{"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\/sk\/post-hoc-testovanie-anova\/","title":{"rendered":"Post Hoc testovanie ANOVA: Nau\u010dte sa analyzova\u0165 s\u00fabory \u00fadajov"},"content":{"rendered":"<p>Boli ste niekedy zvedav\u00ed, ako vedci vyvodzuj\u00fa konkr\u00e9tne z\u00e1very zo skup\u00edn \u00fadajov, ktor\u00e9 sa na prv\u00fd poh\u013ead zdaj\u00fa by\u0165 rovnako z\u00e1hadn\u00e9 ako starovek\u00fd k\u00f3d? Nu\u017e, stane sa to o nie\u010do menej z\u00e1hadn\u00fdm, ke\u010f pochop\u00edte k\u00fazlo post hoc testovania v kontexte ANOVA - anal\u00fdzy rozptylu. T\u00e1to \u0161tatistick\u00e1 met\u00f3da nie je len n\u00e1strojom, je podobn\u00e1 lupe Sherlocka Holmesa, ktor\u00e1 sa pou\u017e\u00edva na odha\u013eovanie skryt\u00fdch pr\u00e1vd v nespo\u010detn\u00fdch \u010d\u00edslach. \u010ci u\u017e ste \u0161tudent, ktor\u00fd sa bor\u00ed s \u00fadajmi svojej diplomovej pr\u00e1ce, alebo sk\u00fasen\u00fd v\u00fdskumn\u00edk, ktor\u00e9ho cie\u013eom s\u00fa spo\u013eahliv\u00e9 v\u00fdsledky, odhalenie sily post hoc testov m\u00f4\u017ee va\u0161e zistenia pov\u00fd\u0161i\u0165 zo zauj\u00edmav\u00fdch na prevratn\u00e9.<\/p>\n\n\n\n<h2 id=\"h-understanding-anova-and-post-hoc-testing\">Pochopenie ANOVA a Post Hoc testovania<\/h2>\n\n\n\n<p>Pri sk\u00faman\u00ed vz\u00e1jomne sa prel\u00ednaj\u00facich konceptov ANOVA a post hoc testovania ich vn\u00edmajte ako partnerov pri snahe o presn\u00fa anal\u00fdzu. Umo\u017e\u0148uj\u00fa n\u00e1m nazrie\u0165 za hranice priemern\u00fdch hodn\u00f4t a sk\u00fama\u0165 hlb\u0161ie nuansy medzi porovn\u00e1van\u00edm viacer\u00fdch skup\u00edn - postupujme v\u0161ak krok za krokom.<\/p>\n\n\n\n<p>S\u00favisiaci \u010dl\u00e1nok: <a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\"><strong>Post Hoc anal\u00fdza: Postup a typy testov<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-introduction-to-anova-and-its-purpose-in-statistical-analysis\">\u00davod do ANOVA a jej \u00fa\u010del v \u0161tatistickej anal\u00fdze<\/h3>\n\n\n\n<p>Anal\u00fdza rozptylu alebo ANOVA, ako je v\u0161eobecne zn\u00e1ma medzi \u0161tatistikmi, je jedn\u00fdm z najmocnej\u0161\u00edch n\u00e1strojov v ich arzen\u00e1li. Pln\u00ed k\u013e\u00fa\u010dov\u00fa funkciu - rozli\u0161uje, \u010di existuj\u00fa \u0161tatisticky v\u00fdznamn\u00e9 rozdiely medzi priemermi skup\u00edn v experimente zah\u0155\u0148aj\u00facom tri alebo viac skup\u00edn. Porovnan\u00edm rozptylov v r\u00e1mci jednotliv\u00fdch skup\u00edn s rozptylmi medzi t\u00fdmito skupinami pom\u00e1ha ANOVA zamietnu\u0165 alebo zachova\u0165 nulov\u00fa hypot\u00e9zu, \u017ee neexistuje \u017eiadny in\u00fd rozptyl ako n\u00e1hodn\u00fd.<\/p>\n\n\n\n<h3 id=\"h-explanation-of-post-hoc-testing-and-its-importance-in-anova\">Vysvetlenie post hoc testovania a jeho v\u00fdznam v ANOVA<\/h3>\n\n\n\n<p>Hoci je ur\u010denie v\u00fdznamnosti vo ve\u013ek\u00fdch s\u00faboroch nevyhnutn\u00e9, \u010do sa stane, ke\u010f n\u00e1m ANOVA povie, \u017ee \"nie\u010do\" sa l\u00ed\u0161i, ale ne\u0161pecifikuje \"\u010do\" a \"kde\"? N\u00e1poveda k post hoc testovaniu! Post hoc testovanie je skratka pre \"after this\" (po tomto) a nadv\u00e4zuje na stopu, ktor\u00fa zanechal omnibusov\u00fd test ANOVA. Jeho \u00falohou je? Presne ur\u010di\u0165, ktor\u00e9 dvojice alebo kombin\u00e1cie medzi na\u0161imi skupinami vykazuj\u00fa v\u00fdznamn\u00e9 rozdiely, a tak umo\u017eni\u0165 v\u00fdskumn\u00edkom robi\u0165 informovan\u00e9 rozhodnutia s dokonalou presnos\u0165ou.<\/p>\n\n\n\n<h3 id=\"h-overview-of-the-process-of-post-hoc-testing-in-anova\">Preh\u013ead procesu post hoc testovania v ANOVA<\/h3>\n\n\n\n<p>Post hoc testovanie sa vykon\u00e1va v\u017edy po z\u00edskan\u00ed v\u00fdznamn\u00e9ho v\u00fdsledku z omnibusov\u00e9ho testu ANOVA - odtia\u013e poch\u00e1dza jeho retrospekt\u00edvny n\u00e1zov. Predstavte si, \u017ee tento proces pozost\u00e1va preva\u017ene z:<\/p>\n\n\n\n<ul>\n<li><strong>V\u00fdber vhodn\u00e9ho post hoc testu<\/strong>: V z\u00e1vislosti od \u0161pecif\u00edk n\u00e1vrhu a tolerancie chybovosti.<\/li>\n\n\n\n<li><strong>\u00daprava p-hodnoty<\/strong>: Korekcia nadhodnoten\u00fdch riz\u00edk spojen\u00fdch s viacn\u00e1sobn\u00fdm porovn\u00e1van\u00edm.<\/li>\n\n\n\n<li><strong>Interpret\u00e1cia v\u00fdsledkov v kontexte<\/strong>: Zabezpe\u010denie s\u00faladu praktick\u00e9ho v\u00fdznamu so \u0161tatistick\u00fdmi zisteniami.<\/li>\n<\/ul>\n\n\n\n<p>Tento disciplinovan\u00fd pr\u00edstup chr\u00e1ni pred falo\u0161n\u00fdmi z\u00e1vermi a z\u00e1rove\u0148 umo\u017e\u0148uje z\u00edska\u0165 cenn\u00e9 poznatky, ktor\u00e9 s\u00fa v s\u00faboroch \u00fadajov skryt\u00e9. Vyzbrojen\u00fd t\u00fdmto pokro\u010dil\u00fdm a z\u00e1rove\u0148 pr\u00edstupn\u00fdm ch\u00e1pan\u00edm m\u00f4\u017ee ka\u017ed\u00fd nast\u00fapi\u0165 na cestu k ovl\u00e1dnutiu svojich d\u00e1tov\u00fdch v\u00fdpoved\u00ed.<\/p>\n\n\n\n<h2 id=\"h-anova-omnibus-test\">ANOVA Omnibus test<\/h2>\n\n\n\n<p>Pri anal\u00fdze s\u00faborov \u00fadajov s viac ako dvoma prostriedkami, aby sme zistili, \u010di sa aspo\u0148 jeden z nich l\u00ed\u0161i od ostatn\u00fdch, je nevyhnutn\u00e1 anal\u00fdza rozptylu (ANOVA). Ale sk\u00f4r ako sa ponor\u00edme do zlo\u017eitost\u00ed post hoc testovania v ANOVA, je nevyhnutn\u00e9 pochopi\u0165 z\u00e1kladn\u00e9 hodnotenie - omnibusov\u00fd test ANOVA. Predstavte si to ako detekt\u00edvny pr\u00edbeh, v ktorom po\u010diato\u010dn\u00e9 d\u00f4kazy poukazuj\u00fa na mo\u017enos\u0165 podozriv\u00e9ho, ale neur\u010duj\u00fa presne koho.