{"id":50301,"date":"2024-02-11T11:03:02","date_gmt":"2024-02-11T14:03:02","guid":{"rendered":"https:\/\/mindthegraph.com\/blog\/machine-learning-in-science-copy\/"},"modified":"2024-02-07T11:16:52","modified_gmt":"2024-02-07T14:16:52","slug":"post-hoc-testing-anova","status":"publish","type":"post","link":"https:\/\/mindthegraph.com\/blog\/cs\/post-hoc-testovani-anova\/","title":{"rendered":"Post Hoc testov\u00e1n\u00ed ANOVA: Nau\u010dte se analyzovat soubory dat"},"content":{"rendered":"<p>Napadlo v\u00e1s n\u011bkdy, jak v\u011bdci vyvozuj\u00ed konkr\u00e9tn\u00ed z\u00e1v\u011bry ze skupin dat, kter\u00e9 se na prvn\u00ed pohled zdaj\u00ed b\u00fdt stejn\u011b z\u00e1hadn\u00e9 jako starov\u011bk\u00fd k\u00f3d? No, z\u00e1hadn\u00e9 to p\u0159estane b\u00fdt, jakmile pochop\u00edte kouzlo post hoc testov\u00e1n\u00ed v kontextu ANOVA - anal\u00fdzy rozptylu. Tato statistick\u00e1 metoda nen\u00ed pouh\u00fdm n\u00e1strojem, je podobn\u00e1 lup\u011b Sherlocka Holmese, kter\u00e1 slou\u017e\u00ed k odhalov\u00e1n\u00ed skryt\u00fdch pravd v nes\u010detn\u00fdch \u010d\u00edslech. A\u0165 u\u017e jste student, kter\u00fd se pot\u00fdk\u00e1 s daty sv\u00e9 diplomov\u00e9 pr\u00e1ce, nebo zku\u0161en\u00fd v\u00fdzkumn\u00edk usiluj\u00edc\u00ed o z\u00edsk\u00e1n\u00ed spolehliv\u00fdch v\u00fdsledk\u016f, odhalen\u00ed s\u00edly post hoc test\u016f m\u016f\u017ee va\u0161e zji\u0161t\u011bn\u00ed pov\u00fd\u0161it ze zaj\u00edmav\u00fdch na p\u0159evratn\u00e1.<\/p>\n\n\n\n<h2 id=\"h-understanding-anova-and-post-hoc-testing\">Porozum\u011bn\u00ed ANOV\u011a a Post Hoc testov\u00e1n\u00ed<\/h2>\n\n\n\n<p>P\u0159i pronik\u00e1n\u00ed do vz\u00e1jemn\u011b se prol\u00ednaj\u00edc\u00edch koncept\u016f ANOVA a post hoc testov\u00e1n\u00ed je berte jako partnery p\u0159i snaze o p\u0159esnou anal\u00fdzu. Umo\u017e\u0148uj\u00ed n\u00e1m nahl\u00e9dnout za hranice pr\u016fm\u011brn\u00fdch hodnot a zkoumat hlub\u0161\u00ed nuance mezi porovn\u00e1v\u00e1n\u00edm v\u00edce skupin - postupujme v\u0161ak krok za krokem.<\/p>\n\n\n\n<p>Souvisej\u00edc\u00ed \u010dl\u00e1nek: <a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\"><strong>Post Hoc anal\u00fdza: Postup a typy test\u016f<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-introduction-to-anova-and-its-purpose-in-statistical-analysis\">\u00davod do ANOVA a jej\u00ed \u00fa\u010del ve statistick\u00e9 anal\u00fdze<\/h3>\n\n\n\n<p>Anal\u00fdza rozptylu, neboli ANOVA, jak se j\u00ed mezi statistiky b\u011b\u017en\u011b \u0159\u00edk\u00e1, je jedn\u00edm z nejmocn\u011bj\u0161\u00edch n\u00e1stroj\u016f v jejich arzen\u00e1lu. Pln\u00ed z\u00e1sadn\u00ed funkci - rozli\u0161uje, zda existuj\u00ed statisticky v\u00fdznamn\u00e9 rozd\u00edly mezi pr\u016fm\u011bry skupin v experimentu zahrnuj\u00edc\u00edm t\u0159i nebo v\u00edce skupin. Porovn\u00e1n\u00edm rozptyl\u016f v r\u00e1mci jednotliv\u00fdch skupin s rozptyly mezi t\u011bmito skupinami pom\u00e1h\u00e1 ANOVA zam\u00edtnout nebo zachovat nulovou hypot\u00e9zu, \u017ee neexistuje \u017e\u00e1dn\u00fd rozptyl, kter\u00fd by nebyl zp\u016fsoben n\u00e1hodou.<\/p>\n\n\n\n<h3 id=\"h-explanation-of-post-hoc-testing-and-its-importance-in-anova\">Vysv\u011btlen\u00ed post hoc testov\u00e1n\u00ed a jeho v\u00fdznamu v ANOVA<\/h3>\n\n\n\n<p>Zat\u00edmco identifikace v\u00fdznamnosti ve velk\u00fdch souborech je z\u00e1sadn\u00ed, co se stane, kdy\u017e n\u00e1m ANOVA \u0159ekne, \u017ee se \"n\u011bco\" li\u0161\u00ed, ale nespecifikuje, \"co\" a \"kde\"? Na \u0159adu p\u0159ich\u00e1z\u00ed post hoc testov\u00e1n\u00ed! Post hoc testov\u00e1n\u00ed, zkr\u00e1cen\u011b \"po tomhle\", navazuje na stopu, kterou zanechal omnibusov\u00fd test ANOVA. Jeho posl\u00e1n\u00edm je? P\u0159esn\u011b ur\u010dit, kter\u00e9 dvojice nebo kombinace mezi na\u0161imi skupinami vykazuj\u00ed v\u00fdznamn\u00e9 rozd\u00edly, a umo\u017enit tak v\u00fdzkumn\u00edk\u016fm \u010dinit informovan\u00e1 rozhodnut\u00ed s dokonalou p\u0159esnost\u00ed.<\/p>\n\n\n\n<h3 id=\"h-overview-of-the-process-of-post-hoc-testing-in-anova\">P\u0159ehled procesu post hoc testov\u00e1n\u00ed v ANOVA<\/h3>\n\n\n\n<p>Post hoc testov\u00e1n\u00ed se prov\u00e1d\u00ed v\u017edy po z\u00edsk\u00e1n\u00ed v\u00fdznamn\u00e9ho v\u00fdsledku z omnibusov\u00e9ho testu ANOVA - odtud jeho retrospektivn\u00ed n\u00e1zev. P\u0159edstavte si tento proces, kter\u00fd se skl\u00e1d\u00e1 p\u0159ev\u00e1\u017en\u011b z:<\/p>\n\n\n\n<ul>\n<li><strong>V\u00fdb\u011br vhodn\u00e9ho post hoc testu<\/strong>: V z\u00e1vislosti na specifik\u00e1ch n\u00e1vrhu a toleranci chybovosti.<\/li>\n\n\n\n<li><strong>\u00daprava p-hodnot<\/strong>: Oprava nadhodnocen\u00fdch rizik spojen\u00fdch s v\u00edcen\u00e1sobn\u00fdm srovn\u00e1v\u00e1n\u00edm.<\/li>\n\n\n\n<li><strong>Interpretace v\u00fdsledk\u016f v kontextu<\/strong>: Zaji\u0161t\u011bn\u00ed souladu praktick\u00e9ho v\u00fdznamu se statistick\u00fdmi zji\u0161t\u011bn\u00edmi.<\/li>\n<\/ul>\n\n\n\n<p>Tento disciplinovan\u00fd p\u0159\u00edstup chr\u00e1n\u00ed p\u0159ed fale\u0161n\u00fdmi z\u00e1v\u011bry a z\u00e1rove\u0148 umo\u017e\u0148uje z\u00edskat cenn\u00e9 poznatky, kter\u00e9 v souborech dat d\u0159\u00edmaj\u00ed. Vyzbrojen\u00ed t\u00edmto pokro\u010dil\u00fdm a z\u00e1rove\u0148 p\u0159\u00edstupn\u00fdm porozum\u011bn\u00edm m\u016f\u017ee ka\u017ed\u00e9ho nasm\u011brovat na cestu k ovl\u00e1dnut\u00ed sv\u00fdch datov\u00fdch narativ\u016f.<\/p>\n\n\n\n<h2 id=\"h-anova-omnibus-test\">ANOVA Omnibus test<\/h2>\n\n\n\n<p>P\u0159i anal\u00fdze soubor\u016f dat s v\u00edce ne\u017e dv\u011bma prost\u0159edky, kdy je t\u0159eba zjistit, zda se alespo\u0148 jeden z nich li\u0161\u00ed od ostatn\u00edch, je nezbytn\u00e1 anal\u00fdza rozptylu (ANOVA). Ne\u017e se v\u0161ak pono\u0159\u00edme do slo\u017eitost\u00ed post hoc testov\u00e1n\u00ed v ANOVA, je nezbytn\u00e9 pochopit z\u00e1kladn\u00ed hodnocen\u00ed - omnibusov\u00fd test ANOVA. P\u0159edstavte si to jako detektivn\u00ed p\u0159\u00edb\u011bh, kde prvotn\u00ed d\u016fkazy ukazuj\u00ed na mo\u017enost podez\u0159el\u00e9ho, ale neur\u010duj\u00ed p\u0159esn\u011b koho.