{"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\/lv\/pec-anova-testesanas\/","title":{"rendered":"Post Hoc test\u0113\u0161ana ANOVA: uzziniet, k\u0101 analiz\u0113t datu kopas"},"content":{"rendered":"<p>Vai j\u016bs k\u0101dreiz ir p\u0101r\u0146\u0113mis zin\u0101tk\u0101re par to, k\u0101 p\u0113tnieki izdara konkr\u0113tus secin\u0101jumus no datu grup\u0101m, kas pirmaj\u0101 br\u012bd\u012b \u0161\u0137iet tikpat nosl\u0113pumainas k\u0101 senais kods? Tas k\u013c\u016bst maz\u0101k nosl\u0113pumains, kad izprotat, kas sl\u0113pjas aiz post hoc test\u0113\u0161anas ANOVA - Varian\u010du anal\u012bzes - kontekst\u0101. \u0160\u012b statistikas metode nav tikai instruments, t\u0101 ir l\u012bdz\u012bga \u0160erloka Holmsa palielin\u0101majam stiklam, ko izmanto, lai atkl\u0101tu sl\u0113pto paties\u012bbu neskait\u0101mos skait\u013cos. Neatkar\u012bgi no t\u0101, vai esat students, kas c\u012bn\u0101s ar sava diplomdarba datiem, vai pieredz\u0113jis p\u0113tnieks, kura m\u0113r\u0137is ir ieg\u016bt p\u0101rliecino\u0161us rezult\u0101tus, post hoc testu sp\u0113ka atkl\u0101\u0161ana var padar\u012bt j\u016bsu secin\u0101jumus no interesantiem par revolucion\u0101riem.<\/p>\n\n\n\n<h2 id=\"h-understanding-anova-and-post-hoc-testing\">Izpratne par ANOVA un Post Hoc test\u0113\u0161anu<\/h2>\n\n\n\n<p>Izp\u0113tot savstarp\u0113ji saist\u012btos ANOVA un post hoc test\u0113\u0161anas j\u0113dzienus, uzskatiet tos par partneriem prec\u012bzas anal\u012bzes mekl\u0113jumos. T\u0101s dod mums iesp\u0113ju iel\u016bkoties t\u0101l\u0101k par vid\u0113j\u0101m v\u0113rt\u012bb\u0101m un izp\u0113t\u012bt dzi\u013c\u0101kas nianses starp vair\u0101ku grupu sal\u012bdzin\u0101jumiem - bet turpin\u0101sim soli pa solim.<\/p>\n\n\n\n<p>Saist\u012bts raksts: <a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\"><strong>Post Hoc anal\u012bze: Process un testu veidi<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-introduction-to-anova-and-its-purpose-in-statistical-analysis\">Ievads ANOVA un t\u0101s m\u0113r\u0137is statistiskaj\u0101 anal\u012bz\u0113<\/h3>\n\n\n\n<p>Varian\u010du anal\u012bze jeb ANOVA, k\u0101 to m\u0113dz d\u0113v\u0113t statisti\u0137i, ir viens no sp\u0113c\u012bg\u0101kajiem r\u012bkiem vi\u0146u arsen\u0101l\u0101. T\u0101 pilda \u013coti svar\u012bgu funkciju - \u013cauj noteikt, vai eksperiment\u0101, kur\u0101 piedal\u0101s tr\u012bs vai vair\u0101k grupas, past\u0101v statistiski noz\u012bm\u012bgas at\u0161\u0137ir\u012bbas starp grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem. Sal\u012bdzinot dispersijas atsevi\u0161\u0137\u0101s grup\u0101s ar dispersij\u0101m starp \u0161\u012bm grup\u0101m, ANOVA pal\u012bdz noraid\u012bt vai saglab\u0101t nulles hipot\u0113zi, ka nepast\u0101v nek\u0101das dispersijas, iz\u0146emot gad\u012bjuma rakstura at\u0161\u0137ir\u012bbas.<\/p>\n\n\n\n<h3 id=\"h-explanation-of-post-hoc-testing-and-its-importance-in-anova\">Paskaidrojums par post hoc test\u0113\u0161anu un t\u0101s noz\u012bmi ANOVA test\u0113\u0161an\u0101<\/h3>\n\n\n\n<p>Lai gan noz\u012bm\u012bguma noteik\u0161ana liel\u0101s kop\u0101s ir b\u016btiska, kas notiek, ja ANOVA nor\u0101da, ka \"kaut kas\" at\u0161\u0137iras, bet nepreciz\u0113, \"kas\" un \"kur\"? Post hoc test\u0113\u0161ana! Ar sa\u012bsin\u0101jumu no \"p\u0113c tam\" post hoc test\u0113\u0161ana seko l\u012bdzi p\u0113d\u0101m, ko atst\u0101j ANOVA omnibus tests. T\u0101s uzdevums? Prec\u012bzi noteikt, kuri p\u0101ri vai kombin\u0101cijas starp m\u016bsu grup\u0101m uzr\u0101da b\u016btiskas at\u0161\u0137ir\u012bbas, t\u0101d\u0113j\u0101di \u013caujot p\u0113tniekiem pie\u0146emt pamatotus l\u0113mumus ar nevainojamu precizit\u0101ti.<\/p>\n\n\n\n<h3 id=\"h-overview-of-the-process-of-post-hoc-testing-in-anova\">P\u0101rskats par ANOVA post hoc test\u0113\u0161anas procesu<\/h3>\n\n\n\n<p>Post hoc test\u0113\u0161ana vienm\u0113r tiek veikta p\u0113c tam, kad ANOVA omnibus test\u0101 ir ieg\u016bts noz\u012bm\u012bgs rezult\u0101ts - no t\u0101 ar\u012b izriet t\u0101s retrospekt\u012bvais nosaukums. Iedom\u0101jieties, ka \u0161is process liel\u0101koties sast\u0101v no:<\/p>\n\n\n\n<ul>\n<li><strong>Atbilsto\u0161a post hoc testa izv\u0113le<\/strong>: Atkar\u012bb\u0101 no konstrukcijas specifikas un k\u013c\u016bdu koeficienta pielaides.