<\/p>\n\n\n\n<p>S\u00favisiaci \u010dl\u00e1nok: <a href=\"https:\/\/mindthegraph.com\/blog\/one-way-anova\/\"><strong>Jednosmern\u00e1 ANOVA: porozumenie, vedenie a prezent\u00e1cia<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-detailed-explanation-of-the-anova-omnibus-test\">Podrobn\u00e9 vysvetlenie omnibusov\u00e9ho testu ANOVA<\/h3>\n\n\n\n<p>Omnibusov\u00fd test ANOVA vynik\u00e1 t\u00fdm, \u017ee n\u00e1m umo\u017e\u0148uje porovn\u00e1va\u0165 prostriedky viacer\u00fdch skup\u00edn s\u00fa\u010dasne namiesto toho, aby sme vykonali mno\u017estvo testov pre ka\u017ed\u00fa hladinu v\u00fdznamnosti ka\u017edej mo\u017enej dvojice, \u010do by nepochybne zv\u00fd\u0161ilo riziko chyby typu I - falo\u0161ne pozit\u00edvnu mieru. \"Omnibus\" v jeho n\u00e1zve nazna\u010duje, \u017ee tento test m\u00e1 celkov\u00fd poh\u013ead - spolo\u010dne kontroluje, \u010di existuje nejak\u00fd \u0161tatisticky v\u00fdznamn\u00fd rozdiel medzi priemermi skup\u00edn.<\/p>\n\n\n\n<p>Takto sa to vyv\u00edja: Za\u010dneme t\u00fdm, \u017ee vypo\u010d\u00edtame samostatn\u00e9 rozptyly v r\u00e1mci skup\u00edn a medzi skupinami. Ak s\u00fa na\u0161e skupiny vn\u00fatorne pomerne vyrovnan\u00e9, ale navz\u00e1jom sa v\u00fdrazne l\u00ed\u0161ia, je to spo\u013eahliv\u00fd ukazovate\u013e, \u017ee nie v\u0161etky skupinov\u00e9 priemery s\u00fa rovnak\u00e9. V podstate h\u013ead\u00e1me variabilitu medzi skupinami b v r\u00e1mci skupiny, ktor\u00fa nemo\u017eno vysvetli\u0165 len n\u00e1hodou v porovnan\u00ed s variabilitou v r\u00e1mci skupiny - \u010do by sme o\u010dak\u00e1vali od n\u00e1hodn\u00fdch v\u00fdkyvov.<\/p>\n\n\n\n<h3 id=\"h-understanding-the-f-statistic-and-its-interpretation\">Pochopenie F-\u0161tatistiky a jej interpret\u00e1cia<\/h3>\n\n\n\n<p>Pri vykon\u00e1van\u00ed omnibusov\u00e9ho testu ANOVA vypo\u010d\u00edtame tzv. F-\u0161tatistiku - hodnotu odvoden\u00fa z delenia rozptylu medzi skupinami rozptylom v r\u00e1mci skupiny. Ve\u013ek\u00e1 hodnota F m\u00f4\u017ee nazna\u010dova\u0165 v\u00fdznamn\u00e9 rozdiely medzi priemermi skup\u00edn, preto\u017ee nazna\u010duje, \u017ee variabilita medzi skupinami je vy\u0161\u0161ia v porovnan\u00ed s variabilitou v r\u00e1mci skupiny.<\/p>\n\n\n\n<p>Tu je v\u0161ak najd\u00f4le\u017eitej\u0161ia opatrnos\u0165: F-\u0161tatistika sa riadi \u0161pecifick\u00fdm rozdelen\u00edm pri nulovej hypot\u00e9ze (ktor\u00e1 predpoklad\u00e1, \u017ee medzi priemermi na\u0161ich skup\u00edn nie je \u017eiadny rozdiel). Predt\u00fdm, ako urob\u00edme z\u00e1very len na z\u00e1klade tejto \u0161tatistiky, odk\u00e1\u017eeme na toto F-rozdelenie s oh\u013eadom na na\u0161e stupne vo\u013enosti t\u00fdkaj\u00face sa medzi skupinami aj v r\u00e1mci skup\u00edn, \u010d\u00edm z\u00edskame p-hodnotu.<\/p>\n\n\n\n<h3 id=\"h-interpreting-the-results-of-the-omnibus-test\">Interpret\u00e1cia v\u00fdsledkov omnibusov\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>Tak\u017ee ste vykonali anal\u00fdzu a po porovnan\u00ed vypo\u010d\u00edtanej F-\u0161tatistiky s pr\u00edslu\u0161n\u00fdm rozdelen\u00edm m\u00e1te v ruk\u00e1ch t\u00fa najd\u00f4le\u017eitej\u0161iu p-hodnotu - ale \u010do teraz? Ak t\u00e1to p-hodnota klesne pod va\u0161u prahov\u00fa hodnotu - \u010dasto 0,05 - dostaneme sa na \u00fazemie zamietnutia na\u0161ej nulovej hypot\u00e9zy. To nazna\u010duje siln\u00fd d\u00f4kaz o neexistencii \u00fa\u010dinku vo v\u0161etk\u00fdch skupin\u00e1ch.<\/p>\n\n\n\n<p>Av\u0161ak - a t\u00e1to \u010das\u0165 je k\u013e\u00fa\u010dov\u00e1 - zastre\u0161uj\u00face odmietnutie n\u00e1s nevedie k tomu, ktor\u00e9 konkr\u00e9tne prostriedky sa l\u00ed\u0161ia, ani o ko\u013eko; ne\u0161pecifikuje, \"kto to urobil\" v na\u0161ej predch\u00e1dzaj\u00facej detekt\u00edvnej anal\u00f3gii. Informuje n\u00e1s len o tom, \u017ee v na\u0161ej zostave je nie\u010do, \u010do stoj\u00ed za \u010fal\u0161ie sk\u00famanie - \u010do n\u00e1s priamo vedie k post hoc testovaniu v ANOVA, aby sme odhalili tieto podrobn\u00e9 rozdiely medzi konkr\u00e9tnymi dvojicami alebo kombin\u00e1ciami skup\u00edn.<\/p>\n\n\n\n<p>Pochopenie toho, kedy a pre\u010do post hoc testy nasleduj\u00fa po omnibusovom teste ANOVA, zabezpe\u010duje v\u00fdskumn\u00edkom zodpovedn\u00e9 zaobch\u00e1dzanie s ich zisteniami bez pred\u010dasn\u00e9ho alebo nespr\u00e1vneho prechodu k asoci\u00e1ci\u00e1m alebo kauz\u00e1lnym tvrdeniam - a z\u00e1rove\u0148 napom\u00e1ha jasnej komunik\u00e1cii v ich oblastiach \u0161t\u00fadia.<\/p>\n\n\n\n<h2 id=\"h-need-for-post-hoc-testing-in-anova\">Potreba post hoc testovania v ANOVA<\/h2>\n\n\n\n<h3 id=\"h-exploring-the-limitations-of-the-omnibus-test\">Sk\u00famanie obmedzen\u00ed s\u00fahrnn\u00e9ho testu<\/h3>\n\n\n\n<p>Ke\u010f rozober\u00e1m zlo\u017eitos\u0165 \u0161tatistickej anal\u00fdzy, je nevyhnutn\u00e9 uzna\u0165, \u017ee n\u00e1stroje ako anal\u00fdza rozptylu (ANOVA) s\u00fa s\u00edce mocn\u00e9, ale maj\u00fa svoje hranice. Omnibusov\u00fd test ANOVA n\u00e1m \u00fa\u010dinne hovor\u00ed, \u010di niekde medzi na\u0161imi skupinami existuje \u0161tatisticky v\u00fdznamn\u00fd rozdiel. Predpokladajme v\u0161ak, \u017ee by ste sk\u00famali vplyv r\u00f4znych vyu\u010dovac\u00edch met\u00f3d na v\u00fdsledky \u017eiakov. V takom pr\u00edpade by omnibusov\u00fd test mohol odhali\u0165 rozdiely medzi v\u0161etk\u00fdmi testovan\u00fdmi met\u00f3dami, ale neur\u010d\u00ed, kde tieto rozdiely spo\u010d\u00edvaj\u00fa - ktor\u00e9 dvojice alebo kombin\u00e1cie vyu\u010dovac\u00edch met\u00f3d sa od seba v\u00fdznamne l\u00ed\u0161ia.