<\/p>\n\n\n\n<p>Souvisej\u00edc\u00ed \u010dl\u00e1nek: <a href=\"https:\/\/mindthegraph.com\/blog\/one-way-anova\/\"><strong>Jednosm\u011brn\u00e1 ANOVA: porozum\u011bn\u00ed, proveden\u00ed a prezentace<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-detailed-explanation-of-the-anova-omnibus-test\">Podrobn\u00e9 vysv\u011btlen\u00ed omnibusov\u00e9ho testu ANOVA<\/h3>\n\n\n\n<p>ANOVA omnibus test vynik\u00e1 t\u00edm, \u017ee n\u00e1m umo\u017e\u0148uje porovn\u00e1vat v\u00edce skupinov\u00fdch pr\u016fm\u011br\u016f najednou, m\u00edsto abychom prov\u00e1d\u011bli \u010detn\u00e9 testy pro ka\u017edou hladinu v\u00fdznamnosti v\u0161ech mo\u017en\u00fdch dvojic, co\u017e by nepochybn\u011b zv\u00fd\u0161ilo riziko chyby typu I - fale\u0161n\u011b pozitivn\u00edch v\u00fdsledk\u016f. Slovo \"omnibus\" v n\u00e1zvu nazna\u010duje, \u017ee tento test m\u00e1 celkov\u00fd pohled - hromadn\u011b se ov\u011b\u0159uje, zda mezi pr\u016fm\u011bry skupin existuje n\u011bjak\u00fd statisticky v\u00fdznamn\u00fd rozd\u00edl.<\/p>\n\n\n\n<p>Takto se to vyv\u00edj\u00ed: Za\u010dneme v\u00fdpo\u010dtem odd\u011blen\u00fdch rozptyl\u016f v r\u00e1mci skupin a mezi skupinami. Pokud jsou na\u0161e skupiny vnit\u0159n\u011b pom\u011brn\u011b vyrovnan\u00e9, ale navz\u00e1jem se v\u00fdrazn\u011b li\u0161\u00ed, je to solidn\u00ed ukazatel toho, \u017ee ne v\u0161echny skupinov\u00e9 pr\u016fm\u011bry jsou stejn\u00e9. V podstat\u011b hled\u00e1me variabilitu mezi skupinami b v r\u00e1mci skupiny, kterou nelze vysv\u011btlit pouze n\u00e1hodou vzhledem k variabilit\u011b uvnit\u0159 skupiny - to, co bychom o\u010dek\u00e1vali od n\u00e1hodn\u00fdch v\u00fdkyv\u016f.<\/p>\n\n\n\n<h3 id=\"h-understanding-the-f-statistic-and-its-interpretation\">Porozum\u011bn\u00ed statistice F a jej\u00ed interpretaci<\/h3>\n\n\n\n<p>P\u0159i prov\u00e1d\u011bn\u00ed omnibusov\u00e9ho testu ANOVA vypo\u010d\u00edt\u00e1me takzvanou F-statistiku - hodnotu z\u00edskanou vyd\u011blen\u00edm rozptylu mezi skupinami rozptylem uvnit\u0159 skupiny. Velk\u00e1 hodnota F m\u016f\u017ee nazna\u010dovat v\u00fdznamn\u00e9 rozd\u00edly mezi pr\u016fm\u011bry skupin, proto\u017ee nazna\u010duje, \u017ee variabilita mezi skupinami je vy\u0161\u0161\u00ed ve srovn\u00e1n\u00ed s variabilitou uvnit\u0159 skupin.<\/p>\n\n\n\n<p>Zde je v\u0161ak na m\u00edst\u011b opatrnost: F-statistika se \u0159\u00edd\u00ed specifick\u00fdm rozd\u011blen\u00edm p\u0159i nulov\u00e9 hypot\u00e9ze (kter\u00e1 p\u0159edpokl\u00e1d\u00e1, \u017ee mezi pr\u016fm\u011bry na\u0161ich skupin nen\u00ed \u017e\u00e1dn\u00fd rozd\u00edl). Ne\u017e u\u010din\u00edme z\u00e1v\u011bry zalo\u017een\u00e9 pouze na t\u00e9to statistice, odk\u00e1\u017eeme na toto F-rozd\u011blen\u00ed s ohledem na na\u0161e stupn\u011b volnosti t\u00fdkaj\u00edc\u00ed se jak mezi skupinami, tak uvnit\u0159 skupin, \u010d\u00edm\u017e z\u00edsk\u00e1me p-hodnotu.<\/p>\n\n\n\n<h3 id=\"h-interpreting-the-results-of-the-omnibus-test\">Interpretace v\u00fdsledk\u016f souhrnn\u00e9ho testu<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/images.surferseo.art\/13a9a93f-5e2f-44b6-93cc-f8f1290e4196.jpeg\" alt=\"\"\/><figcaption class=\"wp-element-caption\"><em><strong>Zdroj: <a href=\"https:\/\/pixabay.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pixabay<\/a><\/strong><\/em><\/figcaption><\/figure><\/div>\n\n\n<p>Provedli jste tedy anal\u00fdzu a po porovn\u00e1n\u00ed vypo\u010dten\u00e9 F-statistiky s p\u0159\u00edslu\u0161n\u00fdm rozd\u011blen\u00edm m\u00e1te v ruce onu d\u016fle\u017eitou p-hodnotu - ale co te\u010f? Pokud tato p-hodnota klesne pod va\u0161i prahovou hodnotu - \u010dasto 0,05 - dost\u00e1v\u00e1me se do oblasti zam\u00edtnut\u00ed na\u0161\u00ed nulov\u00e9 hypot\u00e9zy. To nazna\u010duje siln\u00fd d\u016fkaz proti neexistenci \u00fa\u010dinku ve v\u0161ech skupin\u00e1ch.<\/p>\n\n\n\n<p>Nicm\u00e9n\u011b - a tato \u010d\u00e1st je kl\u00ed\u010dov\u00e1 - zast\u0159e\u0161uj\u00edc\u00ed odm\u00edtnut\u00ed n\u00e1s nevede k tomu, kter\u00e9 konkr\u00e9tn\u00ed prost\u0159edky se li\u0161\u00ed, ani o kolik; neur\u010duje, \"kdo to ud\u011blal\" v na\u0161\u00ed d\u0159\u00edv\u011bj\u0161\u00ed detektivn\u00ed analogii. Pouze n\u00e1s informuje, \u017ee v na\u0161\u00ed sestav\u011b je n\u011bco, co stoj\u00ed za dal\u0161\u00ed zkoum\u00e1n\u00ed - co\u017e n\u00e1s p\u0159\u00edmo vede k post hoc testov\u00e1n\u00ed v ANOVA, abychom tyto detailn\u00ed rozd\u00edly mezi konkr\u00e9tn\u00edmi dvojicemi nebo kombinacemi skupin odhalili.<\/p>\n\n\n\n<p>Pochopen\u00ed toho, kdy a pro\u010d post hoc testy n\u00e1sleduj\u00ed po omnibusov\u00e9m testu ANOVA, zajist\u00ed, \u017ee v\u00fdzkumn\u00ed pracovn\u00edci budou se sv\u00fdmi zji\u0161t\u011bn\u00edmi zach\u00e1zet zodpov\u011bdn\u011b, ani\u017e by p\u0159ed\u010dasn\u011b nebo nespr\u00e1vn\u011b p\u0159ech\u00e1zeli k asociac\u00edm nebo kauz\u00e1ln\u00edm tvrzen\u00edm - a z\u00e1rove\u0148 napom\u016f\u017ee jasn\u00e9 komunikaci v jejich oborech studia.<\/p>\n\n\n\n<h2 id=\"h-need-for-post-hoc-testing-in-anova\">Pot\u0159eba post hoc testov\u00e1n\u00ed v ANOVA<\/h2>\n\n\n\n<h3 id=\"h-exploring-the-limitations-of-the-omnibus-test\">Zkoum\u00e1n\u00ed omezen\u00ed souhrnn\u00e9ho testu<\/h3>\n\n\n\n<p>Kdy\u017e rozeb\u00edr\u00e1m slo\u017eitost statistick\u00e9 anal\u00fdzy, je nutn\u00e9 si uv\u011bdomit, \u017ee n\u00e1stroje jako anal\u00fdza rozptylu (ANOVA) jsou sice mocn\u00e9, ale maj\u00ed sv\u00e9 hranice. Omnibusov\u00fd test ANOVA n\u00e1m efektivn\u011b \u0159\u00edk\u00e1, zda n\u011bkde mezi na\u0161imi skupinami existuje statisticky v\u00fdznamn\u00fd rozd\u00edl. P\u0159edpokl\u00e1dejme v\u0161ak, \u017ee byste zkoumali vliv r\u016fzn\u00fdch vyu\u010dovac\u00edch metod na v\u00fdkon \u017e\u00e1k\u016f. V takov\u00e9m p\u0159\u00edpad\u011b by omnibusov\u00fd test mohl odhalit rozd\u00edly mezi v\u0161emi testovan\u00fdmi metodami, ale neur\u010d\u00ed, kde tyto rozd\u00edly le\u017e\u00ed - kter\u00e9 dvojice nebo kombinace v\u00fdukov\u00fdch metod se od sebe v\u00fdznamn\u011b li\u0161\u00ed.<\/p>\n\n\n\n<p>Podstata je n\u00e1sleduj\u00edc\u00ed: ANOVA sice dok\u00e1\u017ee ozna\u010dit, zda se alespo\u0148 dv\u011b skupiny li\u0161\u00ed, ale o podrobnostech ml\u010d\u00ed. To je jako v\u011bd\u011bt, \u017ee m\u00e1te v\u00fdhern\u00ed los, ani\u017e byste znali jeho hodnotu - jist\u011b byste cht\u011bli p\u00e1trat hloub\u011bji po podrobnostech?