<\/li>\n\n\n\n<li><strong>P-v\u0113rt\u012bbu kori\u0123\u0113\u0161ana<\/strong>: Korekcija, lai \u0146emtu v\u0113r\u0101 paaugstin\u0101tus riskus, kas saist\u012bti ar vair\u0101kk\u0101rt\u0113ju sal\u012bdzin\u0101\u0161anu.<\/li>\n\n\n\n<li><strong>Rezult\u0101tu interpret\u0101cija kontekst\u0101<\/strong>: Praktisk\u0101 noz\u012bm\u012bguma nodro\u0161in\u0101\u0161ana atbilsto\u0161i statistikas rezult\u0101tiem.<\/li>\n<\/ul>\n\n\n\n<p>\u0160\u012b disciplin\u0113t\u0101 pieeja pasarg\u0101 no k\u013c\u016bdainiem secin\u0101jumiem, vienlaikus ieg\u016bstot v\u0113rt\u012bgas atzi\u0146as, kas datu kop\u0101s ir apsl\u0113ptas. Bru\u0146ojoties ar \u0161o progres\u012bvo, bet pieejamo izpratni, ikviens var uzs\u0101kt ce\u013cu uz savu datu st\u0101st\u012bjumu p\u0101rzin\u0101\u0161anu.<\/p>\n\n\n\n<h2 id=\"h-anova-omnibus-test\">ANOVA Omnibus tests<\/h2>\n\n\n\n<p>Analiz\u0113jot datu kopas ar vair\u0101k nek\u0101 diviem vid\u0113jiem r\u0101d\u012bt\u0101jiem, lai saprastu, vai vismaz viens no tiem at\u0161\u0137iras no p\u0101r\u0113jiem, ir svar\u012bgi izmantot vari\u0101ciju anal\u012bzi (ANOVA). Ta\u010du, pirms m\u0113s iedzi\u013cin\u0101mies ANOVA post hoc test\u0113\u0161anas nians\u0113s, ir b\u016btiski saprast pamatv\u0113rt\u0113jumu - ANOVA omnibus testu. Iedom\u0101jieties to k\u0101 detekt\u012bvst\u0101stu, kur\u0101 s\u0101kotn\u0113jie pier\u0101d\u012bjumi nor\u0101da uz aizdom\u0101s turam\u0101 iesp\u0113jam\u012bbu, bet prec\u012bzi nenor\u0101da, kas tas ir.<\/p>\n\n\n\n<p>Saist\u012bts raksts: <a href=\"https:\/\/mindthegraph.com\/blog\/one-way-anova\/\"><strong>Vienvirziena ANOVA: izpratne, vad\u012b\u0161ana un prezent\u0113\u0161ana<\/strong><\/a><\/p>\n\n\n\n<h3 id=\"h-detailed-explanation-of-the-anova-omnibus-test\">ANOVA omnibus testa detaliz\u0113ts skaidrojums<\/h3>\n\n\n\n<p>ANOVA omnibus tests izce\u013cas ar to, ka tas \u013cauj sal\u012bdzin\u0101t vair\u0101ku grupu vid\u0113jos lielumus vienlaic\u012bgi, nevis veikt daudzus testus katram iesp\u0113jamajam p\u0101ra noz\u012bm\u012bguma l\u012bmenim, kas neap\u0161aub\u0101mi palielin\u0101tu I tipa k\u013c\u016bdas risku - viltus pozit\u012bvo rezult\u0101tu skaitu. V\u0101rds \"omnibus\" t\u0101 nosaukum\u0101 nor\u0101da, ka \u0161is tests tiek veikts no visp\u0101r\u0113jas perspekt\u012bvas - tas kop\u012bgi p\u0101rbauda, vai starp grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem past\u0101v statistiski noz\u012bm\u012bga at\u0161\u0137ir\u012bba.<\/p>\n\n\n\n<p>L\u016bk, k\u0101 tas notiek: S\u0101kam ar atsevi\u0161\u0137u vari\u0101ciju apr\u0113\u0137in\u0101\u0161anu grup\u0101s un starp grup\u0101m. Ja m\u016bsu grupas iek\u0161\u0113ji ir diezgan viendab\u012bgas, bet iev\u0113rojami at\u0161\u0137iras viena no otras, tas ir dro\u0161s r\u0101d\u012bt\u0101js, ka ne visu grupu vid\u0113jie r\u0101d\u012bt\u0101ji ir vien\u0101di. B\u016bt\u012bb\u0101 m\u0113s mekl\u0113jam starpgrupu b grupas iek\u0161\u0113j\u0101s vari\u0101cijas, ko nevar izskaidrot tikai ar nejau\u0161\u012bbu sal\u012bdzin\u0101jum\u0101 ar grupas iek\u0161\u0113j\u0101m vari\u0101cij\u0101m - ko m\u0113s sagaid\u012btu no nejau\u0161\u0101m sv\u0101rst\u012bb\u0101m.<\/p>\n\n\n\n<h3 id=\"h-understanding-the-f-statistic-and-its-interpretation\">Izpratne par F-statistiku un t\u0101s interpret\u0101cija<\/h3>\n\n\n\n<p>Veicot ANOVA omnibus testu, m\u0113s apr\u0113\u0137in\u0101m t\u0101 saukto F-statistiku - v\u0113rt\u012bbu, kas ieg\u016bta, dalot dispersiju starp grup\u0101m ar dispersiju grupas iek\u0161ien\u0113. Liela F-v\u0113rt\u012bba var nor\u0101d\u012bt uz b\u016btisk\u0101m at\u0161\u0137ir\u012bb\u0101m starp grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem, jo t\u0101 liecina, ka main\u012bba starp grup\u0101m ir liel\u0101ka sal\u012bdzin\u0101jum\u0101 ar main\u012bbu grupas iek\u0161ien\u0113.