<\/p>\n\n\n\n<p>Podstata je nasledovn\u00e1: hoci ANOVA dok\u00e1\u017ee ozna\u010di\u0165, \u010di sa aspo\u0148 dve skupiny l\u00ed\u0161ia, o podrobnostiach ml\u010d\u00ed. To je ako vedie\u0165, \u017ee m\u00e1te v\u00fdhern\u00fd \u017ereb v lot\u00e9rii, bez toho, aby ste poznali jeho hodnotu - ur\u010dite by ste chceli p\u00e1tra\u0165 hlb\u0161ie po konkr\u00e9tnych \u00fadajoch?<\/p>\n\n\n\n<h3 id=\"h-understanding-why-post-hoc-tests-are-necessary\">Pochopenie, pre\u010do s\u00fa potrebn\u00e9 post hoc testy<\/h3>\n\n\n\n<p>Pr\u00e1ve pri sk\u00faman\u00ed \u0161pecif\u00edk je potrebn\u00e9 vykona\u0165 post hoc testovanie ANOVA. Ke\u010f ANOVA zam\u00e1va zelenou vlajkou signalizuj\u00facou celkov\u00fa v\u00fdznamnos\u0165, zost\u00e1vaj\u00fa n\u00e1m dr\u00e1\u017ediv\u00e9 ot\u00e1zky: Ktor\u00e9 skupiny presne sp\u00f4sobuj\u00fa tieto rozdiely? Je ka\u017ed\u00e1 skupina odli\u0161n\u00e1 od ostatn\u00fdch, alebo s\u00fa hnacou silou zmeny len konkr\u00e9tne skupiny?<\/p>\n\n\n\n<p>Snaha odpoveda\u0165 na tieto ot\u00e1zky bez \u010fal\u0161ieho pos\u00fadenia predstavuje riziko vyvodenia nepresn\u00fdch z\u00e1verov zalo\u017een\u00fdch sk\u00f4r na v\u0161eobecn\u00fdch trendoch ne\u017e na konkr\u00e9tnych rozdieloch. Post hoc testy s\u00fa vybaven\u00e9 pr\u00edstupom jemnej kombin\u00e1cie, ktor\u00fd roz\u010dle\u0148uje \u00fadaje a poskytuje podrobn\u00fd poh\u013ead na porovnania jednotliv\u00fdch skup\u00edn po tom, \u010do va\u0161a p\u00f4vodn\u00e1 ANOVA pouk\u00e1zala na \u0161irok\u00e9 rozdiely medzi skupinami.<\/p>\n\n\n\n<p>Tieto n\u00e1sledn\u00e9 hodnotenia presne ur\u010duj\u00fa, ktor\u00e9 kontrasty s\u00fa v\u00fdznamn\u00e9, a preto s\u00fa nevyhnutn\u00e9 pri vytv\u00e1ran\u00ed podrobn\u00e9ho ch\u00e1pania va\u0161ich v\u00fdsledkov.<\/p>\n\n\n\n<h3 id=\"h-the-concept-of-experiment-wise-error-rate\">Koncept chybovosti experimentu<\/h3>\n\n\n\n<p>K\u013e\u00fa\u010dov\u00fd z\u00e1kladn\u00fd princ\u00edp pri rozhodovan\u00ed, kedy je post hoc testovanie nevyhnutn\u00e9, spo\u010d\u00edva v tom, \u010do \u0161tatistici naz\u00fdvaj\u00fa \"chybovos\u0165 experimentu\". T\u00e1 sa vz\u0165ahuje na pravdepodobnos\u0165 sp\u00e1chania aspo\u0148 jednej chyby typu I po\u010das v\u0161etk\u00fdch testov hypot\u00e9z vykonan\u00fdch v r\u00e1mci experimentu - nielen na jedno porovnanie, ale kumulat\u00edvne na v\u0161etky mo\u017en\u00e9 testy post hoc p\u00e1rov\u00e9ho porovnania.<\/p>\n\n\n\n<p>Predstavte si, \u017ee ochutn\u00e1vate r\u00f4zne d\u00e1vky su\u0161ienok a sna\u017e\u00edte sa zisti\u0165, \u010di niektor\u00e1 chu\u0165 vynik\u00e1 ako chutnej\u0161ia. Ka\u017edou ochutn\u00e1vkou sa zvy\u0161uje pravdepodobnos\u0165 nespr\u00e1vneho vyhl\u00e1senia jednej d\u00e1vky za najlep\u0161iu len v\u010faka n\u00e1hode - \u010d\u00edm viac porovnan\u00ed urob\u00edte, t\u00fdm vy\u0161\u0161ie je riziko nespr\u00e1vneho \u00fasudku, preto\u017ee niektor\u00e9 zistenia m\u00f4\u017eu by\u0165 falo\u0161n\u00fdm poplachom.<\/p>\n\n\n\n<p>Post hoc testovanie vn\u00e1\u0161a do n\u00e1\u0161ho \u0161tatistick\u00e9ho s\u00faboru sofistikovanos\u0165 t\u00fdm, \u017ee zoh\u013ead\u0148uje t\u00fato kumulat\u00edvnu chybu a kontroluje ju pomocou upraven\u00fdch p-hodn\u00f4t - postup ur\u010den\u00fd nielen na zv\u00fd\u0161enie presnosti, ale aj d\u00f4very v platnos\u0165 a spo\u013eahlivos\u0165 na\u0161ich z\u00e1verov.<\/p>\n\n\n\n<h2 id=\"h-different-post-hoc-testing-methods\">R\u00f4zne met\u00f3dy post-Hoc testovania<\/h2>\n\n\n\n<p>Po vykonan\u00ed anal\u00fdzy ANOVA, ktor\u00e1 v\u00e1m povie, \u010di existuje \u0161tatisticky v\u00fdznamn\u00fd vplyv medzi priemermi skup\u00edn, je celkom be\u017en\u00e9, \u017ee si kladiete ot\u00e1zku, v \u010dom vlastne spo\u010d\u00edvaj\u00fa rozdiely. Tu prich\u00e1dza na rad post hoc testovanie - predstavte si ho ako bli\u017e\u0161ie nahliadnutie do pr\u00edbehu va\u0161ich \u00fadajov, aby ste pochopili \u00falohu ka\u017edej postavy. Po\u010fme sa do toho hlb\u0161ie ponori\u0165 pomocou nieko\u013ek\u00fdch met\u00f3d, ktor\u00e9 osvet\u013euj\u00fa tieto nuansovan\u00e9 pr\u00edbehy.<\/p>\n\n\n\n<h3 id=\"h-tukey-s-method\">Tukeyho met\u00f3da<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-tukey-s-method-and-its-application-in-anova\">Vysvetlenie Tukeyho met\u00f3dy a jej pou\u017eitie v ANOVA<\/h4>\n\n\n\n<p><strong>Tukeyho \u010destn\u00fd signifikantn\u00fd rozdiel (HSD)<\/strong> je jedn\u00fdm z najpou\u017e\u00edvanej\u0161\u00edch post hoc testov po ANOVA. Ke\u010f ste zistili, \u017ee nie v\u0161etky skupinov\u00e9 priemery s\u00fa rovnak\u00e9, ale potrebujete vedie\u0165, ktor\u00e9 konkr\u00e9tne priemery sa l\u00ed\u0161ia, nastupuje Tukeyho met\u00f3da. Porovn\u00e1va v\u0161etky mo\u017en\u00e9 dvojice stredn\u00fdch hodn\u00f4t, pri\u010dom kontroluje chybovos\u0165 typu I v t\u00fdchto porovnaniach. T\u00e1to vlastnos\u0165 ju rob\u00ed obzvl\u00e1\u0161\u0165 u\u017eito\u010dnou, ke\u010f pracujete s viacer\u00fdmi skupinami a vy\u017eadujete testy viacn\u00e1sobn\u00e9ho porovnania a robustn\u00fa anal\u00fdzu.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values\">V\u00fdpo\u010det a interpret\u00e1cia upraven\u00fdch p-hodnot<\/h4>\n\n\n\n<p>Tukeyho met\u00f3da zah\u0155\u0148a v\u00fdpo\u010det s\u00faboru \"upraven\u00fdch\" p-hodnot pre ka\u017ed\u00e9 p\u00e1rov\u00e9 porovnanie medzi priemermi skup\u00edn. V\u00fdpo\u010det sa opiera o rozdelenie \u0161tudovan\u00e9ho rozsahu, ktor\u00e9 zoh\u013ead\u0148uje rozptyly v r\u00e1mci skupiny aj medzi skupinami - to v\u0161etko je dos\u0165 n\u00e1ro\u010dn\u00e9, ale k\u013e\u00fa\u010dov\u00e9 pre interpret\u00e1ciu nu\u00e1ns vo va\u0161ich \u00fadajoch. D\u00f4le\u017eit\u00e9 je, aby ste tieto p-hodnoty upravili tak, aby zoh\u013ead\u0148ovali zv\u00fd\u0161en\u00fd potenci\u00e1l ch\u00fdb typu I v d\u00f4sledku viacn\u00e1sobn\u00fdch porovnan\u00ed. Ak konkr\u00e9tna upraven\u00e1 p-hodnota klesne pod hranicu v\u00fdznamnosti (zvy\u010dajne 0,05), m\u00f4\u017eete vyhl\u00e1si\u0165, \u017ee medzi t\u00fdmito dvoma skupinov\u00fdmi priemermi je v\u00fdznamn\u00fd rozdiel.