<\/p>\n\n\n\n<h3 id=\"h-understanding-why-post-hoc-tests-are-necessary\">Pochopen\u00ed toho, pro\u010d jsou post hoc testy nezbytn\u00e9<\/h3>\n\n\n\n<p>P\u0159esn\u011b tady je pot\u0159eba se zam\u011b\u0159it na podrobnosti a prov\u00e9st post hoc testov\u00e1n\u00ed ANOVA. Jakmile ANOVA m\u00e1vne zelen\u00fdm praporkem signalizuj\u00edc\u00edm celkovou v\u00fdznamnost, zb\u00fdvaj\u00ed n\u00e1m jen dr\u00e1\u017ediv\u00e9 ot\u00e1zky: Kter\u00e9 skupiny p\u0159esn\u011b tyto rozd\u00edly zp\u016fsobuj\u00ed? Li\u0161\u00ed se ka\u017ed\u00e1 skupina od ostatn\u00edch, nebo jsou hnac\u00ed silou zm\u011bny jen ty konkr\u00e9tn\u00ed?<\/p>\n\n\n\n<p>Snaha o zodpov\u011bzen\u00ed t\u011bchto ot\u00e1zek bez dal\u0161\u00edho posouzen\u00ed p\u0159edstavuje riziko vyvozen\u00ed nep\u0159esn\u00fdch z\u00e1v\u011br\u016f zalo\u017een\u00fdch na obecn\u00fdch trendech, nikoli na konkr\u00e9tn\u00edch rozd\u00edlech. Post hoc testy jsou vybaveny p\u0159\u00edstupem jemn\u00e9 kombinace, kter\u00fd roz\u010dle\u0148uje data a poskytuje detailn\u00ed vhled do srovn\u00e1n\u00ed jednotliv\u00fdch skupin pot\u00e9, co va\u0161e po\u010d\u00e1te\u010dn\u00ed ANOVA pouk\u00e1zala na \u0161irok\u00e9 rozd\u00edly mezi skupinami.<\/p>\n\n\n\n<p>Tato n\u00e1sledn\u00e1 hodnocen\u00ed p\u0159esn\u011b ur\u010duj\u00ed, kter\u00e9 kontrasty jsou v\u00fdznamn\u00e9, a jsou tak nepostradateln\u00e1 p\u0159i vytv\u00e1\u0159en\u00ed detailn\u00edho porozum\u011bn\u00ed v\u00fdsledk\u016fm.<\/p>\n\n\n\n<h3 id=\"h-the-concept-of-experiment-wise-error-rate\">Koncept chybovosti experimentu<\/h3>\n\n\n\n<p>Z\u00e1sadn\u00ed princip, na kter\u00e9m je zalo\u017eeno rozhodov\u00e1n\u00ed o tom, kdy je post hoc testov\u00e1n\u00ed nezbytn\u00e9, spo\u010d\u00edv\u00e1 v tom, \u010demu statistici \u0159\u00edkaj\u00ed \"m\u00edra chybovosti experimentu\". Jedn\u00e1 se o pravd\u011bpodobnost sp\u00e1ch\u00e1n\u00ed alespo\u0148 jedn\u00e9 chyby typu I v r\u00e1mci v\u0161ech test\u016f hypot\u00e9z proveden\u00fdch v r\u00e1mci experimentu - nikoli pouze v r\u00e1mci jednoho srovn\u00e1n\u00ed, ale kumulativn\u011b v r\u00e1mci v\u0161ech mo\u017en\u00fdch test\u016f post hoc p\u00e1rov\u00e9ho srovn\u00e1n\u00ed.<\/p>\n\n\n\n<p>P\u0159edstavte si, \u017ee ochutn\u00e1v\u00e1te r\u016fzn\u00e9 \u0161ar\u017ee su\u0161enek a sna\u017e\u00edte se zjistit, zda n\u011bkter\u00e1 chu\u0165 vynik\u00e1 jako chutn\u011bj\u0161\u00ed. Ka\u017edou ochutn\u00e1vkou se zvy\u0161uje pravd\u011bpodobnost, \u017ee jednu v\u00e1rku nespr\u00e1vn\u011b prohl\u00e1s\u00edte za nejlep\u0161\u00ed pouze d\u00edky n\u00e1hod\u011b - \u010d\u00edm v\u00edce porovn\u00e1n\u00ed provedete, t\u00edm vy\u0161\u0161\u00ed je riziko chybn\u00e9ho \u00fasudku, proto\u017ee n\u011bkter\u00e1 zji\u0161t\u011bn\u00ed mohou b\u00fdt fale\u0161n\u00fdm poplachem.<\/p>\n\n\n\n<p>Post hoc testov\u00e1n\u00ed p\u0159in\u00e1\u0161\u00ed do na\u0161eho statistick\u00e9ho n\u00e1stroje sofistikovanost t\u00edm, \u017ee zohled\u0148uje tuto kumulativn\u00ed chybu a kontroluje ji pomoc\u00ed upraven\u00fdch p-hodnot - postup ur\u010den\u00fd nejen pro zv\u00fd\u0161en\u00ed p\u0159esnosti, ale tak\u00e9 pro d\u016fv\u011bru v platnost a spolehlivost na\u0161ich z\u00e1v\u011br\u016f.<\/p>\n\n\n\n<h2 id=\"h-different-post-hoc-testing-methods\">R\u016fzn\u00e9 metody post-Hoc testov\u00e1n\u00ed<\/h2>\n\n\n\n<p>Po proveden\u00ed anal\u00fdzy ANOVA, kter\u00e1 v\u00e1m \u0159ekne, zda existuje statisticky v\u00fdznamn\u00fd vliv mezi pr\u016fm\u011bry skupin, je pom\u011brn\u011b \u010dast\u00e9 se pt\u00e1t, v \u010dem vlastn\u011b rozd\u00edly spo\u010d\u00edvaj\u00ed. Pr\u00e1v\u011b zde p\u0159ich\u00e1z\u00ed na \u0159adu post hoc testov\u00e1n\u00ed - p\u0159edstavte si ho jako bli\u017e\u0161\u00ed nahl\u00e9dnut\u00ed do p\u0159\u00edb\u011bhu va\u0161ich dat, abyste pochopili roli ka\u017ed\u00e9 postavy. Poj\u010fme se do t\u00e9to problematiky pono\u0159it hloub\u011bji pomoc\u00ed n\u011bkolika metod, kter\u00e9 tyto nuance p\u0159\u00edb\u011bh\u016f osv\u011btluj\u00ed.<\/p>\n\n\n\n<h3 id=\"h-tukey-s-method\">Tukeyho metoda<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-tukey-s-method-and-its-application-in-anova\">Vysv\u011btlen\u00ed Tukeyho metody a jej\u00ed pou\u017eit\u00ed v ANOVA<\/h4>\n\n\n\n<p><strong>Tukeyho \u010destn\u00fd signifikantn\u00ed rozd\u00edl (HSD)<\/strong> je jedn\u00edm z nejpou\u017e\u00edvan\u011bj\u0161\u00edch post hoc test\u016f po ANOVA. Kdy\u017e zjist\u00edte, \u017ee ne v\u0161echny pr\u016fm\u011bry skupin jsou stejn\u00e9, ale pot\u0159ebujete v\u011bd\u011bt, kter\u00e9 konkr\u00e9tn\u00ed pr\u016fm\u011bry se li\u0161\u00ed, nastupuje Tukeyho metoda. Porovn\u00e1v\u00e1 v\u0161echny mo\u017en\u00e9 dvojice pr\u016fm\u011br\u016f a z\u00e1rove\u0148 kontroluje m\u00edru chyby typu I v t\u011bchto porovn\u00e1n\u00edch. Tato vlastnost ji \u010din\u00ed obzvl\u00e1\u0161t\u011b u\u017eite\u010dnou, pokud pracujete s v\u00edce skupinami a vy\u017eadujete testy v\u00edcen\u00e1sobn\u00e9ho porovn\u00e1n\u00ed robustn\u00ed anal\u00fdzu.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values\">V\u00fdpo\u010det a interpretace upraven\u00fdch p-hodnot<\/h4>\n\n\n\n<p>Tukeyho metoda zahrnuje v\u00fdpo\u010det souboru \"upraven\u00fdch\" p-hodnot pro ka\u017ed\u00e9 p\u00e1rov\u00e9 srovn\u00e1n\u00ed pr\u016fm\u011br\u016f skupin. V\u00fdpo\u010det vych\u00e1z\u00ed ze studovan\u00e9ho rozd\u011blen\u00ed rozsahu, kter\u00e9 zohled\u0148uje rozptyly uvnit\u0159 skupiny i mezi skupinami - to v\u0161e je pom\u011brn\u011b slo\u017eit\u00e9, ale pro interpretaci nuanc\u00ed v datech z\u00e1sadn\u00ed. D\u016fle\u017eit\u00e9 je, abyste tyto p-hodnoty upravili tak, aby zohled\u0148ovaly zv\u00fd\u0161en\u00fd potenci\u00e1l chyb typu I v d\u016fsledku v\u00edcen\u00e1sobn\u00fdch srovn\u00e1n\u00ed. Pokud ur\u010dit\u00e1 upraven\u00e1 p-hodnota klesne pod pr\u00e1h v\u00fdznamnosti (obvykle 0,05), m\u016f\u017eete prohl\u00e1sit, \u017ee mezi t\u011bmito dv\u011bma skupinov\u00fdmi pr\u016fm\u011bry je v\u00fdznamn\u00fd rozd\u00edl.<\/p>\n\n\n\n<h4 id=\"h-using-simultaneous-confidence-intervals-with-tukey-s-method\">Pou\u017eit\u00ed simult\u00e1nn\u00edch interval\u016f spolehlivosti s Tukeyho metodou<\/h4>\n\n\n\n<p>Dal\u0161\u00edm mocn\u00fdm aspektem Tukeyho testu je jeho schopnost vytv\u00e1\u0159et sou\u010dasn\u011b intervaly spolehlivosti pro v\u0161echny rozd\u00edly pr\u016fm\u011br\u016f. Toto vizu\u00e1ln\u00ed zn\u00e1zorn\u011bn\u00ed pr\u016fm\u011brn\u00fdch rozd\u00edl\u016f pom\u00e1h\u00e1 v\u00fdzkumn\u00edk\u016fm nejen zjistit, kter\u00e9 skupiny se li\u0161\u00ed, ale tak\u00e9 pochopit velikost a sm\u011br t\u011bchto rozd\u00edl\u016f - co\u017e je neoceniteln\u00fd poznatek p\u0159i vykreslov\u00e1n\u00ed budouc\u00edho v\u00fdzkumu nebo praktick\u00fdch aplikac\u00ed.