom obmedzen\u00ed, ktor\u00fd je dan\u00fd po\u010dtom pou\u017eit\u00fdch \u0161tatist\u00edk vypo\u010d\u00edtan\u00fdch z v\u00fdberov\u00fdch \u00fadajov. Celkov\u00fd po\u010det stup\u0148ov vo\u013enosti je o jeden men\u0161\u00ed ako celkov\u00fd po\u010det \u00fadajov vo v\u00fdberovom s\u00fabore (<em>n<\/em> \u2013 1)<em>.<\/em> Po\u010det stup\u0148ov vo\u013enosti v&nbsp;r\u00e1mci modelu je o jeden men\u0161\u00ed ako po\u010det pou\u017eit\u00fdch skup\u00edn (<em>m<\/em> \u2013 1). Po\u010det stup\u0148ov vo\u013enosti chyby je celkov\u00fd po\u010det \u00fadajov m\u00ednus po\u010det skup\u00edn (<em>n<\/em> \u2013 <em>m).<\/em><\/p>\n\n\n\n<p class=\"has-small-font-size\">Hodnota p ur\u010duje, na akej hladine v\u00fdznamnosti je mo\u017en\u00e9 zamietn\u00fa\u0165 nulov\u00fa hypot\u00e9zu o zhode stredn\u00fdch hodn\u00f4t. Porovn\u00e1v\u00e1 sa\u00a0s dopredu stanoven\u00fdm \u010d\u00edslom (naj\u010dastej\u0161ie s\u00a0hodnotou 0,05 resp. 0,01). Ak je hodnota men\u0161ia, alebo rovn\u00e1 stanovenej hranici tak nulov\u00fa hypot\u00e9zu zamietame.<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>Vzorov\u00e9 \u00fadaje 1.6 <\/strong><a>(zdroj: Datab\u00e1za \u00fadajov projektu KEGA)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Vzorov\u00e9 \u00fadaje predstavuje s\u00fabor \u00fadajov telesn\u00fdch mier \u0161tudentov, ktor\u00fd obsahu nasledovn\u00e9 premenn\u00e9:<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>PORADIE<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; poradov\u00e9 \u010d\u00edslo z\u00e1znamu<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>POHL<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mu\u017e &#8211; M, \u017eena &#8211; Z<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>VEK<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; vek v rokoch<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>ROK<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; rok merania<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>HMOT<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; hmotnos\u0165 (kg)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>VYSKA<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; telesn\u00e1 v\u00fd\u0161ka (cm)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>OBVODH<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; obvod hrudn\u00edka (cm)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>OBVODP<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; obvod p\u00e1sa (cm)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>OBVODZ<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; obvod z\u00e1p\u00e4stia (cm)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>KRUZOK<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u0161tudijn\u00fd kr\u00fa\u017eok<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>BMI<\/strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; index telesnej hmotnosti (Body Mass Index)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>INDEXHP<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 relat\u00edvny index (pomer obvodu hrudn\u00edka a obvodu p\u00e1sa, %)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"658\" height=\"162\" src=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-3.png\" alt=\"\" class=\"wp-image-669\" srcset=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-3.png 658w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-3-300x74.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-small-font-size\"><strong>Praktick\u00e9 pou\u017eitie programu SAS (SAS En<\/strong>terprise Guide)<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>Pr\u00edklad 1.1 <\/strong>(SAS) &#8211; jednofaktorov\u00e1 anal\u00fdza rozptylu<\/p>\n\n\n\n<p class=\"has-small-font-size\">\u00dalohy (Tasks): Analyze &#8211; ANOVA &#8211; One-Way ANOVA<\/p>\n\n\n\n<p class=\"has-small-font-size\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Overte nulov\u00fa hypot\u00e9zu, \u017ee neexistuje \u0161tatisticky preukazn\u00fd rozdiel medzi priemern\u00fdmi hodnotami ukazovate\u013ea BMI (index telesnej hmotnosti) v\u00a0skupin\u00e1ch \u0161tudentov pod\u013ea rokov zis\u0165ovania telesn\u00fdch mier (pou\u017eite hranicu spo\u013eahlivosti 95 %, alfa = 0,05). Rovnak\u00fa hypot\u00e9zu overte aj v\u00a0trieden\u00ed pod\u013ea pohlavia \u0161tudentov.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"710\" height=\"674\" src=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-4.png\" alt=\"\" class=\"wp-image-670\" srcset=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-4.png 710w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-4-300x285.png 300w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-4-527x500.png 527w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-small-font-size\">Pred samotn\u00fdm pou\u017eit\u00edm jednofaktorovej anal\u00fdzy rozptylu mus\u00edme uskuto\u010dni\u0165 overenie predpokladu, \u017ee hodnoten\u00fd ukazovate\u013e m\u00e1 pribli\u017ene norm\u00e1lne rozdelenie po\u010detnosti. Na overenie predpokladu pou\u017eijeme distribu\u010dn\u00fa anal\u00fdzu hodnoten\u00e9ho ukazovate\u013ea BMI.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"677\" height=\"747\" src=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-5.png\" alt=\"\" class=\"wp-image-671\" srcset=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-5.png 677w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-5-272x300.png 272w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-5-453x500.png 453w\" sizes=\"(max-width: 677px) 100vw, 677px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"665\" height=\"363\" src=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-6.png\" alt=\"\" class=\"wp-image-672\" srcset=\"https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-6.png 665w, https:\/\/e-biostat.uniag.sk\/wp-content\/uploads\/2022\/05\/obrazok-6-300x164.png 300w\" sizes=\"(max-width: 665px) 100vw, 665px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-small-font-size\">Na z\u00e1klade grafick\u00e9ho zn\u00e1zornenia distribu\u010dnej anal\u00fdzy m\u00f4\u017eeme kon\u0161tatova\u0165, \u017ee hodnoten\u00fd ukazovate\u013e m\u00e1 pribli\u017ene norm\u00e1lne rozdelenie a\u00a0preto m\u00f4\u017eeme uskuto\u010dni\u0165 samotn\u00fa jednofaktorov\u00fa anal\u00fdzu rozptylu. Potvrdzuj\u00fa to aj grafy pravdepodobnosti normality percent\u00edl, preto\u017ee jednotliv\u00e9 body le\u017eia v pribli\u017enej priamke, \u010do nazna\u010duje, \u017ee \u00fadaje s\u00fa pribli\u017ene norm\u00e1lne rozlo\u017een\u00e9. Grafick\u00e9 pos\u00fadenie normality je \u00faplne posta\u010duj\u00face. \u010c\u00edseln\u00e9 testy potvrdenie normality nemus\u00edme v\u00a0tomto pr\u00edpade pou\u017ei\u0165.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Anal\u00fdza rozptylu je parametrick\u00e1 \u0161tatistick\u00e1 met\u00f3da vytvoren\u00e1 na vz\u00e1jomn\u00e9 porovn\u00e1vanie znakov viacer\u00fdch skup\u00edn (faktorov, \u010dinite\u013eov), ktor\u00fdch po\u010det je v\u00e4\u010d\u0161\u00ed ako dve. Ve\u013emi zjednodu\u0161ene sa m\u00f4\u017ee poveda\u0165, \u017ee je to v <a href=\"https:\/\/e-biostat.uniag.sk\/?p=654\" class=\"more-link\">[&hellip;]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"Layout":"1c-narrow"},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/654"}],"collection":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=654"}],"version-history":[{"count":6,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/654\/revisions"}],"predecessor-version":[{"id":673,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=\/wp\/v2\/posts\/654\/revisions\/673"}],"wp:attachment":[{"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/e-biostat.uniag.sk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}