<\/p>\n\n\n\n<p>Ta\u010du \u0161eit ir j\u0101iev\u0113ro piesardz\u012bba: F-statistika atbilst \u012bpa\u0161am sadal\u012bjumam nulles hipot\u0113zes gad\u012bjum\u0101 (kas paredz, ka starp m\u016bsu grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem nav at\u0161\u0137ir\u012bbu). Pirms izdar\u012bt secin\u0101jumus, pamatojoties tikai uz \u0161o statistiku, m\u0113s atsaucamies uz \u0161o F sadal\u012bjumu, \u0146emot v\u0113r\u0101 m\u016bsu br\u012bv\u012bbas pak\u0101pes gan starp grup\u0101m, gan grupas iek\u0161ien\u0113, t\u0101d\u0113j\u0101di ieg\u016bstot p-v\u0113rt\u012bbu.<\/p>\n\n\n\n<h3 id=\"h-interpreting-the-results-of-the-omnibus-test\">Visp\u0101r\u0113j\u0101 testa rezult\u0101tu interpret\u0101cija<\/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>Avots: <a href=\"https:\/\/pixabay.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pixabay<\/a><\/strong><\/em><\/figcaption><\/figure><\/div>\n\n\n<p>T\u0101tad esat veicis anal\u012bzi un p\u0113c apr\u0113\u0137in\u0101t\u0101s F-statistikas sal\u012bdzin\u0101\u0161anas ar atbilsto\u0161o sadal\u012bjumu esat ieguvis svar\u012bgo p-v\u0113rt\u012bbu, bet kas tagad? Ja \u0161\u012b p-v\u0113rt\u012bba ir zem\u0101ka par j\u016bsu robe\u017ev\u0113rt\u012bbu - bie\u017ei vien 0,05 -, m\u0113s sasniedzam nulles hipot\u0113zes noraid\u012b\u0161anas teritoriju. Tas liecina par sp\u0113c\u012bgu pier\u0101d\u012bjumu tam, ka vis\u0101s grup\u0101s nav ietekmes.<\/p>\n\n\n\n<p>Tom\u0113r - un \u0161\u012b da\u013ca ir \u013coti svar\u012bga - visaptvero\u0161s noraid\u012bjums nevirza m\u016bs uz to, kuri konkr\u0113ti l\u012bdzek\u013ci at\u0161\u0137iras un par cik; tas nepreciz\u0113, \"kas to izdar\u012bja\", k\u0101 tas bija m\u016bsu iepriek\u0161 min\u0113taj\u0101 detekt\u012bva analo\u0123ij\u0101. Tas tikai inform\u0113 m\u016bs, ka ir kaut kas t\u0101ds, ko ir v\u0113rts p\u0113t\u012bt t\u0101l\u0101k m\u016bsu virkn\u0113 - kas m\u016bs tie\u0161i noved pie post hoc test\u0113\u0161anas ANOVA, lai atkl\u0101tu \u0161\u012bs detaliz\u0113t\u0101s at\u0161\u0137ir\u012bbas starp konkr\u0113tiem p\u0101riem vai grupu kombin\u0101cij\u0101m.<\/p>\n\n\n\n<p>Izpratne par to, kad un k\u0101p\u0113c p\u0113c ANOVA omnibus testa j\u0101veic post hoc testi, nodro\u0161ina, ka p\u0113tnieki atbild\u012bgi r\u012bkojas ar ieg\u016btajiem rezult\u0101tiem, p\u0101ragri vai nepareizi neizvirzot asoci\u0101cijas vai c\u0113lo\u0146sakar\u012bbas, vienlaikus veicinot skaidru komunik\u0101ciju sav\u0101s p\u0113t\u012bjumu jom\u0101s.<\/p>\n\n\n\n<h2 id=\"h-need-for-post-hoc-testing-in-anova\">Post Hoc test\u0113\u0161anas nepiecie\u0161am\u012bba ANOVA test\u0113\u0161an\u0101<\/h2>\n\n\n\n<h3 id=\"h-exploring-the-limitations-of-the-omnibus-test\">Visaptvero\u0161\u0101 testa ierobe\u017eojumu izp\u0113te<\/h3>\n\n\n\n<p>Kad es iztirz\u0101ju statistisk\u0101s anal\u012bzes sare\u017e\u0123\u012bt\u012bbu, ir svar\u012bgi atz\u012bt, ka, lai gan t\u0101di instrumenti k\u0101 vari\u0101ciju anal\u012bze (ANOVA) ir sp\u0113c\u012bgi, tiem ir savas robe\u017eas. ANOVA omnibus tests mums efekt\u012bvi par\u0101da, vai kaut kur starp m\u016bsu grup\u0101m past\u0101v statistiski noz\u012bm\u012bga at\u0161\u0137ir\u012bba. Tom\u0113r pie\u0146emsim, ka j\u016bs p\u0113t\u012bj\u0101t da\u017e\u0101du m\u0101c\u012bbu meto\u017eu ietekmi uz skol\u0113nu sekm\u0113m. T\u0101d\u0101 gad\u012bjum\u0101 visaptvero\u0161ais tests var\u0113tu atkl\u0101t at\u0161\u0137ir\u012bbas starp vis\u0101m p\u0101rbaud\u012btaj\u0101m metod\u0113m, bet nepreciz\u0113s, kur \u0161\u012bs at\u0161\u0137ir\u012bbas sl\u0113pjas - kuri m\u0101c\u012bbu meto\u017eu p\u0101ri vai kombin\u0101cijas b\u016btiski at\u0161\u0137iras viena no otras.<\/p>\n\n\n\n<p>B\u016bt\u012bba ir \u0161\u0101da: lai gan ANOVA var atz\u012bm\u0113t, ja vismaz divas grupas at\u0161\u0137iras, t\u0101 neinform\u0113 par deta\u013c\u0101m. Tas ir t\u0101pat k\u0101 zin\u0101t, ka jums ir laimesta loterijas bi\u013cete, nezinot t\u0101s v\u0113rt\u012bbu - j\u016bs noteikti grib\u0113tu iedzi\u013cin\u0101ties, lai uzzin\u0101tu s\u012bk\u0101k?