<\/p>\n\n\n\n<h3 id=\"h-holm-s-method\">Holmova metoda<\/h3>\n\n\n\n<h4 id=\"h-introduction-to-holm-s-method-and-its-advantages-over-other-methods\">\u00davod do Holmovy metody a jej\u00ed v\u00fdhody oproti jin\u00fdm metod\u00e1m<\/h4>\n\n\n\n<p>\u0158azen\u00ed rychlostn\u00edch stup\u0148\u016f, <strong>Holmova metoda<\/strong>, zn\u00e1m\u00fd tak\u00e9 jako Holm\u016fv sekven\u010dn\u00ed Bonferroniho postup, poskytuje alternativn\u00ed zp\u016fsob post hoc testov\u00e1n\u00ed, p\u0159i kter\u00e9m je v centru pozornosti ochrana p\u0159ed chybami typu I - upravuje p-hodnoty jako pe\u010dliv\u00fd kur\u00e1tor, kter\u00fd chr\u00e1n\u00ed cenn\u00e9 artefakty p\u0159ed nevhodn\u00fdm vystaven\u00edm. Jeho nejp\u0159ekvapiv\u011bj\u0161\u00ed v\u00fdhoda spo\u010d\u00edv\u00e1 v procedur\u00e1ln\u00ed flexibilit\u011b; na rozd\u00edl od n\u011bkter\u00fdch metod, kter\u00e9 se op\u00edraj\u00ed o jednostup\u0148ov\u00e9 \u00fapravy, Holm\u016fv postup s postupn\u00fdm sni\u017eov\u00e1n\u00edm nab\u00edz\u00ed v\u011bt\u0161\u00ed s\u00edlu a z\u00e1rove\u0148 obranu proti statistick\u00fdm chyb\u00e1m vypl\u00fdvaj\u00edc\u00edm z mnoha srovn\u00e1n\u00ed.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values-with-holm-s-method\">V\u00fdpo\u010det a interpretace upraven\u00fdch p-hodnot pomoc\u00ed Holmovy metody<\/h4>\n\n\n\n<p>D\u016fkladn\u00e9 se\u0159azen\u00ed zahrnuje se\u0159azen\u00ed na\u0161ich po\u010d\u00e1te\u010dn\u00edch neupraven\u00fdch p-hodnot od nejmen\u0161\u00ed po nejv\u011bt\u0161\u00ed a jejich postupn\u00e9 zkoum\u00e1n\u00ed na z\u00e1klad\u011b upraven\u00fdch \u00farovn\u00ed alfa na z\u00e1klad\u011b jejich po\u0159ad\u00ed - jak\u00fdsi proces \"sestupn\u00e9ho hodnocen\u00ed\", dokud nenaraz\u00edme na hodnotu, kter\u00e1 je tvrdohlav\u011b vy\u0161\u0161\u00ed ne\u017e n\u00e1mi vypo\u010dten\u00e1 prahov\u00e1 hodnota; v tomto bod\u011b jsou vod\u00edtka vy\u0159azena.<\/p>\n\n\n\n<h3 id=\"h-dunnett-s-method\">Dunnettova metoda<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-dunnett-s-method-and-when-it-is-appropriate-to-use-it\">Vysv\u011btlen\u00ed Dunnettovy metody a kdy je vhodn\u00e9 ji pou\u017e\u00edt<\/h4>\n\n\n\n<p>Zde m\u00e1me <strong>Dunnett\u016fv test<\/strong>, se vyzna\u010duje c\u00edlen\u00fdm p\u0159\u00edstupem: porovn\u00e1v\u00e1 v\u00edce skupin o\u0161et\u0159en\u00ed konkr\u00e9tn\u011b s jednou kontroln\u00ed skupinou - b\u011b\u017en\u00fd sc\u00e9n\u00e1\u0159 v klinick\u00fdch studi\u00edch nebo agronomick\u00fdch studi\u00edch, kde m\u016f\u017eete cht\u00edt porovnat nov\u00e1 o\u0161et\u0159en\u00ed se standardem nebo placebem.<\/p>\n\n\n\n<h4 id=\"h-comparing-treatment-groups-to-a-control-group-using-dunnett-s-method\">Srovn\u00e1n\u00ed o\u0161et\u0159en\u00fdch skupin s kontroln\u00ed skupinou pomoc\u00ed Dunnettovy metody<\/h4>\n\n\n\n<p>Na rozd\u00edl od jin\u00fdch p\u0159\u00edstup\u016f, kter\u00e9 rozprost\u00edraj\u00ed \u0161ir\u0161\u00ed s\u00edt\u011b nap\u0159\u00ed\u010d v\u0161emi mo\u017en\u00fdmi srovn\u00e1n\u00edmi, Dunnettova proz\u00edravost se zam\u011b\u0159uje pouze na to, jak si ka\u017ed\u00fd kandid\u00e1t stoj\u00ed vedle n\u00e1mi zvolen\u00e9ho referen\u010dn\u00edho bodu. Pe\u010dliv\u011b tak vypo\u010d\u00edt\u00e1v\u00e1, o kolik v\u011bt\u0161\u00ed p\u00e1ku - nebo ne - z\u00edsk\u00e1me z va\u0161ich z\u00e1sah\u016f oproti tomu, kdy\u017e neud\u011bl\u00e1me v\u016fbec nic nebo z\u016fstaneme u toho, co se dosud osv\u011bd\u010dilo.<\/p>\n\n\n\n<p>Tyto r\u016fzn\u00e9 n\u00e1stroje post hoc testov\u00e1n\u00ed v r\u00e1mci ANOVA n\u00e1m, statistik\u016fm a datov\u00fdm analytik\u016fm, umo\u017e\u0148uj\u00ed odhalit detaily ze soubor\u016f dat, kter\u00e9 p\u0159ekypuj\u00ed potenci\u00e1ln\u00edmi poznatky, je\u017e \u010dekaj\u00ed pod jejich \u010d\u00edseln\u00fdm povrchem - ka\u017ed\u00fd z nich je trochu jinak uzp\u016fsoben k odhalen\u00ed skryt\u00fdch p\u0159\u00edb\u011bh\u016f vetkan\u00fdch do struktury na\u0161ich empirick\u00fdch \u0161et\u0159en\u00ed.<\/p>\n\n\n\n<h2 id=\"h-factors-to-consider-in-choosing-a-post-hoc-test\">Faktory, kter\u00e9 je t\u0159eba zv\u00e1\u017eit p\u0159i v\u00fdb\u011bru post-hoc testu<\/h2>\n\n\n\n<p>Kdy\u017e se pust\u00edte do oblasti ANOVA, po zji\u0161t\u011bn\u00ed v\u00fdznamn\u00e9ho rozd\u00edlu mezi skupinami pomoc\u00ed souhrnn\u00e9ho testu ANOVA je dal\u0161\u00edm krokem \u010dasto pou\u017eit\u00ed post hoc test\u016f, abyste p\u0159esn\u011b ur\u010dili, v \u010dem tyto rozd\u00edly spo\u010d\u00edvaj\u00ed. Nyn\u00ed v\u00e1s sezn\u00e1m\u00edm s jedn\u00edm z rozhoduj\u00edc\u00edch faktor\u016f, kter\u00fd by m\u011bl ovlivnit v\u00fdb\u011br post hoc testu: kontrola chybovosti v rodin\u011b.<\/p>\n\n\n\n<h3 id=\"h-famil-wise-error-rate-control-and-its-significance-in-choosing-a-test-method\">Rodinn\u00e1 kontrola chybovosti a jej\u00ed v\u00fdznam p\u0159i v\u00fdb\u011bru zku\u0161ebn\u00ed metody<\/h3>\n\n\n\n<p>Term\u00edn \"rodinn\u00e1 chybovost\" (FWER) ozna\u010duje pravd\u011bpodobnost, \u017ee p\u0159i prov\u00e1d\u011bn\u00ed v\u00edcen\u00e1sobn\u00fdch p\u00e1rov\u00fdch test\u016f dojde alespo\u0148 k jedn\u00e9 chyb\u011b typu I ze v\u0161ech mo\u017en\u00fdch srovn\u00e1n\u00ed. K chyb\u011b typu I doch\u00e1z\u00ed, kdy\u017e nespr\u00e1vn\u011b dojdete k z\u00e1v\u011bru, \u017ee mezi skupinami existuj\u00ed rozd\u00edly, i kdy\u017e ve skute\u010dnosti neexistuj\u00ed. Pokud nen\u00ed spr\u00e1vn\u011b kontrolov\u00e1na, s t\u00edm, jak v r\u00e1mci ANOVA prov\u00e1d\u00edme st\u00e1le v\u00edce v\u00edcen\u00e1sobn\u00fdch p\u00e1rov\u00fdch srovn\u00e1n\u00ed, pravd\u011bpodobnost ne\u00famysln\u00e9ho prohl\u00e1\u0161en\u00ed nespr\u00e1vn\u00e9 v\u00fdznamnosti balancuje na hran\u011b - co\u017e m\u016f\u017ee va\u0161i studii vyv\u00e9st z omylu.