<\/p>\n\n\n\n<h4 id=\"h-using-simultaneous-confidence-intervals-with-tukey-s-method\">Pou\u017eitie simult\u00e1nnych intervalov spo\u013eahlivosti s Tukeyho met\u00f3dou<\/h4>\n\n\n\n<p>\u010eal\u0161\u00edm siln\u00fdm aspektom Tukeyho testu je jeho schopnos\u0165 vytvori\u0165 s\u00fa\u010dasne intervaly spo\u013eahlivosti pre v\u0161etky priemern\u00e9 rozdiely. Toto vizu\u00e1lne zn\u00e1zornenie priemern\u00fdch rozdielov pom\u00e1ha v\u00fdskumn\u00edkom nielen vidie\u0165, ktor\u00e9 skupiny sa l\u00ed\u0161ia, ale aj pochopi\u0165 ve\u013ekos\u0165 a smer t\u00fdchto rozdielov - \u010do je neocenite\u013en\u00fd poznatok pri vykres\u013eovan\u00ed bud\u00faceho v\u00fdskumu alebo praktick\u00fdch aplik\u00e1ci\u00ed.<\/p>\n\n\n\n<h3 id=\"h-holm-s-method\">Holmova met\u00f3da<\/h3>\n\n\n\n<h4 id=\"h-introduction-to-holm-s-method-and-its-advantages-over-other-methods\">\u00davod do Holmovej met\u00f3dy a jej v\u00fdhody oproti in\u00fdm met\u00f3dam<\/h4>\n\n\n\n<p>Zmena prevodov\u00fdch stup\u0148ov, <strong>Holmova met\u00f3da<\/strong>, zn\u00e1ma aj ako Holmova sekven\u010dn\u00e1 Bonferroniho proced\u00fara, poskytuje alternat\u00edvny sp\u00f4sob post hoc testovania, pri ktorom je v centre pozornosti ochrana pred chybami typu I - upravuje p-hodnoty ako starostliv\u00fd kur\u00e1tor, ktor\u00fd chr\u00e1ni cenn\u00e9 artefakty pred nevhodn\u00fdm vystaven\u00edm. Jeho najprekvapuj\u00facej\u0161ia v\u00fdhoda spo\u010d\u00edva v procedur\u00e1lnej flexibilite; na rozdiel od niektor\u00fdch met\u00f3d, ktor\u00e9 sa zakladaj\u00fa na jednostup\u0148ov\u00fdch \u00faprav\u00e1ch, Holmov postup s postupn\u00fdm zni\u017eovan\u00edm pon\u00faka v\u00e4\u010d\u0161iu silu, pri\u010dom st\u00e1le hr\u00e1 obranu proti \u0161tatistick\u00fdm chyb\u00e1m vypl\u00fdvaj\u00facim z mnoh\u00fdch porovnan\u00ed.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values-with-holm-s-method\">V\u00fdpo\u010det a interpret\u00e1cia upraven\u00fdch p-hodn\u00f4t pomocou Holmovej met\u00f3dy<\/h4>\n\n\n\n<p>Drobnosti zah\u0155\u0148aj\u00fa zoradenie na\u0161ich po\u010diato\u010dn\u00fdch neupraven\u00fdch p-hodn\u00f4t od najmen\u0161ej po najv\u00e4\u010d\u0161iu a ich postupn\u00e9 sk\u00famanie na z\u00e1klade upraven\u00fdch \u00farovn\u00ed alfa na z\u00e1klade ich poradia - ak\u00fdsi proces \"zni\u017eovania\", a\u017e k\u00fdm nenaraz\u00edme na hodnotu, ktor\u00e1 je tvrdohlavo v\u00e4\u010d\u0161ia ako nami vypo\u010d\u00edtan\u00e1 prahov\u00e1 hodnota; v tomto bode sa n\u00e1znaky odstr\u00e1nia.<\/p>\n\n\n\n<h3 id=\"h-dunnett-s-method\">Dunnettova met\u00f3da<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-dunnett-s-method-and-when-it-is-appropriate-to-use-it\">Vysvetlenie Dunnettovej met\u00f3dy a kedy je vhodn\u00e9 ju pou\u017ei\u0165<\/h4>\n\n\n\n<p>Tu m\u00e1me <strong>Dunnettov test<\/strong>, ktor\u00e1 sa vyzna\u010duje cielen\u00fdm pr\u00edstupom: porovn\u00e1vanie viacer\u00fdch lie\u010debn\u00fdch skup\u00edn konkr\u00e9tne s jednou kontrolnou skupinou - be\u017en\u00fd scen\u00e1r v klinick\u00fdch \u0161t\u00fadi\u00e1ch alebo agronomick\u00fdch \u0161t\u00fadi\u00e1ch, kde by ste mohli chcie\u0165 porovna\u0165 nov\u00e9 lie\u010debn\u00e9 postupy so \u0161tandardnou alebo placebovou referen\u010dnou hodnotou.<\/p>\n\n\n\n<h4 id=\"h-comparing-treatment-groups-to-a-control-group-using-dunnett-s-method\">Porovnanie lie\u010debn\u00fdch skup\u00edn s kontrolnou skupinou pomocou Dunnettovej met\u00f3dy<\/h4>\n\n\n\n<p>Na rozdiel od in\u00fdch pr\u00edstupov, ktor\u00e9 roz\u0161iruj\u00fa siete na v\u0161etky mo\u017en\u00e9 porovnania, Dunnettov\u00e1 rozli\u0161uje len to, ako si ka\u017ed\u00fd kandid\u00e1t stoj\u00ed ved\u013ea nami zvolen\u00e9ho referen\u010dn\u00e9ho bodu. Preto starostlivo vypo\u010d\u00edtava, o ko\u013eko v\u00e4\u010d\u0161\u00ed p\u00e1kov\u00fd efekt - alebo nie - z\u00edskame z va\u0161ich z\u00e1sahov v porovnan\u00ed s t\u00fdm, ak neurob\u00edme v\u00f4bec ni\u010d alebo zostaneme pri tom, \u010do bolo doteraz osved\u010den\u00e9.<\/p>\n\n\n\n<p>Tieto r\u00f4zne n\u00e1stroje post hoc testovania v ANOVA umo\u017e\u0148uj\u00fa n\u00e1m \u0161tatistikom aj d\u00e1tov\u00fdm analytikom vy\u010d\u00edta\u0165 detaily zo s\u00faborov \u00fadajov, ktor\u00e9 s\u00fa pln\u00e9 potenci\u00e1lnych poznatkov \u010dakaj\u00facich pod ich \u010d\u00edseln\u00fdm povrchom - ka\u017ed\u00fd z nich je trochu inak prisp\u00f4soben\u00fd na odhalenie skryt\u00fdch pr\u00edbehov, ktor\u00e9 s\u00fa s\u00fa\u010das\u0165ou na\u0161ich empirick\u00fdch v\u00fdskumov.<\/p>\n\n\n\n<h2 id=\"h-factors-to-consider-in-choosing-a-post-hoc-test\">Faktory, ktor\u00e9 treba zv\u00e1\u017ei\u0165 pri v\u00fdbere post-hoc testu<\/h2>\n\n\n\n<p>Ke\u010f sa odv\u00e1\u017eite vst\u00fapi\u0165 do oblasti ANOVA, po identifik\u00e1cii v\u00fdznamn\u00e9ho rozdielu medzi skupinami pomocou s\u00fahrnn\u00e9ho testu ANOVA je \u010fal\u0161\u00edm krokom \u010dasto pou\u017eitie post hoc testovania, aby ste presne ur\u010dili, v \u010dom tieto rozdiely spo\u010d\u00edvaj\u00fa. Teraz v\u00e1m pribl\u00ed\u017eim jeden z rozhoduj\u00facich faktorov, ktor\u00fd by mal ovplyvni\u0165 v\u00fdber post hoc testu: kontrola chybovosti pod\u013ea rod\u00edn.