<\/p>\n\n\n\n<h3 id=\"h-understanding-why-post-hoc-tests-are-necessary\">Izpratne par to, k\u0101p\u0113c ir nepiecie\u0161ami post hoc testi<\/h3>\n\n\n\n<p>Tie\u0161i \u0161eit notiek post hoc test\u0113\u0161ana ANOVA, lai iedzi\u013cin\u0101tos konkr\u0113taj\u0101 situ\u0101cij\u0101. Tikl\u012bdz ANOVA uzvelk za\u013co karogu, kas signaliz\u0113 par visp\u0101r\u0113ju noz\u012bm\u012bgumu, mums atliek uzdot k\u0101rdino\u0161us jaut\u0101jumus: Kuru tie\u0161i grupu d\u0113\u013c ir \u0161\u012bs at\u0161\u0137ir\u012bbas? Vai katra grupa ir at\u0161\u0137ir\u012bga viena no otras, vai ar\u012b izmai\u0146as nosaka tikai konkr\u0113tas grupas?<\/p>\n\n\n\n<p>M\u0113\u0123inot atbild\u0113t uz \u0161iem jaut\u0101jumiem bez papildu nov\u0113rt\u0113juma, past\u0101v risks izdar\u012bt neprec\u012bzus secin\u0101jumus, pamatojoties uz visp\u0101r\u0113j\u0101m tendenc\u0113m, nevis konkr\u0113t\u0101m at\u0161\u0137ir\u012bb\u0101m. Post hoc testi ir apr\u012bkoti ar smalkas kombin\u0101cijas pieeju, kas dezagreg\u0113 datus un sniedz detaliz\u0113tu ieskatu atsevi\u0161\u0137u grupu sal\u012bdzin\u0101jumos p\u0113c tam, kad j\u016bsu s\u0101kotn\u0113j\u0101 ANOVA ir nor\u0101d\u012bjusi uz pla\u0161\u0101m at\u0161\u0137ir\u012bb\u0101m starp grup\u0101m.<\/p>\n\n\n\n<p>\u0160ajos turpm\u0101kajos nov\u0113rt\u0113jumos ir prec\u012bzi noteikts, kuri kontrasti ir b\u016btiski, t\u0101p\u0113c tie ir neaizst\u0101jami, veidojot nians\u0113tu izpratni par j\u016bsu rezult\u0101tiem.<\/p>\n\n\n\n<h3 id=\"h-the-concept-of-experiment-wise-error-rate\">Eksperimenta k\u013c\u016bdas koeficienta j\u0113dziens<\/h3>\n\n\n\n<p>B\u016btisks pamatprincips, kas nosaka, kad ir nepiecie\u0161ams veikt post hoc test\u0113\u0161anu, ir tas, ko statisti\u0137i sauc par \"eksperimenta k\u013c\u016bdu koeficientu\". Tas attiecas uz varb\u016bt\u012bbu, ka tiks pie\u013cauta vismaz viena I tipa k\u013c\u016bda visos eksperimenta ietvaros veiktajos hipot\u0113\u017eu testos - ne tikai katr\u0101 sal\u012bdzin\u0101jum\u0101, bet kumulat\u012bvi visos iesp\u0113jamajos post hoc p\u0101ru sal\u012bdzin\u0101\u0161anas testos.<\/p>\n\n\n\n<p>Iedom\u0101jieties, ka degust\u0113jat da\u017e\u0101das s\u012bkfailu partijas, m\u0113\u0123inot noteikt, vai k\u0101da gar\u0161a izce\u013cas k\u0101 gard\u0101ka. Katrs degust\u0101cijas tests palielina varb\u016bt\u012bbu, ka k\u0101du partiju k\u013c\u016bdaini pasludin\u0101siet par lab\u0101ko tikai nejau\u0161\u012bbas d\u0113\u013c - jo vair\u0101k sal\u012bdzin\u0101jumu j\u016bs veicat, jo liel\u0101ks ir risks, ka j\u016bs k\u013c\u016bdaini nov\u0113rt\u0113siet, jo da\u017ei secin\u0101jumi var\u0113tu b\u016bt viltus trauksme.<\/p>\n\n\n\n<p>Post hoc test\u0113\u0161ana uzlabo m\u016bsu statistikas instrumentu kl\u0101stu, \u0146emot v\u0113r\u0101 \u0161o kumulat\u012bvo k\u013c\u016bdu un kontrol\u0113jot to, izmantojot kori\u0123\u0113t\u0101s p v\u0113rt\u012bbas - proced\u016bra, kas paredz\u0113ta ne tikai papildu precizit\u0101tei, bet ar\u012b p\u0101rliec\u012bbai par m\u016bsu secin\u0101jumu der\u012bgumu un ticam\u012bbu.<\/p>\n\n\n\n<h2 id=\"h-different-post-hoc-testing-methods\">Da\u017e\u0101das post-Hoc test\u0113\u0161anas metodes<\/h2>\n\n\n\n<p>P\u0113c ANOVA anal\u012bzes veik\u0161anas, kas par\u0101da, vai starp grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem ir statistiski noz\u012bm\u012bga ietekme, bie\u017ei vien rodas jaut\u0101jums, kur paties\u012bb\u0101 sl\u0113pjas at\u0161\u0137ir\u012bbas. Tie\u0161i \u0161eit n\u0101k talk\u0101 post hoc test\u0113\u0161ana - iedom\u0101jieties par to k\u0101 par ieskat\u012b\u0161anos tuv\u0101k j\u016bsu datu st\u0101st\u012bjum\u0101, lai saprastu katra t\u0113la lomu. Padzi\u013cin\u0101sim \u0161o jaut\u0101jumu, izmantojot da\u017eas metodes, kas izgaismo \u0161os nians\u0113tos st\u0101stus.