<\/p>\n\n\n\n<p>I kdy\u017e to zn\u00ed hroziv\u011b, nebojte se, pr\u00e1v\u011b proto jsou kontroln\u00ed metody FWER z\u00e1sadn\u00edm prvkem p\u0159i v\u00fdb\u011bru post hoc testu. Tyto metody v podstat\u011b upravuj\u00ed va\u0161e prahy v\u00fdznamnosti nebo p-hodnoty tak, aby souhrnn\u00e9 riziko v\u0161ech test\u016f nep\u0159ekro\u010dilo va\u0161i p\u016fvodn\u00ed \u00farove\u0148 p\u0159ijatelnosti chyb (obvykle 0,05). T\u00edmto zp\u016fsobem m\u016f\u017eeme s jistotou zkoumat specifick\u00e9 skupinov\u00e9 rozd\u00edly, ani\u017e bychom stup\u0148ovali pravd\u011bpodobnost fale\u0161n\u00fdch objev\u016f.<\/p>\n\n\n\n<p>Kontrola FWER zachov\u00e1v\u00e1 integritu va\u0161ich zji\u0161t\u011bn\u00ed a dodr\u017euje v\u011bdeckou p\u0159\u00edsnost nezbytnou pro vz\u00e1jemn\u00e9 hodnocen\u00ed a reprodukovatelnost.<\/p>\n\n\n\n<p>Nyn\u00ed si p\u0159edstavte, \u017ee m\u00e1te p\u0159ed sebou r\u016fzn\u00e9 mo\u017enosti post hoc testov\u00e1n\u00ed - pochopen\u00ed FWER v\u00e1m pom\u016f\u017ee odpov\u011bd\u011bt na kl\u00ed\u010dov\u00e9 ot\u00e1zky:<\/p>\n\n\n\n<ul>\n<li>Kolik srovn\u00e1n\u00ed bude v m\u00e9m pl\u00e1nu studie provedeno?<\/li>\n\n\n\n<li>Jak konzervativn\u00ed mus\u00edm b\u00fdt p\u0159i kontrole chyb typu I vzhledem k oboru nebo v\u00fdzkumn\u00e9 ot\u00e1zce?<\/li>\n<\/ul>\n\n\n\n<p>Nap\u0159\u00edklad Tukeyho HSD (Honestly Significant Difference) je nejvhodn\u011bj\u0161\u00ed, pokud prov\u00e1d\u00edme v\u0161echna mo\u017en\u00e1 p\u00e1rov\u00e1 srovn\u00e1n\u00ed a porovn\u00e1n\u00ed a sna\u017e\u00edme se udr\u017eet chybovost v rodin\u011b na \u00farovni alfa (\u010dasto 0,05). Holmova metoda nastupuje postupnou \u00fapravou p-hodnot a nalezen\u00edm rovnov\u00e1hy - je m\u00e9n\u011b konzervativn\u00ed ne\u017e Bonferroniho metoda, ale st\u00e1le nab\u00edz\u00ed rozumnou ochranu p\u0159ed chybami typu I. A pokud je ve va\u0161em n\u00e1vrhu zahrnuta jedin\u00e1 kontroln\u00ed nebo referen\u010dn\u00ed skupina? Pak m\u016f\u017ee p\u0159ij\u00edt ke slovu Dunnettova metoda, proto\u017ee se konkr\u00e9tn\u011b zab\u00fdv\u00e1 srovn\u00e1n\u00edm s t\u00edmto \u00fast\u0159edn\u00edm \u00fadajem.<\/p>\n\n\n\n<p>Z\u00e1v\u011brem:<\/p>\n\n\n\n<p>\u00da\u010dinn\u00e9 zm\u00edrn\u011bn\u00ed rizik spojen\u00fdch se zv\u00fd\u0161en\u00fdm testov\u00e1n\u00edm hypot\u00e9z vy\u017eaduje chytr\u00fd v\u00fdb\u011br metod statistick\u00e9 anal\u00fdzy. Kdy\u017e se po v\u00fdsledku ANOVA, kter\u00fd nazna\u010duje v\u00fdznamn\u00fd rozptyl mezi skupinami, vrhnete po hlav\u011b do post hoc testov\u00e1n\u00ed, v\u017edy si pamatujte: Je to va\u0161e pojistka zaji\u0161\u0165uj\u00edc\u00ed spolehlivost a platnost z\u00e1v\u011br\u016f vyvozen\u00fdch ze slo\u017eit\u00fdch datov\u00fdch vzorc\u016f.<\/p>\n\n\n\n<h2 id=\"h-case-studies-and-examples\">P\u0159\u00edpadov\u00e9 studie a p\u0159\u00edklady<\/h2>\n\n\n\n<p>Pochopen\u00ed pojm\u016f ve statistice je v\u00fdrazn\u011b pos\u00edleno zkoum\u00e1n\u00edm re\u00e1ln\u00fdch aplikac\u00ed. Poj\u010fme se pod\u00edvat, jak post hoc testov\u00e1n\u00ed ANOVA vdechuje \u017eivot v\u00fdzkumn\u00fdm studi\u00edm a prop\u016fj\u010duje v\u011bdeck\u00fdm \u0161et\u0159en\u00edm p\u0159\u00edsnou metodu pro zkoum\u00e1n\u00ed jejich v\u00fdsledk\u016f.<\/p>\n\n\n\n<h3 id=\"h-discussion-of-real-world-research-studies-where-post-hoc-testing-was-used\">Diskuse o v\u00fdzkumn\u00fdch studi\u00edch, v nich\u017e bylo pou\u017eito post hoc testov\u00e1n\u00ed<\/h3>\n\n\n\n<p>Post hoc anal\u00fdzy a testy, zkouman\u00e9 optikou praktick\u00e9ho pou\u017eit\u00ed, se st\u00e1vaj\u00ed v\u00edce ne\u017e abstraktn\u00edmi matematick\u00fdmi postupy; jsou to n\u00e1stroje, kter\u00e9 v datech rozv\u00edjej\u00ed p\u0159\u00edb\u011bhy. Nap\u0159\u00edklad studie zam\u011b\u0159en\u00e1 na efektivitu r\u016fzn\u00fdch metodik v\u00fduky m\u016f\u017ee pou\u017e\u00edt ANOVA, aby zjistila, zda existuj\u00ed v\u00fdznamn\u00e9 rozd\u00edly ve v\u00fdsledc\u00edch student\u016f v z\u00e1vislosti na v\u00fdukov\u00e9m p\u0159\u00edstupu. Pokud souhrnn\u00fd test p\u0159inese v\u00fdznamn\u00fd v\u00fdsledek, otev\u0159e cestu k post hoc anal\u00fdze - nezbytn\u00e9 pro p\u0159esn\u00e9 ur\u010den\u00ed, kter\u00e9 metody se od sebe li\u0161\u00ed.<\/p>\n\n\n\n<p>Dovolte mi, abych se pod\u011blil o dal\u0161\u00ed p\u0159\u00edklad, kter\u00fd tuto metodiku podtrhuje: P\u0159edstavte si, \u017ee v\u00fdzkumn\u00edci provedli post hoc anal\u00fdzu experimentu hodnot\u00edc\u00edho vliv nov\u00e9ho l\u00e9ku na hladinu krevn\u00edho tlaku. Po\u010d\u00e1te\u010dn\u00ed ANOVA ukazuje, \u017ee hodnoty krevn\u00edho tlaku se v r\u016fzn\u00fdch skupin\u00e1ch d\u00e1vkov\u00e1n\u00ed v pr\u016fb\u011bhu \u010dasu v\u00fdznamn\u011b li\u0161\u00ed. Jako dal\u0161\u00ed d\u016fle\u017eit\u00fd krok nastupuje post hoc testov\u00e1n\u00ed, kter\u00e9 v\u011bdc\u016fm pom\u00e1h\u00e1 porovnat v\u0161echny mo\u017en\u00e9 dvojice d\u00e1vek, aby konkr\u00e9tn\u011b pochopili, kter\u00e9 z nich jsou \u00fa\u010dinn\u00e9 a kter\u00e9 potenci\u00e1ln\u011b \u0161kodliv\u00e9.<\/p>\n\n\n\n<p>Tyto p\u0159\u00edklady ukazuj\u00ed, jak post hoc testov\u00e1n\u00ed po ANOVA nejen\u017ee vede v\u00fdzkumn\u00e9 pracovn\u00edky na jejich cest\u011b za objevem, ale tak\u00e9 zaji\u0161\u0165uje robustnost a p\u0159esnost jejich z\u00e1v\u011br\u016f.<\/p>\n\n\n\n<h3 id=\"h-hands-on-examples-illustrating-the-application-of-different-post-hoc-tests\">Praktick\u00e9 p\u0159\u00edklady ilustruj\u00edc\u00ed pou\u017eit\u00ed r\u016fzn\u00fdch post hoc test\u016f<\/h3>\n\n\n\n<p>Hlub\u0161\u00ed prozkoum\u00e1n\u00ed v\u00edce srovn\u00e1vac\u00edch test\u016f pro konkr\u00e9tn\u00ed aplikace m\u016f\u017ee poskytnout p\u0159ehled o tom, jak rozmanit\u00e9 tyto testy mohou b\u00fdt:<\/p>\n\n\n\n<ul>\n<li><strong>Tukeyho metoda<\/strong>: Vezm\u011bte si zem\u011bd\u011blsk\u00e9 v\u011bdce, kte\u0159\u00ed porovn\u00e1vaj\u00ed v\u00fdnosy plodin u r\u016fzn\u00fdch typ\u016f hnojiv. Po zji\u0161t\u011bn\u00ed v\u00fdznamn\u00fdch rozd\u00edl\u016f ve v\u00fdnosu mezi jednotliv\u00fdmi zp\u016fsoby hnojen\u00ed by Tukeyho metoda mohla p\u0159esn\u011b odhalit, kter\u00e1 hnojiva d\u00e1vaj\u00ed statisticky odli\u0161n\u00e9 v\u00fdnosy ve srovn\u00e1n\u00ed s ostatn\u00edmi - a to v\u0161e p\u0159i kontrole chyby typu I ve v\u0161ech srovn\u00e1n\u00edch.<\/li>\n\n\n\n<li><strong>Holmova metoda<\/strong>: V psychologick\u00e9m v\u00fdzkumu, jeho\u017e c\u00edlem je porozum\u011bt v\u00fdsledk\u016fm terapie, by Holm\u016fv sekven\u010dn\u00ed postup upravil p-hodnoty, pokud se hodnot\u00ed v\u00edce forem l\u00e9\u010dby oproti kontroln\u00edm skupin\u00e1m. To zaji\u0161\u0165uje, \u017ee n\u00e1sledn\u00e1 zji\u0161t\u011bn\u00ed z\u016fstanou spolehliv\u00e1 i pot\u00e9, co se zjist\u00ed, \u017ee n\u011bkter\u00e9 terapie jsou lep\u0161\u00ed ne\u017e \u017e\u00e1dn\u00e1 l\u00e9\u010dba.