<\/p>\n\n\n\n<h3 id=\"h-famil-wise-error-rate-control-and-its-significance-in-choosing-a-test-method\">Kontrola chybovosti pod\u013ea rod\u00edn a jej v\u00fdznam pri v\u00fdbere testovacej met\u00f3dy<\/h3>\n\n\n\n<p>Term\u00edn \"rodinn\u00e1 chybovos\u0165\" (FWER) sa vz\u0165ahuje na pravdepodobnos\u0165, \u017ee pri vykon\u00e1van\u00ed viacn\u00e1sobn\u00fdch p\u00e1rov\u00fdch testov sa vyskytne aspo\u0148 jedna chyba typu I zo v\u0161etk\u00fdch mo\u017en\u00fdch porovnan\u00ed. Chyba typu I nast\u00e1va vtedy, ke\u010f nespr\u00e1vne us\u00fadite, \u017ee medzi skupinami existuj\u00fa rozdiely, hoci v skuto\u010dnosti neexistuj\u00fa. Ak nie je riadne kontrolovan\u00e1, ke\u010f\u017ee v r\u00e1mci ANOVA vykon\u00e1vame \u010doraz viac viac viac p\u00e1rov\u00fdch porovnan\u00ed, pravdepodobnos\u0165 ne\u00famyseln\u00e9ho vyhl\u00e1senia nespr\u00e1vnej v\u00fdznamnosti sa zvy\u0161uje - \u010do m\u00f4\u017ee va\u0161u \u0161t\u00fadiu vyvies\u0165 z omylu.<\/p>\n\n\n\n<p>Aj ke\u010f to znie sk\u013eu\u010duj\u00faco, nebojte sa; pr\u00e1ve preto s\u00fa met\u00f3dy kontroly FWER k\u013e\u00fa\u010dov\u00fdmi prvkami pri v\u00fdbere post hoc testu. Tieto met\u00f3dy v podstate upravuj\u00fa va\u0161e prahy v\u00fdznamnosti alebo p-hodnoty tak, aby spolo\u010dn\u00e9 riziko vo v\u0161etk\u00fdch testoch neprekro\u010dilo va\u0161u p\u00f4vodn\u00fa \u00farove\u0148 akceptovate\u013enosti ch\u00fdb (be\u017ene 0,05). T\u00fdmto sp\u00f4sobom m\u00f4\u017eeme s istotou sk\u00fama\u0165 \u0161pecifick\u00e9 skupinov\u00e9 rozdiely bez toho, aby sme stup\u0148ovali \u0161ance na falo\u0161n\u00e9 zistenia.<\/p>\n\n\n\n<p>Kontrola FWER zachov\u00e1va integritu va\u0161ich zisten\u00ed a udr\u017eiava vedeck\u00fa pr\u00edsnos\u0165 potrebn\u00fa pre vz\u00e1jomn\u00e9 hodnotenie a reprodukovate\u013enos\u0165.<\/p>\n\n\n\n<p>Teraz si predstavte, \u017ee m\u00e1te pred sebou r\u00f4zne mo\u017enosti post hoc testovania - pochopenie FWER v\u00e1m pom\u00f4\u017ee odpoveda\u0165 na k\u013e\u00fa\u010dov\u00e9 ot\u00e1zky:<\/p>\n\n\n\n<ul>\n<li>Ko\u013eko porovnan\u00ed sa vykon\u00e1 v mojom pl\u00e1ne \u0161t\u00fadie?<\/li>\n\n\n\n<li>Ako konzervat\u00edvny mus\u00edm by\u0165 pri kontrole ch\u00fdb typu I vzh\u013eadom na svoju oblas\u0165 alebo v\u00fdskumn\u00fa ot\u00e1zku?<\/li>\n<\/ul>\n\n\n\n<p>Napr\u00edklad Tukeyho HSD (Honestly Significant Difference) je najvhodnej\u0161ia, ke\u010f rob\u00edme v\u0161etky mo\u017en\u00e9 p\u00e1rov\u00e9 porovnania a porovnania a sna\u017e\u00edme sa udr\u017ea\u0165 chybovos\u0165 v rodine rovn\u00fa na\u0161ej hladine alfa (\u010dasto 0,05). Holmova met\u00f3da postupuje vy\u0161\u0161ie t\u00fdm, \u017ee postupne upravuje p-hodnoty a dosahuje rovnov\u00e1hu - je menej konzervat\u00edvna ako Bonferroniho met\u00f3da, ale st\u00e1le poskytuje primeran\u00fa ochranu pred chybami typu I. A ak je vo va\u0161om n\u00e1vrhu zahrnut\u00e1 jedin\u00e1 kontroln\u00e1 alebo referen\u010dn\u00e1 skupina? Dunnettova met\u00f3da m\u00f4\u017ee pr\u00eds\u0165 do \u00favahy, preto\u017ee sa \u0161pecificky zaober\u00e1 porovn\u00e1van\u00edm s t\u00fdmto centr\u00e1lnym \u00fadajom.<\/p>\n\n\n\n<p>Na z\u00e1ver:<\/p>\n\n\n\n<p>\u00da\u010dinn\u00e9 zmiernenie riz\u00edk spojen\u00fdch so zv\u00fd\u0161en\u00fdm testovan\u00edm hypot\u00e9z si vy\u017eaduje rozumn\u00e9 rozhodnutia t\u00fdkaj\u00face sa met\u00f3d \u0161tatistickej anal\u00fdzy. Ke\u010f sa po v\u00fdsledku ANOVA, ktor\u00fd nazna\u010duje v\u00fdznamn\u00fd rozptyl medzi skupinami, vrhnete bezhlavo do post hoc testovania, v\u017edy pam\u00e4tajte: Je to va\u0161a poistka, ktor\u00e1 zabezpe\u010d\u00ed spo\u013eahlivos\u0165 a platnos\u0165 z\u00e1verov vyvoden\u00fdch z komplexn\u00fdch d\u00e1tov\u00fdch modelov.<\/p>\n\n\n\n<h2 id=\"h-case-studies-and-examples\">Pr\u00edpadov\u00e9 \u0161t\u00fadie a pr\u00edklady<\/h2>\n\n\n\n<p>Pochopenie pojmov v \u0161tatistike sa v\u00fdrazne zlep\u0161uje sk\u00faman\u00edm re\u00e1lnych aplik\u00e1ci\u00ed. Po\u010fme sa pozrie\u0165 na to, ako post hoc testovanie ANOVA vdychuje \u017eivot do v\u00fdskumn\u00fdch \u0161t\u00fadi\u00ed a poskytuje vedeck\u00fdm v\u00fdskumom pr\u00edsnu met\u00f3du na sk\u00famanie ich v\u00fdsledkov.<\/p>\n\n\n\n<h3 id=\"h-discussion-of-real-world-research-studies-where-post-hoc-testing-was-used\">Diskusia o re\u00e1lnych v\u00fdskumn\u00fdch \u0161t\u00fadi\u00e1ch, v ktor\u00fdch sa pou\u017eilo post hoc testovanie<\/h3>\n\n\n\n<p>Post hoc anal\u00fdzy a testy, sk\u00faman\u00e9 cez optiku praktick\u00e9ho pou\u017eitia, sa st\u00e1vaj\u00fa viac ne\u017e abstraktn\u00fdmi matematick\u00fdmi postupmi; s\u00fa to n\u00e1stroje, ktor\u00e9 rozv\u00edjaj\u00fa pr\u00edbehy v r\u00e1mci \u00fadajov. Napr\u00edklad v \u0161t\u00fadii zameranej na \u00fa\u010dinnos\u0165 r\u00f4znych vyu\u010dovac\u00edch metod\u00edk sa m\u00f4\u017ee pou\u017ei\u0165 ANOVA na zistenie, \u010di existuj\u00fa v\u00fdznamn\u00e9 rozdiely vo v\u00fdsledkoch \u0161tudentov na z\u00e1klade vyu\u010dovacieho pr\u00edstupu. Ak omnibusov\u00fd test prinesie v\u00fdznamn\u00fd v\u00fdsledok, otvor\u00ed cestu k post hoc anal\u00fdze - nevyhnutnej na presn\u00e9 ur\u010denie toho, ktor\u00e9 met\u00f3dy sa od seba navz\u00e1jom l\u00ed\u0161ia.