<\/p>\n\n\n\n<h3 id=\"h-tukey-s-method\">Tukija metode<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-tukey-s-method-and-its-application-in-anova\">Tukija metodes skaidrojums un t\u0101s pielietojums ANOV\u0100<\/h4>\n\n\n\n<p><strong>Tukija god\u012bg\u0101 noz\u012bm\u012bg\u0101 at\u0161\u0137ir\u012bba (HSD)<\/strong> metode ir viens no vispla\u0161\u0101k izmantotajiem post hoc testiem p\u0113c ANOVA. Ja esat konstat\u0113jis, ka ne visu grupu vid\u0113jie lielumi ir vien\u0101di, bet jums ir j\u0101zina, kuri konkr\u0113ti vid\u0113jie lielumi at\u0161\u0137iras, izmantojiet Tukija metodi. T\u0101 sal\u012bdzina visus iesp\u0113jamos vid\u0113jo v\u0113rt\u012bbu p\u0101rus, vienlaikus kontrol\u0113jot I tipa k\u013c\u016bdu l\u012bmeni \u0161ajos sal\u012bdzin\u0101jumos. \u0160\u012b \u012bpa\u0161\u012bba padara \u0161o metodi \u012bpa\u0161i noder\u012bgu, ja str\u0101d\u0101jat ar vair\u0101k\u0101m grup\u0101m un jums ir nepiecie\u0161ami vair\u0101ku sal\u012bdzin\u0101jumu testi, kas ir sp\u0113c\u012bga anal\u012bze.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values\">Kori\u0123\u0113to p-v\u0113rt\u012bbu apr\u0113\u0137in\u0101\u0161ana un interpret\u0101cija<\/h4>\n\n\n\n<p>Tukija metode ietver \"kori\u0123\u0113to\" p-v\u0113rt\u012bbu kopuma apr\u0113\u0137in\u0101\u0161anu katram p\u0101ru sal\u012bdzin\u0101jumam starp grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem. Apr\u0113\u0137ins balst\u0101s uz stud\u0113t\u0101 diapazona sadal\u012bjumu, \u0146emot v\u0113r\u0101 gan grupas iek\u0161\u0113j\u0101s, gan starpgrupu dispersijas - tas viss ir diezgan sare\u017e\u0123\u012bti, bet \u013coti svar\u012bgi, lai interpret\u0113tu nianses j\u016bsu datos. Svar\u012bgi ir kori\u0123\u0113t \u0161\u012bs p-v\u0113rt\u012bbas, lai \u0146emtu v\u0113r\u0101 liel\u0101ku I tipa k\u013c\u016bdu iesp\u0113jam\u012bbu, ko rada daudzk\u0101rt\u0113ji sal\u012bdzin\u0101jumi. Ja konkr\u0113t\u0101 kori\u0123\u0113t\u0101 p-v\u0113rt\u012bba ir zem\u0101ka par noz\u012bm\u012bguma slieksni (parasti 0,05), tad voil\u00e0 - j\u016bs varat pazi\u0146ot, ka starp \u0161o divu grupu vid\u0113jiem r\u0101d\u012bt\u0101jiem ir noz\u012bm\u012bga at\u0161\u0137ir\u012bba.<\/p>\n\n\n\n<h4 id=\"h-using-simultaneous-confidence-intervals-with-tukey-s-method\">Vienlaic\u012bgu ticam\u012bbas interv\u0101lu izmanto\u0161ana ar Tukija metodi<\/h4>\n\n\n\n<p>V\u0113l viens sp\u0113c\u012bgs Tukija testa aspekts ir t\u0101 sp\u0113ja vienlaic\u012bgi izveidot ticam\u012bbas interv\u0101lus vis\u0101m vid\u0113j\u0101m at\u0161\u0137ir\u012bb\u0101m. \u0160is vizu\u0101lais vid\u0113jo at\u0161\u0137ir\u012bbu att\u0113lojums pal\u012bdz p\u0113tniekiem ne tikai redz\u0113t, kuras grupas at\u0161\u0137iras, bet ar\u012b izprast \u0161o at\u0161\u0137ir\u012bbu lielumu un virzienu - tas ir nenov\u0113rt\u0113jams ieskats, pl\u0101nojot turpm\u0101kos p\u0113t\u012bjumus vai praktiskos lietojumus.<\/p>\n\n\n\n<h3 id=\"h-holm-s-method\">Holm metode<\/h3>\n\n\n\n<h4 id=\"h-introduction-to-holm-s-method-and-its-advantages-over-other-methods\">Ievads Holm metod\u0113 un t\u0101s priek\u0161roc\u012bbas sal\u012bdzin\u0101jum\u0101 ar cit\u0101m metod\u0113m<\/h4>\n\n\n\n<p>P\u0101rnesumu p\u0101rsl\u0113g\u0161ana, <strong>Holm metode<\/strong>, kas paz\u012bstama ar\u012b k\u0101 Holma sec\u012bg\u0101 Bonferroni proced\u016bra, nodro\u0161ina alternat\u012bvu post hoc test\u0113\u0161anas veidu, kur\u0101 galven\u0101 noz\u012bme ir aizsardz\u012bbai pret I tipa k\u013c\u016bd\u0101m - t\u0101 kori\u0123\u0113 p-v\u0113rt\u012bbas k\u0101 r\u016bp\u012bgs kurators, kas pasarg\u0101 v\u0113rt\u012bgus artefaktus no nepamatotas iedarb\u012bbas. T\u0101s p\u0101rsteidzo\u0161\u0101k\u0101 priek\u0161roc\u012bba ir proced\u016bras elast\u012bba; at\u0161\u0137ir\u012bb\u0101 no da\u017e\u0101m metod\u0113m, kas balst\u0101s uz vienpak\u0101pju korekcij\u0101m, Holm pak\u0101penisk\u0101 pieeja pied\u0101v\u0101 liel\u0101ku jaudu, vienlaikus aizsarg\u0101joties pret statistikas k\u013c\u016bd\u0101m, kas rodas daudzu sal\u012bdzin\u0101jumu rezult\u0101t\u0101.