<\/li>\n\n\n\n<li><strong>Dunnettova metoda<\/strong>: Dunnettova metoda se \u010dasto pou\u017e\u00edv\u00e1 v klinick\u00fdch studi\u00edch se skupinou placeba, kdy se ka\u017ed\u00e1 l\u00e9\u010dba porovn\u00e1v\u00e1 p\u0159\u00edmo s placebem. Studie hodnot\u00edc\u00ed n\u011bkolik nov\u00fdch l\u00e9k\u016f proti bolesti ve srovn\u00e1n\u00ed s placebem by mohla vyu\u017e\u00edt Dunnettovu metodu k rozli\u0161en\u00ed, zda m\u00e1 n\u011bkter\u00fd nov\u00fd l\u00e9k lep\u0161\u00ed \u00fa\u010dinek, ani\u017e by se zv\u00fd\u0161ilo riziko fale\u0161n\u011b pozitivn\u00edch v\u00fdsledk\u016f v d\u016fsledku v\u00edcen\u00e1sobn\u00e9ho srovn\u00e1n\u00ed.<\/li>\n<\/ul>\n\n\n\n<p>Tyto st\u0159\u00edpky z r\u016fzn\u00fdch obor\u016f zd\u016fraz\u0148uj\u00ed, jak p\u0159izp\u016fsoben\u00e9 post hoc testov\u00e1n\u00ed v ANOVA d\u00e1v\u00e1 podstatu ni\u017e\u0161\u00ed statistick\u00e9 s\u00edle v\u00fdznamnosti - p\u0159em\u011b\u0148uje \u010d\u00edsla na smyslupln\u00e9 poznatky, kter\u00e9 mohou pomoci formovat pr\u016fmysl a zlep\u0161ovat \u017eivoty.<\/p>\n\n\n\n<h2 id=\"h-statistical-power-in-post-hoc-testing\">Statistick\u00e1 s\u00edla p\u0159i post-Hoc testov\u00e1n\u00ed<\/h2>\n\n\n\n<h3 id=\"h-explanation-of-statistical-power-and-its-importance-in-post-hoc-testing-decision-making\">Vysv\u011btlen\u00ed statistick\u00e9 s\u00edly a jej\u00edho v\u00fdznamu p\u0159i rozhodov\u00e1n\u00ed o post hoc testech<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/images.surferseo.art\/290f22f3-906a-4d32-bf9f-a332b21fa8bb.jpeg\" alt=\"\"\/><figcaption class=\"wp-element-caption\"><em><strong>Zdroj: <a href=\"https:\/\/pixabay.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pixabay<\/a><\/strong><\/em><\/figcaption><\/figure><\/div>\n\n\n<p>P\u0159i diskusi o slo\u017eitostech post hoc testov\u00e1n\u00ed v\u00fdsledk\u016f ANOVA je nezbytn\u00e9 pochopit koncept, kter\u00fd je z\u00e1kladem testov\u00e1n\u00ed hypot\u00e9z - statistickou s\u00edlu. Zjednodu\u0161en\u011b \u0159e\u010deno, statistick\u00e1 s\u00edla je pravd\u011bpodobnost, \u017ee studie odhal\u00ed \u00fa\u010dinek, pokud skute\u010dn\u011b existuje. To se prom\u00edt\u00e1 do zji\u0161t\u011bn\u00ed skute\u010dn\u00fdch rozd\u00edl\u016f mezi skupinami, pokud skute\u010dn\u011b existuj\u00ed.<\/p>\n\n\n\n<p>Vysok\u00e1 statistick\u00e1 s\u00edla sni\u017euje pravd\u011bpodobnost, \u017ee se dopust\u00edme chyby typu II, kter\u00e1 nastane, kdy\u017e nezjist\u00edme rozd\u00edl, kter\u00fd skute\u010dn\u011b existuje. Chr\u00e1n\u00ed na\u0161e v\u00fdsledky p\u0159ed fale\u0161n\u011b negativn\u00edmi v\u00fdsledky, \u010d\u00edm\u017e posiluje spolehlivost z\u00e1v\u011br\u016f vyvozen\u00fdch z na\u0161\u00ed anal\u00fdzy. Tento faktor se st\u00e1v\u00e1 obzvl\u00e1\u0161t\u011b d\u016fle\u017eit\u00fdm p\u0159i post hoc testech pot\u00e9, co ANOVA nazna\u010dila v\u00fdznamn\u00e9 rozd\u00edly mezi skupinami.<\/p>\n\n\n\n<p>Dosa\u017een\u00ed vysok\u00e9 statistick\u00e9 s\u00edly v praxi \u010dasto znamen\u00e1 zajistit, aby va\u0161e studie m\u011bla dostate\u010dn\u011b velk\u00fd vzorek. Zat\u00edmco p\u0159\u00edli\u0161 mal\u00fd vzorek nemus\u00ed p\u0159esn\u011b odr\u00e1\u017eet skute\u010dn\u00e9 skupinov\u00e9 rozd\u00edly, mimo\u0159\u00e1dn\u011b velk\u00e9 vzorky by mohly odhalit statisticky v\u00fdznamn\u00e9, ale prakticky irelevantn\u00ed rozd\u00edly. Proto je vyv\u00e1\u017een\u00ed t\u011bchto hledisek z\u00e1sadn\u00ed pro p\u0159esv\u011bd\u010div\u00e9 rozhodov\u00e1n\u00ed v jak\u00e9mkoli v\u00fdzkumn\u00e9m prost\u0159ed\u00ed zahrnuj\u00edc\u00edm post hoc testov\u00e1n\u00ed ANOVA.<\/p>\n\n\n\n<h3 id=\"h-managing-power-trade-offs-by-reducing-the-number-of-comparisons\">\u0158\u00edzen\u00ed v\u00fdkonov\u00fdch kompromis\u016f sn\u00ed\u017een\u00edm po\u010dtu porovn\u00e1v\u00e1n\u00ed<\/h3>\n\n\n\n<p>Aby se v\u00fdzkumn\u00edci vypo\u0159\u00e1dali s potenci\u00e1ln\u00edmi \u00faskal\u00edmi spojen\u00fdmi s v\u00edcen\u00e1sobn\u00fdm srovn\u00e1v\u00e1n\u00edm po proveden\u00ed metody ANOVA, m\u011bli by uv\u00e1\u017eliv\u011b zvl\u00e1dnout kompromis mezi zachov\u00e1n\u00edm dostate\u010dn\u00e9 statistick\u00e9 s\u00edly a kontrolou zv\u00fd\u0161en\u00e9ho rizika chyb typu I (fale\u0161n\u011b pozitivn\u00edch v\u00fdsledk\u016f). Zde jsou uvedeny \u00fa\u010dinn\u00e9 strategie:<\/p>\n\n\n\n<ul>\n<li>Stanoven\u00ed priorit: Ur\u010dete, kter\u00e1 porovn\u00e1n\u00ed jsou pro va\u0161e hypot\u00e9zy nejd\u016fle\u017eit\u011bj\u0161\u00ed, a ta up\u0159ednostn\u011bte pro dal\u0161\u00ed zkoum\u00e1n\u00ed.<\/li>\n\n\n\n<li>Konsolidace: M\u00edsto zkoum\u00e1n\u00ed v\u0161ech mo\u017en\u00fdch p\u00e1rov\u00fdch srovn\u00e1n\u00ed mezi jednotliv\u00fdmi \u00farovn\u011bmi l\u00e9\u010dby se zam\u011b\u0159te pouze na porovn\u00e1n\u00ed ka\u017ed\u00e9 l\u00e9\u010debn\u00e9 skupiny s kontroln\u00ed skupinou nebo spojte l\u00e9\u010debn\u00e9 skupiny do smyslupln\u00fdch kategori\u00ed.<\/li>\n<\/ul>\n\n\n\n<p>Promy\u0161len\u00fdm v\u00fdb\u011brem men\u0161\u00edho po\u010dtu srovn\u00e1n\u00ed v\u00fdzkumn\u00edci nejen zvy\u0161uj\u00ed \u0161anci, \u017ee si jejich studie zachov\u00e1 robustn\u00ed statistickou s\u00edlu, ale tak\u00e9 sni\u017euj\u00ed m\u00edru chybovosti experimentu, ani\u017e by zahlcuj\u00edc\u00ed korek\u010dn\u00ed postupy sni\u017eovaly jejich objevitelsk\u00fd potenci\u00e1l.<\/p>\n\n\n\n<p>Zach\u00e1zen\u00ed s touto k\u0159ehkou rovnov\u00e1hou proz\u00edrav\u011b zaji\u0161\u0165uje, \u017ee podstatn\u011b d\u016fle\u017eit\u00e1 zji\u0161t\u011bn\u00ed vyniknou, a z\u00e1rove\u0148 potvrzuje metodologickou p\u0159\u00edsnost - co\u017e je z\u00e1sadn\u00ed bod rovnov\u00e1hy pro v\u0161echny studie vyu\u017e\u00edvaj\u00edc\u00ed post hoc testov\u00e1n\u00ed v r\u00e1mci ANOVA.