<\/p>\n\n\n\n<p>Dovo\u013ete mi, aby som sa podelil o \u010fal\u0161\u00ed pr\u00edklad, ktor\u00fd poukazuje na t\u00fato metodiku: predstavte si, \u017ee v\u00fdskumn\u00edci vykonali post hoc anal\u00fdzu experimentu, v ktorom hodnotili vplyv nov\u00e9ho lieku na hladinu krvn\u00e9ho tlaku. Po\u010diato\u010dn\u00e1 ANOVA ukazuje, \u017ee hodnoty krvn\u00e9ho tlaku sa v priebehu \u010dasu medzi jednotliv\u00fdmi skupinami d\u00e1vkovania v\u00fdrazne l\u00ed\u0161ia. Post hoc testovanie je \u010fal\u0161\u00edm d\u00f4le\u017eit\u00fdm krokom, ktor\u00fd pom\u00e1ha vedcom porovna\u0165 v\u0161etky mo\u017en\u00e9 dvojice d\u00e1vok, aby konkr\u00e9tne pochopili, ktor\u00e9 z nich s\u00fa \u00fa\u010dinn\u00e9 a ktor\u00e9 potenci\u00e1lne \u0161kodliv\u00e9.<\/p>\n\n\n\n<p>Tieto pr\u00edklady ukazuj\u00fa, ako post hoc testovanie po ANOVA nielen vedie v\u00fdskumn\u00edkov na ich ceste objavovania, ale tie\u017e zabezpe\u010duje robustnos\u0165 a presnos\u0165 ich z\u00e1verov.<\/p>\n\n\n\n<h3 id=\"h-hands-on-examples-illustrating-the-application-of-different-post-hoc-tests\">Praktick\u00e9 pr\u00edklady ilustruj\u00face pou\u017eitie r\u00f4znych post hoc testov<\/h3>\n\n\n\n<p>Hlb\u0161ie presk\u00famanie viacer\u00fdch porovn\u00e1vac\u00edch testov pre konkr\u00e9tne aplik\u00e1cie m\u00f4\u017ee poskytn\u00fa\u0165 preh\u013ead o tom, ak\u00e9 r\u00f4znorod\u00e9 m\u00f4\u017eu tieto testy by\u0165:<\/p>\n\n\n\n<ul>\n<li><strong>Tukeyho met\u00f3da<\/strong>: Zoberte si, \u017ee po\u013enohospod\u00e1rski vedci porovn\u00e1vaj\u00fa v\u00fdnosy plod\u00edn pri viacer\u00fdch typoch hnoj\u00edv. Po zisten\u00ed v\u00fdznamnej ANOVA, ktor\u00e1 zist\u00ed rozdielne v\u00fdnosy medzi jednotliv\u00fdmi o\u0161etreniami, by Tukeyho met\u00f3da mohla presne odhali\u0165, ktor\u00e9 hnojiv\u00e1 prin\u00e1\u0161aj\u00fa \u0161tatisticky odli\u0161n\u00e9 \u00farody v porovnan\u00ed s ostatn\u00fdmi - a to v\u0161etko pri kontrole chyby typu I vo v\u0161etk\u00fdch porovnaniach.<\/li>\n\n\n\n<li><strong>Holmova met\u00f3da<\/strong>: V psychologickom v\u00fdskume zameranom na pochopenie v\u00fdsledkov terapie by Holmov sekven\u010dn\u00fd postup upravil p-hodnoty, ke\u010f sa hodnot\u00ed viacero foriem lie\u010dby oproti kontroln\u00fdm skupin\u00e1m. T\u00fdm sa zabezpe\u010d\u00ed, \u017ee n\u00e1sledn\u00e9 zistenia zostan\u00fa spo\u013eahliv\u00e9 aj po zisten\u00ed, \u017ee niektor\u00e9 terapie prekon\u00e1vaj\u00fa \u017eiadnu lie\u010dbu.<\/li>\n\n\n\n<li><strong>Dunnettova met\u00f3da<\/strong>: Dunnettova met\u00f3da, ktor\u00e1 sa \u010dasto pou\u017e\u00edva v klinick\u00fdch \u0161t\u00fadi\u00e1ch so skupinou s placebom, porovn\u00e1va ka\u017ed\u00fa lie\u010dbu priamo s placebom. \u0160t\u00fadia, v ktorej sa hodnot\u00ed nieko\u013eko nov\u00fdch liekov na zmiernenie bolesti v porovnan\u00ed s placebom, by mohla vyu\u017ei\u0165 Dunnettovu met\u00f3du na rozl\u00ed\u0161enie, \u010di m\u00e1 niektor\u00fd nov\u00fd liek lep\u0161\u00ed \u00fa\u010dinok bez toho, aby sa zv\u00fd\u0161ilo riziko falo\u0161ne pozit\u00edvnych v\u00fdsledkov v d\u00f4sledku viacn\u00e1sobn\u00e9ho porovn\u00e1vania.<\/li>\n<\/ul>\n\n\n\n<p>Tieto \u00faryvky z r\u00f4znych oblast\u00ed zd\u00f4raz\u0148uj\u00fa, ako prisp\u00f4soben\u00e9 post hoc testovanie v ANOVA d\u00e1va podstatu ni\u017e\u0161ej \u0161tatistickej sile v\u00fdznamnosti - premie\u0148a \u010d\u00edsla na zmyslupln\u00e9 poznatky, ktor\u00e9 m\u00f4\u017eu pom\u00f4c\u0165 formova\u0165 priemyseln\u00e9 odvetvia a zlep\u0161i\u0165 \u017eivoty.<\/p>\n\n\n\n<h2 id=\"h-statistical-power-in-post-hoc-testing\">\u0160tatistick\u00e1 sila pri post-Hoc testovan\u00ed<\/h2>\n\n\n\n<h3 id=\"h-explanation-of-statistical-power-and-its-importance-in-post-hoc-testing-decision-making\">Vysvetlenie \u0161tatistickej sily a jej v\u00fdznamu pri rozhodovan\u00ed o post hoc testovan\u00ed<\/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>Pri diskusii o zlo\u017eitosti post hoc testovania v\u00fdsledkov ANOVA je nevyhnutn\u00e9 pochopi\u0165 koncept, ktor\u00fd je z\u00e1kladom testovania hypot\u00e9z - \u0161tatistick\u00fa silu. Zjednodu\u0161ene povedan\u00e9, \u0161tatistick\u00e1 sila je pravdepodobnos\u0165, \u017ee \u0161t\u00fadia odhal\u00ed \u00fa\u010dinok, ak skuto\u010dne existuje. To sa premieta do zistenia skuto\u010dn\u00fdch rozdielov medzi skupinami, ak skuto\u010dne existuj\u00fa.<\/p>\n\n\n\n<p>Vysok\u00e1 \u0161tatistick\u00e1 sila zni\u017euje pravdepodobnos\u0165, \u017ee sa dopust\u00edme chyby typu II, ktor\u00e1 nastane, ke\u010f nezist\u00edme rozdiel, ktor\u00fd v skuto\u010dnosti existuje. Chr\u00e1ni na\u0161e v\u00fdsledky pred falo\u0161ne negat\u00edvnymi v\u00fdsledkami, \u010d\u00edm posil\u0148uje spo\u013eahlivos\u0165 z\u00e1verov vypl\u00fdvaj\u00facich z na\u0161ej anal\u00fdzy. Tento faktor sa st\u00e1va obzvl\u00e1\u0161\u0165 d\u00f4le\u017eit\u00fdm po\u010das post hoc testov po tom, \u010do ANOVA nazna\u010dila v\u00fdznamn\u00e9 rozdiely medzi skupinami.<\/p>\n\n\n\n<p>Dosiahnutie vysokej \u0161tatistickej sily v praxi \u010dasto znamen\u00e1, \u017ee va\u0161a \u0161t\u00fadia m\u00e1 primeran\u00fa ve\u013ekos\u0165 vzorky. Zatia\u013e \u010do pr\u00edli\u0161 mal\u00e1 vzorka nemus\u00ed presne odr\u00e1\u017ea\u0165 skuto\u010dn\u00e9 skupinov\u00e9 rozdiely, v\u00fdnimo\u010dne ve\u013ek\u00e9 vzorky by mohli odhali\u0165 \u0161tatisticky v\u00fdznamn\u00e9, ale prakticky irelevantn\u00e9 rozdiely. Preto je vyv\u00e1\u017eenie t\u00fdchto h\u013ead\u00edsk rozhoduj\u00face pre presved\u010div\u00e9 rozhodovanie v akomko\u013evek v\u00fdskumnom prostred\u00ed zah\u0155\u0148aj\u00facom post hoc testovanie ANOVA.