<\/p>\n\n\n\n<h4 id=\"h-calculation-and-interpretation-of-adjusted-p-values-with-holm-s-method\">Kori\u0123\u0113to p-v\u0113rt\u012bbu apr\u0113\u0137in\u0101\u0161ana un interpret\u0101cija ar Holm metodi<\/h4>\n\n\n\n<p>S\u012bk\u0101kais process ietver m\u016bsu s\u0101kotn\u0113jo nekori\u0123\u0113to p-v\u0113rt\u012bbu sak\u0101rto\u0161anu no vismaz\u0101k\u0101s l\u012bdz liel\u0101kajai un to sec\u012bgu p\u0101rbaudi, sal\u012bdzinot ar modific\u0113tiem alfa l\u012bme\u0146iem, pamatojoties uz to ranga poz\u012bciju - sava veida \"pak\u0101pju pazemin\u0101\u0161anas\" process, l\u012bdz tiek sasniegta v\u0113rt\u012bba, kas ir liel\u0101ka par m\u016bsu apr\u0113\u0137in\u0101to slieksni; \u0161aj\u0101 br\u012bd\u012b nor\u0101des tiek no\u0146emtas.<\/p>\n\n\n\n<h3 id=\"h-dunnett-s-method\">Danketa metode<\/h3>\n\n\n\n<h4 id=\"h-explanation-of-dunnett-s-method-and-when-it-is-appropriate-to-use-it\">Dunnett metodes skaidrojums un gad\u012bjumi, kad to ir lietder\u012bgi izmantot<\/h4>\n\n\n\n<p>\u0160eit mums ir <strong>D\u016bneta tests<\/strong>, izce\u013cas ar m\u0113r\u0137tiec\u012bgu pieeju: vair\u0101ku \u0101rst\u0113\u0161anas grupu sal\u012bdzin\u0101\u0161ana konkr\u0113ti ar vienu kontroles grupu - ierasts scen\u0101rijs kl\u012bniskajos p\u0113t\u012bjumos vai agronomiskajos p\u0113t\u012bjumos, kur var b\u016bt nepiecie\u0161ams nov\u0113rt\u0113t jaunu \u0101rst\u0113\u0161anu sal\u012bdzin\u0101jum\u0101 ar standarta vai placebo etalonu.<\/p>\n\n\n\n<h4 id=\"h-comparing-treatment-groups-to-a-control-group-using-dunnett-s-method\">Apstr\u0101des grupu sal\u012bdzin\u0101\u0161ana ar kontroles grupu, izmantojot Dunnett metodi<\/h4>\n\n\n\n<p>At\u0161\u0137ir\u012bb\u0101 no cit\u0101m pieej\u0101m, kas liek pla\u0161\u0101kus t\u012bklus visiem iesp\u0113jamajiem sal\u012bdzin\u0101jumiem, Dunnets v\u0113r\u012bgi raug\u0101s tikai uz to, k\u0101 katrs kandid\u0101ts izskat\u0101s l\u012bdz\u0101s m\u016bsu izv\u0113l\u0113tajam atskaites punktam. T\u0101d\u0113j\u0101di tas r\u016bp\u012bgi apr\u0113\u0137ina, cik daudz vair\u0101k sviras efekta - vai ar\u012b ne - m\u0113s ieg\u016bstam no j\u016bsu iejauk\u0161an\u0101s sal\u012bdzin\u0101jum\u0101 ar to, ja nedar\u012btu neko vai paliktu pie t\u0101, kas l\u012bdz \u0161im ir bijis p\u0101rbaud\u012bts un pareizs.<\/p>\n\n\n\n<p>\u0160ie da\u017e\u0101die ANOVA post hoc test\u0113\u0161anas r\u012bki \u013cauj gan statisti\u0137iem, gan datu anal\u012bti\u0137iem izzin\u0101t deta\u013cas no datu kop\u0101m, kas p\u0101rpilnas ar potenci\u0101l\u0101m atzi\u0146\u0101m, kuras gaida zem to skaitlisk\u0101s virsmas - katrs no tiem ir nedaudz at\u0161\u0137ir\u012bgi piel\u0101gots, lai atkl\u0101tu sl\u0113ptos st\u0101stus, kas ieausti m\u016bsu emp\u012brisko p\u0113t\u012bjumu audum\u0101.<\/p>\n\n\n\n<h2 id=\"h-factors-to-consider-in-choosing-a-post-hoc-test\">Faktori, kas j\u0101\u0146em v\u0113r\u0101, izv\u0113loties post-hoc testu<\/h2>\n\n\n\n<p>Kad esat uzs\u0101cis ANOVA testu, p\u0113c tam, kad, izmantojot visaptvero\u0161o ANOVA testu, ir konstat\u0113tas b\u016btiskas at\u0161\u0137ir\u012bbas starp grup\u0101m, n\u0101kamais solis bie\u017ei ir izmantot post hoc test\u0113\u0161anu, lai prec\u012bzi noteiktu, kur tie\u0161i \u0161\u012bs at\u0161\u0137ir\u012bbas ir. \u013baujiet man j\u016bs iepaz\u012bstin\u0101t ar vienu no b\u016btisk\u0101kajiem faktoriem, kam vajadz\u0113tu ietekm\u0113t to, k\u0101du post hoc testu izv\u0113laties, proti, \u0123imenes k\u013c\u016bdu koeficienta kontroli.<\/p>\n\n\n\n<h3 id=\"h-famil-wise-error-rate-control-and-its-significance-in-choosing-a-test-method\">\u0122imenes k\u013c\u016bdu skaita kontrole un t\u0101s noz\u012bme testa metodes izv\u0113l\u0113<\/h3>\n\n\n\n<p>Termins \"\u0123imenes k\u013c\u016bdu koeficients\" (FWER) attiecas uz varb\u016bt\u012bbu, ka, veicot vair\u0101kus p\u0101ru testus, starp visiem iesp\u0113jamiem sal\u012bdzin\u0101jumiem tiks pie\u013cauta vismaz viena I tipa k\u013c\u016bda. I tipa k\u013c\u016bda rodas tad, ja j\u016bs k\u013c\u016bdaini secin\u0101t, ka starp grup\u0101m past\u0101v at\u0161\u0137ir\u012bbas, lai gan paties\u012bb\u0101 to nav. Ja to pien\u0101c\u012bgi nekontrol\u0113, jo arvien bie\u017e\u0101k ANOVA sist\u0113m\u0101 veicam vair\u0101kus p\u0101ru sal\u012bdzin\u0101jumus, pieaug varb\u016bt\u012bba, ka net\u012b\u0161i pazi\u0146osiet par k\u013c\u016bdainu noz\u012bm\u012bgumu, un tas var novest j\u016bsu p\u0113t\u012bjumu l\u012bdz k\u013c\u016bdainam rezult\u0101tam.