<\/p>\n\n\n\n<h2 id=\"h-summary-and-conclusion\">Shrnut\u00ed a z\u00e1v\u011br<\/h2>\n\n\n\n<h3 id=\"h-recap-of-key-points-covered-in-the-content-outline\">Rekapitulace kl\u00ed\u010dov\u00fdch bod\u016f obsa\u017een\u00fdch v osnov\u011b obsahu<\/h3>\n\n\n\n<p>V tomto \u010dl\u00e1nku jsme pro\u0161li krajinou anal\u00fdzy rozptylu (ANOVA) a jej\u00edho kritick\u00e9ho pr\u016fvodce -. <strong>post hoc testov\u00e1n\u00ed ANOVA<\/strong>. Pro za\u010d\u00e1tek jsme si vytvo\u0159ili z\u00e1kladn\u00ed p\u0159edstavu o metod\u011b ANOVA, kter\u00e1 se pou\u017e\u00edv\u00e1 k rozli\u0161en\u00ed, zda existuj\u00ed statisticky v\u00fdznamn\u00e9 rozd\u00edly mezi pr\u016fm\u011bry t\u0159\u00ed nebo v\u00edce nez\u00e1visl\u00fdch skupin.<\/p>\n\n\n\n<p>Pronikli jsme do \u00faskal\u00ed post hoc testov\u00e1n\u00ed, kter\u00e9 je nezbytn\u00e9, pokud \u00favodn\u00ed ANOVA p\u0159inese v\u00fdznamn\u00e9 v\u00fdsledky. Zjistili jsme, \u017ee ANOVA n\u00e1m sice m\u016f\u017ee \u0159\u00edci, \u017ee se li\u0161\u00ed alespo\u0148 dv\u011b skupiny, ale neur\u010duje, kter\u00e9 skupiny a kolik se od sebe li\u0161\u00ed. K tomu slou\u017e\u00ed post hoc testy.<\/p>\n\n\n\n<p>B\u011bhem diskuse jsme pro\u0161li r\u016fzn\u00fdmi odbo\u010dkami:<\/p>\n\n\n\n<ul>\n<li>Kritick\u00e1 povaha omnibusov\u00e9ho testu ANOVA, kter\u00fd pou\u017e\u00edv\u00e1 F-statistiku k ur\u010den\u00ed celkov\u00e9ho rozptylu.<\/li>\n\n\n\n<li>V\u00fdznam p\u0159esn\u00e9 interpretace t\u011bchto v\u00fdsledk\u016f pro \u0159\u00e1dnou statistickou anal\u00fdzu.<\/li>\n<\/ul>\n\n\n\n<p>Kdy\u017e se uk\u00e1zala omezen\u00ed, jako je chybovost experimentu, pochopili jsme, pro\u010d je post hoc testov\u00e1n\u00ed nejen u\u017eite\u010dn\u00e9, ale i nezbytn\u00e9. Nab\u00edz\u00ed zp\u0159esn\u011bn\u00e9 poznatky t\u00edm, \u017ee kontroluje tyto m\u00edry chyb a umo\u017e\u0148uje v\u00edcen\u00e1sobn\u00e1 srovn\u00e1n\u00ed, ani\u017e by se zv\u00fd\u0161ila pravd\u011bpodobnost chyb typu I.<\/p>\n\n\n\n<p>P\u0159i na\u0161\u00ed v\u00fdprav\u011b za r\u016fzn\u00fdmi metodami, jako je Tukeyova, Holmova a Dunnettova, jste si pravd\u011bpodobn\u011b v\u0161imli, \u017ee slou\u017e\u00ed k jedine\u010dn\u00fdm \u00fa\u010del\u016fm - a\u0165 u\u017e jde o porovn\u00e1v\u00e1n\u00ed v\u00edcen\u00e1sobn\u00fdch srovn\u00e1n\u00ed v\u0161ech mo\u017en\u00fdch dvojic pr\u016fm\u011br\u016f, nebo o zam\u011b\u0159en\u00ed na srovn\u00e1n\u00ed jedn\u00e9 kontroln\u00ed skupiny.<\/p>\n\n\n\n<p>V\u00fdb\u011br post hoc testu je t\u0159eba pe\u010dliv\u011b zv\u00e1\u017eit. Kontrola chybovosti neprob\u00edh\u00e1 izolovan\u011b; jakell post hoc testy, je t\u0159eba zv\u00e1\u017eit faktory souvisej\u00edc\u00ed s chybovost\u00ed v rodin\u011b.<\/p>\n\n\n\n<p>Zapojen\u00ed p\u0159\u00edklad\u016f z re\u00e1ln\u00e9ho sv\u011bta do na\u0161\u00ed diskuse pomohlo tyto koncep\u010dn\u00ed \u00favahy pevn\u011b zasadit do praktick\u00fdch sc\u00e9n\u00e1\u0159\u016f pou\u017eit\u00ed.<\/p>\n\n\n\n<p>Nakonec jsme se dotkli statistick\u00e9 s\u00edly, co\u017e je d\u016fle\u017eit\u00e9. Zat\u00edmco sn\u00ed\u017een\u00ed po\u010dtu srovn\u00e1n\u00ed je n\u011bkdy pova\u017eov\u00e1no za sn\u00ed\u017een\u00ed kompromis\u016f v oblasti s\u00edly\", strategick\u00e9 rozhodov\u00e1n\u00ed zde zaji\u0161\u0165uje robustnost zji\u0161t\u011bn\u00ed i p\u0159i pou\u017eit\u00ed v\u00edce post hoc test\u016f.<\/p>\n\n\n\n<h3 id=\"h-concluding-thoughts-on-the-importance-and-significance-of-post-hoc-testing-in-anova\">Z\u00e1v\u011bre\u010dn\u00e9 my\u0161lenky o d\u016fle\u017eitosti a v\u00fdznamu post hoc testov\u00e1n\u00ed v ANOVA<\/h3>\n\n\n\n<p>Na z\u00e1v\u011br t\u00e9to zasv\u011bcen\u00e9 exkurze do <strong>post hoc testov\u00e1n\u00ed ANOVA<\/strong>, p\u0159ipome\u0148me si, pro\u010d m\u00e1 pono\u0159en\u00ed se do hloubky pr\u00e1v\u011b na tomto \u00fazem\u00ed statistick\u00e9 anal\u00fdzy tak velk\u00fd v\u00fdznam. Ve v\u00fdzkumn\u00fdch souvislostech sahaj\u00edc\u00edch od pr\u016flomov\u00fdch objev\u016f ve zdravotnictv\u00ed a\u017e po p\u0159evratn\u00fd technologick\u00fd v\u00fdvoj m\u016f\u017ee m\u00edt zaji\u0161t\u011bn\u00ed toho, aby na\u0161e zji\u0161t\u011bn\u00ed byla nejen statisticky relevantn\u00ed, ale tak\u00e9 prakticky v\u00fdznamn\u00e1, z\u00e1sadn\u00ed v\u00fdznam.<\/p>\n\n\n\n<p>Rozumn\u00e9 pou\u017eit\u00ed post hoc test\u016f po ANOVA n\u00e1m umo\u017e\u0148uje p\u0159ekro\u010dit pouhou detekci rozd\u00edl\u016f a pustit se do zkoum\u00e1n\u00ed toho, jak\u00e9 jsou tyto rozd\u00edly - a jejich velikosti - s dostate\u010dnou p\u0159esnost\u00ed a jistotou, aby bylo mo\u017en\u00e9 rozhoduj\u00edc\u00edm zp\u016fsobem ovlivnit dal\u0161\u00ed v\u00fdzkumn\u00e9 cesty nebo politick\u00e1 rozhodnut\u00ed.<\/p>\n\n\n\n<p>Jako dychtiv\u00ed v\u011bdci a oddan\u00ed odborn\u00edci, kte\u0159\u00ed se pohybuj\u00ed ve sv\u011bt\u011b st\u00e1le v\u00edce zalo\u017een\u00e9m na datech, takov\u00e9 p\u0159\u00edstupy nejen zp\u0159es\u0148uj\u00ed na\u0161e ch\u00e1p\u00e1n\u00ed - ale roz\u0161i\u0159uj\u00ed mo\u017enosti. Post hoc testy i nad\u00e1le dr\u017e\u00ed pochode\u0148 vysoko osv\u011btluj\u00edc\u00ed nuance uprost\u0159ed n\u011bkdy ohromuj\u00edc\u00edch soubor\u016f dat - maj\u00e1k sm\u011b\u0159uj\u00edc\u00ed k p\u0159esv\u011bd\u010div\u00fdm poznatk\u016fm zv\u011bt\u0161uj\u00edc\u00edm na\u0161i schopnost \u010dinit informovan\u00e1 rozhodnut\u00ed zalo\u017een\u00e1 na robustn\u00edch analytick\u00fdch procesech, kter\u00e9 horliv\u011b obstoj\u00ed p\u0159i kontrole jak ve v\u011bdeck\u00fdch kruz\u00edch, tak na pol\u00edch, kde se objevuj\u00ed pr\u016fkopnick\u00e9 inovace v\u00e1\u017en\u011b sledovan\u00e9 kv\u016fli spole\u010densk\u00e9mu prosp\u011bchu s mnohostrann\u00fdm rozsahem v\u011brn\u00fdm tomu, co inspiruje ka\u017ed\u00e9 nov\u00e9 hled\u00e1n\u00ed \"...nep\u0159edv\u00eddan\u00fdch vzorc\u016f\".<\/p>\n\n\n\n<p>P\u0159es to v\u0161echno z\u016fst\u00e1v\u00e1 moje nad\u011bje nezlomn\u00e1: k\u00e9\u017e va\u0161e vlastn\u00ed anal\u00fdzy p\u0159inesou plodn\u00e9 porozum\u011bn\u00ed protkan\u00e9 jasnost\u00ed, kter\u00e1 si zaslou\u017e\u00ed ocen\u011bn\u00ed a nakonec zlep\u0161\u00ed \u017eivoty, jich\u017e se dotknou postupy zalo\u017een\u00e9 na d\u016fkazech, kter\u00e9 stoj\u00ed nad\u010dasov\u011b na p\u0159\u00edsn\u00fdch statistick\u00fdch z\u00e1kladech definuj\u00edc\u00edch ne\u00fanavn\u011b trvaj\u00edc\u00ed rozd\u00edly... v honb\u011b za pravdou, kter\u00e1 je st\u00e1le nepolapiteln\u00e1, ale v\u011b\u010dn\u011b l\u00e1kav\u00e1.<\/p>\n\n\n\n<h2 id=\"h-experience-the-power-of-visual-mastery-simplifying-complexity-with-mind-the-graph\"><br>Vyzkou\u0161ejte si s\u00edlu vizu\u00e1ln\u00edho mistrovstv\u00ed: Zjednodu\u0161en\u00ed slo\u017eitosti s Mind the Graph!