<\/p>\n\n\n\n<h3 id=\"h-managing-power-trade-offs-by-reducing-the-number-of-comparisons\">Riadenie kompromisov v oblasti v\u00fdkonu zn\u00ed\u017een\u00edm po\u010dtu porovn\u00e1van\u00ed<\/h3>\n\n\n\n<p>Na rie\u0161enie potenci\u00e1lnych \u00faskal\u00ed spojen\u00fdch s viacn\u00e1sobn\u00fdmi porovnaniami po vykonan\u00ed met\u00f3dy ANOVA by v\u00fdskumn\u00edci mali rozumne zvl\u00e1dnu\u0165 kompromis medzi zachovan\u00edm dostato\u010dnej \u0161tatistickej sily a kontrolou zv\u00fd\u0161en\u00e9ho rizika ch\u00fdb typu I (falo\u0161ne pozit\u00edvnych v\u00fdsledkov). Tu s\u00fa uveden\u00e9 \u00fa\u010dinn\u00e9 strat\u00e9gie:<\/p>\n\n\n\n<ul>\n<li>Stanovenie prior\u00edt: Ur\u010dite, ktor\u00e9 porovnania s\u00fa pre va\u0161e hypot\u00e9zy najd\u00f4le\u017eitej\u0161ie, a ur\u010dte ich priority pre \u010fal\u0161ie sk\u00famanie.<\/li>\n\n\n\n<li>Konsolid\u00e1cia: Namiesto sk\u00famania v\u0161etk\u00fdch mo\u017en\u00fdch p\u00e1rov\u00fdch porovnan\u00ed medzi \u00farov\u0148ami lie\u010dby sa zamerajte len na porovnanie ka\u017edej skupiny lie\u010dby s kontrolnou skupinou alebo spojte skupiny lie\u010dby do zmyslupln\u00fdch kateg\u00f3ri\u00ed.<\/li>\n<\/ul>\n\n\n\n<p>Premyslen\u00fdm v\u00fdberom men\u0161ieho po\u010dtu porovnan\u00ed v\u00fdskumn\u00edci nielen\u017ee zvy\u0161uj\u00fa \u0161ancu, \u017ee si ich \u0161t\u00fadia zachov\u00e1 robustn\u00fa \u0161tatistick\u00fa silu, ale tie\u017e zni\u017euj\u00fa chybovos\u0165 experimentu bez toho, aby sa pre\u0165a\u017euj\u00face korek\u010dn\u00e9 postupy premietli do ich objavn\u00e9ho potenci\u00e1lu.<\/p>\n\n\n\n<p>Rie\u0161enie tejto krehkej rovnov\u00e1hy bystro zabezpe\u010duje, \u017ee podstatne d\u00f4le\u017eit\u00e9 zistenia vynikn\u00fa a z\u00e1rove\u0148 sa potvrd\u00ed metodologick\u00e1 pr\u00edsnos\u0165 - \u010do je z\u00e1kladn\u00fd bod rovnov\u00e1hy pre v\u0161etky \u0161t\u00fadie, ktor\u00e9 pou\u017e\u00edvaj\u00fa post hoc testovanie v r\u00e1mci ANOVA.<\/p>\n\n\n\n<h2 id=\"h-summary-and-conclusion\">Zhrnutie a z\u00e1ver<\/h2>\n\n\n\n<h3 id=\"h-recap-of-key-points-covered-in-the-content-outline\">Rekapitul\u00e1cia k\u013e\u00fa\u010dov\u00fdch bodov uveden\u00fdch v osnove obsahu<\/h3>\n\n\n\n<p>V tomto \u010dl\u00e1nku sme pre\u0161li krajinou anal\u00fdzy rozptylu (ANOVA) a jej kritick\u00e9ho sprievodcu - <strong>post hoc testovanie ANOVA<\/strong>. Na \u00favod sme si vytvorili z\u00e1kladn\u00fa predstavu o ANOVA, ktor\u00e1 sa pou\u017e\u00edva na zistenie, \u010di existuj\u00fa \u0161tatisticky v\u00fdznamn\u00e9 rozdiely medzi priemermi troch alebo viacer\u00fdch nez\u00e1visl\u00fdch skup\u00edn.<\/p>\n\n\n\n<p>Venovali sme sa zlo\u017eitosti post hoc testovania, ktor\u00e9 je nevyhnutn\u00e9, ke\u010f po\u010diato\u010dn\u00e1 ANOVA prinesie v\u00fdznamn\u00e9 v\u00fdsledky. Zistili sme, \u017ee ANOVA n\u00e1m s\u00edce dok\u00e1\u017ee poveda\u0165, \u017ee aspo\u0148 dve skupiny sa l\u00ed\u0161ia, ale ne\u0161pecifikuje, ktor\u00e9 skupiny alebo ko\u013eko sa od seba l\u00ed\u0161ia. Na to sl\u00fa\u017eia post hoc testy.<\/p>\n\n\n\n<p>Po\u010das diskusie sme pre\u0161li r\u00f4znymi z\u00e1krutami:<\/p>\n\n\n\n<ul>\n<li>Kritick\u00e1 povaha omnibusov\u00e9ho testu ANOVA, ktor\u00fd pou\u017e\u00edva F-\u0161tatistiku na ur\u010denie celkov\u00e9ho rozptylu.<\/li>\n\n\n\n<li>V\u00fdznam presnej interpret\u00e1cie t\u00fdchto v\u00fdsledkov pre spo\u013eahliv\u00fa \u0161tatistick\u00fa anal\u00fdzu.<\/li>\n<\/ul>\n\n\n\n<p>Ke\u010f sa uk\u00e1zali obmedzenia, ako napr\u00edklad chybovos\u0165 experimentu, pochopili sme, pre\u010do je post hoc testovanie nielen u\u017eito\u010dn\u00e9, ale aj potrebn\u00e9. Pon\u00faka spresnen\u00e9 poznatky t\u00fdm, \u017ee kontroluje tieto miery ch\u00fdb a umo\u017e\u0148uje viacn\u00e1sobn\u00e9 porovn\u00e1vanie bez toho, aby sa zv\u00fd\u0161ila pravdepodobnos\u0165 ch\u00fdb typu I.<\/p>\n\n\n\n<p>Pri na\u0161ej exped\u00edcii r\u00f4znymi met\u00f3dami, ako s\u00fa Tukeyho, Holmova a Dunnettova, ste si pravdepodobne v\u0161imli, \u017ee sl\u00fa\u017eia na jedine\u010dn\u00e9 \u00fa\u010dely - \u010di u\u017e ide o porovn\u00e1vanie viacer\u00fdch porovnan\u00ed v\u0161etk\u00fdch mo\u017en\u00fdch p\u00e1rov stredn\u00fdch hodn\u00f4t, alebo o zameranie sa na porovnanie jednej kontrolnej skupiny.<\/p>\n\n\n\n<p>V\u00fdber post hoc testu si vy\u017eaduje d\u00f4kladn\u00e9 zv\u00e1\u017eenie. Kontrola chybovosti sa neuskuto\u010d\u0148uje izolovane; akoell post hoc testy, je potrebn\u00e9 zv\u00e1\u017ei\u0165 faktory s\u00favisiace s chybovos\u0165ou jednotliv\u00fdch rod\u00edn.<\/p>\n\n\n\n<p>Zapojenie re\u00e1lnych pr\u00edkladov do na\u0161ej diskusie pomohlo tieto koncep\u010dn\u00e9 \u00favahy pevne zakotvi\u0165 do praktick\u00fdch aplika\u010dn\u00fdch scen\u00e1rov.<\/p>\n\n\n\n<p>Nakoniec, \u010do je v\u0161ak d\u00f4le\u017eit\u00e9, sme sa dotkli \u0161tatistickej sily. Zatia\u013e \u010do zn\u00ed\u017eenie po\u010dtu porovnan\u00ed sa niekedy pova\u017euje za zn\u00ed\u017eenie kompromisov v oblasti sily\", strategick\u00e9 rozhodovanie tu zabezpe\u010duje robustnos\u0165 zisten\u00ed aj pri zapojen\u00ed viacer\u00fdch post hoc testov.<\/p>\n\n\n\n<h3 id=\"h-concluding-thoughts-on-the-importance-and-significance-of-post-hoc-testing-in-anova\">Z\u00e1vere\u010dn\u00e9 my\u0161lienky o d\u00f4le\u017eitosti a v\u00fdzname post hoc testovania v ANOVA<\/h3>\n\n\n\n<p>Na z\u00e1ver tejto zasv\u00e4tenej exkurzie do <strong>post hoc testovanie ANOVA<\/strong>, pripome\u0148me si, pre\u010do m\u00e1 ponorenie sa do tohto konkr\u00e9tneho \u00fazemia \u0161tatistickej anal\u00fdzy tak\u00fd ve\u013ek\u00fd v\u00fdznam. Vo v\u00fdskumn\u00fdch kontextoch, ktor\u00e9 siahaj\u00fa od prelomov\u00fdch objavov v zdravotn\u00edctve a\u017e po prelomov\u00fd technologick\u00fd v\u00fdvoj, m\u00f4\u017ee ma\u0165 zabezpe\u010denie toho, aby na\u0161e zistenia boli nielen \u0161tatisticky relevantn\u00e9, ale aj prakticky v\u00fdznamn\u00e9, z\u00e1sadn\u00fd v\u00fdznam.