<\/p>\n\n\n\n<p>Pat ja tas izklaus\u0101s bied\u0113jo\u0161i, nevajag baid\u012bties - tie\u0161i t\u0101p\u0113c FWER kontroles metodes ir iz\u0161\u0137iro\u0161s elements, izv\u0113loties post hoc testu. B\u016bt\u012bb\u0101 \u0161\u012bs metodes kori\u0123\u0113 j\u016bsu noz\u012bm\u012bguma sliek\u0161\u0146us vai p-v\u0113rt\u012bbas t\u0101, lai visu testu kop\u0113jais risks nep\u0101rsniegtu s\u0101kotn\u0113jo pie\u013caujamo k\u013c\u016bdu l\u012bmeni (parasti 0,05). \u0160\u0101di r\u012bkojoties, m\u0113s varam dro\u0161i izp\u0113t\u012bt konkr\u0113tas grupu at\u0161\u0137ir\u012bbas, nepalielinot k\u013c\u016bdainu atkl\u0101jumu iesp\u0113jam\u012bbu.<\/p>\n\n\n\n<p>FWER kontrole nodro\u0161ina j\u016bsu secin\u0101jumu integrit\u0101ti un uztur zin\u0101tnisko stingr\u012bbu, kas nepiecie\u0161ama sal\u012bdzino\u0161ai nov\u0113rt\u0113\u0161anai un reproduc\u0113jam\u012bbai.<\/p>\n\n\n\n<p>Tagad iedom\u0101jieties, ka saskaraties ar da\u017e\u0101d\u0101m post hoc test\u0113\u0161anas iesp\u0113j\u0101m - FWER izpratne pal\u012bdz\u0113s jums atbild\u0113t uz galvenajiem jaut\u0101jumiem:<\/p>\n\n\n\n<ul>\n<li>Cik daudz sal\u012bdzin\u0101jumu tiks veikti man\u0101 p\u0113t\u012bjuma pl\u0101n\u0101?<\/li>\n\n\n\n<li>Cik piesardz\u012bgam man j\u0101b\u016bt, kontrol\u0113jot I tipa k\u013c\u016bdas, \u0146emot v\u0113r\u0101 manu jomu vai p\u0113t\u012bjuma jaut\u0101jumu?<\/li>\n<\/ul>\n\n\n\n<p>Piem\u0113ram, Tukija HSD (Honestly Significant Difference - god\u012bgi noz\u012bm\u012bga at\u0161\u0137ir\u012bba) ir vispiem\u0113rot\u0101kais, ja m\u0113s veicam visus iesp\u0113jamos p\u0101ru sal\u012bdzin\u0101jumus un sal\u012bdzin\u0101jumus un cen\u0161amies, lai m\u016bsu \u0123imenes k\u013c\u016bdu koeficients b\u016btu vien\u0101ds ar m\u016bsu alfa l\u012bmeni (bie\u017ei vien 0,05). Holma metode ir augst\u0101ka pak\u0101pe, sec\u012bgi kori\u0123\u0113jot p-v\u0113rt\u012bbas un pan\u0101kot l\u012bdzsvaru - t\u0101 ir maz\u0101k konservat\u012bva nek\u0101 Bonferroni metode, bet joproj\u0101m nodro\u0161ina sapr\u0101t\u012bgu aizsardz\u012bbu pret I tipa k\u013c\u016bd\u0101m. Un, ja j\u016bsu projekt\u0101 ir viena kontroles vai references grupa? Dunnett metode var noder\u0113t, jo t\u0101 \u012bpa\u0161i attiecas uz sal\u012bdzin\u0101jumiem ar \u0161o centr\u0101lo skaitli.<\/p>\n\n\n\n<p>Nobeigum\u0101:<\/p>\n\n\n\n<p>Lai efekt\u012bvi mazin\u0101tu riskus, kas saist\u012bti ar pastiprin\u0101tu hipot\u0113\u017eu test\u0113\u0161anu, ir j\u0101izv\u0113las gudras statistisk\u0101s anal\u012bzes metodes. Ja p\u0113c ANOVA rezult\u0101ta, kas nor\u0101da uz noz\u012bm\u012bgu at\u0161\u0137ir\u012bbu starp grup\u0101m, tiek veikta post hoc test\u0113\u0161ana, vienm\u0113r atcerieties: Tas nav tikai statistisks \u017eargons, tas ir j\u016bsu dro\u0161\u012bbas l\u012bdzeklis, kas nodro\u0161ina no sare\u017e\u0123\u012btiem datu mode\u013ciem izdar\u012bto secin\u0101jumu ticam\u012bbu un pamatot\u012bbu.<\/p>\n\n\n\n<h2 id=\"h-case-studies-and-examples\">Gad\u012bjumu izp\u0113te un piem\u0113ri<\/h2>\n\n\n\n<p>Izpratni par statistikas j\u0113dzieniem iev\u0113rojami uzlabo re\u0101lu pielietojumu izp\u0113te. Izp\u0113t\u012bsim, k\u0101 post hoc test\u0113\u0161ana ANOVA atdz\u012bvina p\u0113t\u012bjumus, nodro\u0161inot zin\u0101tniskajiem p\u0113t\u012bjumiem stingru metodi, lai izp\u0113t\u012btu to rezult\u0101tus.