<\/h2>\n\n\n\n<p>Odhalte potenci\u00e1l bezchybn\u00e9 vizu\u00e1ln\u00ed komunikace, proto\u017ee nov\u011b definujeme zp\u016fsob, jak\u00fdm ch\u00e1pete slo\u017eit\u00e9 koncepty. V \u00e9\u0159e, kter\u00e9 dominuj\u00ed vizu\u00e1ln\u00ed efekty, se pochopen\u00ed slo\u017eit\u00fdch my\u0161lenek, dokonce i tak z\u00e1hadn\u00fdch, jako je kvantov\u00e1 fyzika, st\u00e1v\u00e1 hra\u010dkou d\u00edky naprost\u00e9 \u00fa\u010dinnosti grafiky.<\/p>\n\n\n\n<p>Vydejte se na vizu\u00e1ln\u00ed cestu s <a href=\"https:\/\/mindthegraph.com\/?utm_source=blog&amp;utm_medium=content\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a>, v\u00e1\u0161 dokonal\u00fd spole\u010dn\u00edk p\u0159i p\u0159em\u011bn\u011b slo\u017eit\u00fdch sd\u011blen\u00ed na poutav\u00e9 vizu\u00e1ln\u00ed efekty. S v\u00edce ne\u017e tis\u00edcovkou pe\u010dliv\u011b zpracovan\u00fdch ilustrac\u00ed v na\u0161\u00ed galerii jsou mo\u017enosti neomezen\u00e9. N\u00e1\u0161 \u0161pi\u010dkov\u00fd inteligentn\u00ed tv\u016frce plak\u00e1t\u016f v\u00e1m umo\u017en\u00ed bez n\u00e1mahy vytv\u00e1\u0159et plak\u00e1ty, kter\u00e9 vyniknou.<\/p>\n\n\n\n<p>Pro\u010d se spokojit s oby\u010dejnost\u00ed, kdy\u017e m\u016f\u017eete m\u00edt vizu\u00e1ln\u00ed mistrovsk\u00e9 d\u00edlo na m\u00edru? Vyu\u017eijte zku\u0161enost\u00ed na\u0161eho talentovan\u00e9ho t\u00fdmu a upravte ilustrace podle sv\u00fdch jedine\u010dn\u00fdch pot\u0159eb. Mind the Graph nen\u00ed jen n\u00e1stroj; je to va\u0161e br\u00e1na do sv\u011bta, kde vizu\u00e1ln\u00ed efekty mluv\u00ed hlasit\u011bji ne\u017e slova.<\/p>\n\n\n\n<p>Jste p\u0159ipraveni pos\u00edlit svou komunika\u010dn\u00ed hru? Zaregistrujte se zdarma a za\u010dn\u011bte tvo\u0159it. Va\u0161e sd\u011blen\u00ed, na\u0161e vizu\u00e1ly - bezchybn\u00e1 kombinace!<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/mindthegraph.com\/?utm_source=blog&amp;utm_medium=content\"><img decoding=\"async\" loading=\"lazy\" width=\"648\" height=\"535\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2022\/11\/beautiful-poster-templates.png\" alt=\"beautiful-poster-templates\" class=\"wp-image-25482\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2022\/11\/beautiful-poster-templates.png 648w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2022\/11\/beautiful-poster-templates-300x248.png 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2022\/11\/beautiful-poster-templates-15x12.png 15w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2022\/11\/beautiful-poster-templates-100x83.png 100w\" sizes=\"(max-width: 648px) 100vw, 648px\" \/><\/a><\/figure><\/div>\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"is-layout-flex wp-block-buttons\">\n<div class=\"wp-block-button aligncenter\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mindthegraph.com\/?utm_source=blog&amp;utm_medium=content\" style=\"border-radius:50px;background-color:#dc1866\" target=\"_blank\" rel=\"noreferrer noopener\">Za\u010dn\u011bte tvo\u0159it s Mind the Graph<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Zjist\u011bte, jak\u00e9 jsou z\u00e1klady post hoc testov\u00e1n\u00ed ANOVA. Zdokonalte se ve statistick\u00e9 anal\u00fdze a odhalte v\u00fdznam sv\u00fdch datov\u00fdch soubor\u016f.<\/p>","protected":false},"author":4,"featured_media":50304,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[959,28],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Post Hoc Testing ANOVA: Learn How to Analyze Data Sets<\/title>\n<meta name=\"description\" content=\"Discover the ins and outs of post hoc testing ANOVA. Perfect your statistical analysis and uncover the significance of your data sets.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mindthegraph.com\/blog\/cs\/post-hoc-testovani-anova\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Post Hoc Testing ANOVA: Learn How to Analyze Data Sets\" \/>\n<meta property=\"og:description\" content=\"Discover the ins and outs of post hoc testing ANOVA. 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Perfect your statistical analysis and uncover the significance of your data sets.","twitter_image":"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/02\/post-hoc-testing-anova-blog.jpg","twitter_misc":{"Written by":"Fabricio Pamplona","Est. reading time":"18 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/mindthegraph.com\/blog\/post-hoc-testing-anova\/","url":"https:\/\/mindthegraph.com\/blog\/post-hoc-testing-anova\/","name":"Post Hoc Testing ANOVA: Learn How to Analyze Data Sets","isPartOf":{"@id":"https:\/\/mindthegraph.com\/blog\/#website"},"datePublished":"2024-02-11T14:03:02+00:00","dateModified":"2024-02-07T14:16:52+00:00","author":{"@id":"https:\/\/mindthegraph.com\/blog\/#\/schema\/person\/c8eaee6d8007ac319523c3ddc98cedd3"},"description":"Discover the ins and outs of post hoc testing ANOVA. 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He has a Ph.D. and solid scientific background in Psychopharmacology and experience as a Guest Researcher at the Max Planck Institute of Psychiatry (Germany) and Researcher in D'Or Institute for Research and Education (IDOR, Brazil). Fabricio holds over 2500 citations in Google Scholar. He has 10 years of experience in small innovative businesses, with relevant experience in product design and innovation management. Connect with him on LinkedIn - Fabricio Pamplona.","sameAs":["http:\/\/mindthegraph.com","https:\/\/www.linkedin.com\/in\/fabriciopamplona"],"url":"https:\/\/mindthegraph.com\/blog\/cs\/author\/fabricio\/"}]}},"_links":{"self":[{"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/posts\/50301"}],"collection":[{"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/comments?post=50301"}],"version-history":[{"count":3,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/posts\/50301\/revisions"}],"predecessor-version":[{"id":50305,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/posts\/50301\/revisions\/50305"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/media\/50304"}],"wp:attachment":[{"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/media?parent=50301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/categories?post=50301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/cs\/wp-json\/wp\/v2\/tags?post=50301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}