<\/p>\n\n\n\n<p>Rozumn\u00e9 pou\u017e\u00edvanie post hoc testov po ANOVA n\u00e1m umo\u017e\u0148uje prekro\u010di\u0165 r\u00e1mec jednoduch\u00e9ho zis\u0165ovania rozdielov a pusti\u0165 sa do sk\u00famania toho, ak\u00e9 s\u00fa tieto rozdiely - a ich ve\u013ekosti - s presnos\u0165ou a istotou dostato\u010dne ve\u013ekou na to, aby sme mohli rozhoduj\u00facim sp\u00f4sobom ovplyvni\u0165 \u010fal\u0161ie v\u00fdskumn\u00e9 cesty alebo politick\u00e9 rozhodnutia.<\/p>\n\n\n\n<p>Ako horliv\u00ed vedci a zanieten\u00ed odborn\u00edci, ktor\u00ed sa pohybuj\u00fa vo svete, ktor\u00fd je \u010doraz viac zalo\u017een\u00fd na \u00fadajoch, tak\u00e9to pr\u00edstupy nielen spres\u0148uj\u00fa na\u0161e ch\u00e1panie - ale aj roz\u0161iruj\u00fa mo\u017enosti. Post hoc testy na\u010falej dr\u017eia vysoko polo\u017een\u00fa pochode\u0148 osvet\u013euj\u00facu nuansovan\u00e9 detaily uprostred niekedy ohromuj\u00facich s\u00faborov \u00fadajov - maj\u00e1k smeruj\u00faci k presved\u010div\u00fdm poznatkom zv\u00e4\u010d\u0161uj\u00facim na\u0161u schopnos\u0165 prij\u00edma\u0165 informovan\u00e9 rozhodnutia zalo\u017een\u00e9 na robustn\u00fdch analytick\u00fdch procesoch, ktor\u00e9 horlivo odol\u00e1vaj\u00fa kontrole vo vedeck\u00fdch kruhoch aj na poliach priekopn\u00edckych inov\u00e1ci\u00ed, ktor\u00e9 sa \u00faprimne usiluj\u00fa o spolo\u010densk\u00fd prospech s mnohorozmern\u00fdm rozsahom, \u010do in\u0161piruje ka\u017ed\u00e9 nov\u00e9 h\u013eadanie \"...nepredv\u00eddan\u00fdch z\u00e1konitost\u00ed\".<\/p>\n\n\n\n<p>Cez to v\u0161etko zost\u00e1va moja n\u00e1dej nezlomn\u00e1: nech va\u0161e vlastn\u00e9 anal\u00fdzy prin\u00e1\u0161aj\u00fa plodn\u00e9 porozumenie pretkan\u00e9 jasnos\u0165ou, ktor\u00e1 si zasl\u00fa\u017ei ocenenie a v kone\u010dnom d\u00f4sledku zlep\u0161uje \u017eivoty, ktor\u00fdch sa dot\u00fdkaj\u00fa postupy zalo\u017een\u00e9 na d\u00f4kazoch, stojace nad\u010dasovo na pr\u00edsnych \u0161tatistick\u00fdch z\u00e1kladoch, ktor\u00e9 ne\u00fanavne definuj\u00fa rozdiely... v snahe o dosiahnutie pravdy, ktor\u00e1 je v\u017edy nepolapite\u013en\u00e1, ale ve\u010dne l\u00e1kav\u00e1.<\/p>\n\n\n\n<h2 id=\"h-experience-the-power-of-visual-mastery-simplifying-complexity-with-mind-the-graph\"><br>Za\u017eite silu vizu\u00e1lneho majstrovstva: Zjednodu\u0161enie zlo\u017eitosti s Mind the Graph!<\/h2>\n\n\n\n<p>Odha\u013ete potenci\u00e1l bezchybnej vizu\u00e1lnej komunik\u00e1cie, ke\u010f nanovo definujeme sp\u00f4sob, ak\u00fdm ch\u00e1pete zlo\u017eit\u00e9 koncepty. V \u00e9re, ktorej dominuj\u00fa vizu\u00e1lne efekty, sa pochopenie zlo\u017eit\u00fdch my\u0161lienok, dokonca aj nie\u010doho tak z\u00e1hadn\u00e9ho, ako je kvantov\u00e1 fyzika, st\u00e1va hra\u010dkou v\u010faka samotnej \u00fa\u010dinnosti grafiky.<\/p>\n\n\n\n<p>Vydajte sa na vizu\u00e1lnu 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 spolo\u010dn\u00edk pri transform\u00e1cii zlo\u017eit\u00fdch spr\u00e1v do podmaniv\u00fdch vizu\u00e1lov. S viac ako tis\u00edckou starostlivo spracovan\u00fdch ilustr\u00e1ci\u00ed v na\u0161ej gal\u00e9rii s\u00fa mo\u017enosti neobmedzen\u00e9. N\u00e1\u0161 \u0161pi\u010dkov\u00fd inteligentn\u00fd tvorca plag\u00e1tov v\u00e1m umo\u017en\u00ed bez n\u00e1mahy vytv\u00e1ra\u0165 plag\u00e1ty, ktor\u00e9 vynikn\u00fa.<\/p>\n\n\n\n<p>Pre\u010do sa uspokoji\u0165 s oby\u010dajn\u00fdm, ke\u010f m\u00f4\u017eete ma\u0165 vizu\u00e1lne majstrovsk\u00e9 dielo na mieru? Vyu\u017eite odborn\u00e9 znalosti n\u00e1\u0161ho talentovan\u00e9ho t\u00edmu a prisp\u00f4sobte ilustr\u00e1cie va\u0161im jedine\u010dn\u00fdm potreb\u00e1m. Mind the Graph nie je len n\u00e1stroj; je to va\u0161a br\u00e1na do sveta, kde vizu\u00e1lne prvky hovoria hlasnej\u0161ie ako slov\u00e1.<\/p>\n\n\n\n<p>Ste pripraven\u00ed posilni\u0165 svoju komunika\u010dn\u00fa hru? Zaregistrujte sa zadarmo a za\u010dnite tvori\u0165 hne\u010f teraz. Va\u0161e posolstvo, na\u0161e vizu\u00e1ly - bezchybn\u00e1 kombin\u00e1cia!<\/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\u010dnite tvori\u0165 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>Objavte z\u00e1kutia post hoc testovania ANOVA. Zdokona\u013ete svoju \u0161tatistick\u00fa anal\u00fdzu a odha\u013ete v\u00fdznamnos\u0165 svojich s\u00faborov \u00fadajov.<\/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\/sk\/post-hoc-testovanie-anova\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\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\/sk\/author\/fabricio\/"}]}},"_links":{"self":[{"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/posts\/50301"}],"collection":[{"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/comments?post=50301"}],"version-history":[{"count":3,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/posts\/50301\/revisions"}],"predecessor-version":[{"id":50305,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/posts\/50301\/revisions\/50305"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/media\/50304"}],"wp:attachment":[{"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/media?parent=50301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/categories?post=50301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/sk\/wp-json\/wp\/v2\/tags?post=50301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}