<\/p>\n\n\n\n<h3 id=\"h-discussion-of-real-world-research-studies-where-post-hoc-testing-was-used\">Diskusija par re\u0101l\u0101s pasaules p\u0113t\u012bjumiem, kuros tika izmantota post hoc test\u0113\u0161ana<\/h3>\n\n\n\n<p>Izp\u0113t\u012btas caur praktisk\u0101 pielietojuma prizmu, post hoc anal\u012bzes un testi k\u013c\u016bst par kaut ko vair\u0101k nek\u0101 abstrakt\u0101m matem\u0101tisk\u0101m proced\u016br\u0101m; tie ir r\u012bki, kas izv\u0113r\u0161 narat\u012bvus datu ietvaros. Piem\u0113ram, p\u0113t\u012bjum\u0101, kur\u0101 galven\u0101 uzman\u012bba tiek piev\u0113rsta da\u017e\u0101du m\u0101c\u012bbu metodiku efektivit\u0101tei, var izmantot ANOVA, lai noteiktu, vai past\u0101v b\u016btiskas at\u0161\u0137ir\u012bbas skol\u0113nu rezult\u0101tos atkar\u012bb\u0101 no m\u0101c\u012bbu pieejas. Ja omnibus tests dod noz\u012bm\u012bgu rezult\u0101tu, tas paver ce\u013cu post hoc anal\u012bzei, kas ir b\u016btiska, lai prec\u012bzi noteiktu, kuras metodes at\u0161\u0137iras viena no otras.<\/p>\n\n\n\n<p>\u013baujiet man dal\u012bties ar v\u0113l vienu piem\u0113ru, kas izce\u013c \u0161o metodolo\u0123iju: iedom\u0101jieties, ka p\u0113tnieki veica eksperimenta post hoc anal\u012bzi, nov\u0113rt\u0113jot jaunu z\u0101\u013cu ietekmi uz asinsspiediena l\u012bmeni. S\u0101kotn\u0113j\u0101 ANOVA liecina, ka asinsspiediena r\u0101d\u012bjumi laika gait\u0101 iev\u0113rojami at\u0161\u0137iras da\u017e\u0101d\u0101s devu grup\u0101s. Post hoc test\u0113\u0161ana ir \u013coti svar\u012bgs n\u0101kamais solis, kas pal\u012bdz zin\u0101tniekiem sal\u012bdzin\u0101t visus iesp\u0113jamos devu p\u0101rus, lai saprastu, kuras devas ir efekt\u012bvas un kuras potenci\u0101li kait\u012bgas.<\/p>\n\n\n\n<p>\u0160ie piem\u0113ri par\u0101da, k\u0101 post hoc test\u0113\u0161ana p\u0113c ANOVA ne tikai pal\u012bdz p\u0113tniekiem veikt atkl\u0101jumus, bet ar\u012b nodro\u0161ina secin\u0101jumu stabilit\u0101ti un precizit\u0101ti.<\/p>\n\n\n\n<h3 id=\"h-hands-on-examples-illustrating-the-application-of-different-post-hoc-tests\">Praktiski piem\u0113ri, kas ilustr\u0113 da\u017e\u0101du post hoc testu piem\u0113ro\u0161anu.<\/h3>\n\n\n\n<p>Padzi\u013cin\u0101ta vair\u0101ku sal\u012bdzin\u0101\u0161anas testu izp\u0113te konkr\u0113tiem lietojumiem var sniegt ieskatu par to, cik da\u017e\u0101di var b\u016bt \u0161ie testi:<\/p>\n\n\n\n<ul>\n<li><strong>Tukija metode<\/strong>: Apsveriet lauksaimniec\u012bbas zin\u0101tniekus, kas sal\u012bdzina kult\u016braugu ra\u017eas, izmantojot vair\u0101kus m\u0113slojuma veidus. P\u0113c noz\u012bm\u012bgas ANOVA, kur\u0101 konstat\u0113tas at\u0161\u0137ir\u012bgas ra\u017eas starp apstr\u0101des veidiem, ar Tukija metodi var\u0113tu prec\u012bzi noteikt, kuri m\u0113slo\u0161anas l\u012bdzek\u013ci dod statistiski at\u0161\u0137ir\u012bgas ra\u017eas sal\u012bdzin\u0101jum\u0101 ar citiem, vienlaikus kontrol\u0113jot I tipa k\u013c\u016bdu visos sal\u012bdzin\u0101jumos.<\/li>\n\n\n\n<li><strong>Holm metode<\/strong>: Psiholo\u0123iskajos p\u0113t\u012bjumos, kuru m\u0113r\u0137is ir izprast terapijas rezult\u0101tus, Holm sec\u012bg\u0101 proced\u016bra kori\u0123\u0113 p-v\u0113rt\u012bbas, ja vair\u0101kas \u0101rst\u0113\u0161anas formas tiek v\u0113rt\u0113tas sal\u012bdzin\u0101jum\u0101 ar kontroles grup\u0101m. Tas nodro\u0161ina, ka turpm\u0101kie secin\u0101jumi paliek ticami ar\u012b p\u0113c tam, kad atkl\u0101jas, ka konkr\u0113tas terapijas ir lab\u0101kas nek\u0101 bez \u0101rst\u0113\u0161anas.<\/li>\n\n\n\n<li><strong>Danketa metode<\/strong>: Dunnett metodi bie\u017ei izmanto kl\u012bniskajos p\u0113t\u012bjumos ar placebo grupu, sal\u012bdzinot katru \u0101rst\u0113\u0161anu tie\u0161i ar placebo. P\u0113t\u012bjum\u0101, kur\u0101 nov\u0113rt\u0113 vair\u0101kus jaunus prets\u0101pju medikamentus sal\u012bdzin\u0101jum\u0101 ar placebo, var izmantot Dunnett metodi, lai noteiktu, vai k\u0101dam no jaunajiem medikamentiem ir lab\u0101ka iedarb\u012bba, nepalielinot viltus pozit\u012bvu rezult\u0101tu risku daudzk\u0101rt\u0113ju sal\u012bdzin\u0101jumu d\u0113\u013c.<\/li>\n<\/ul>\n\n\n\n<p>\u0160ajos fragmentos no da\u017e\u0101d\u0101m jom\u0101m ir uzsv\u0113rts, k\u0101 piel\u0101gota ANOVA post hoc test\u0113\u0161ana pie\u0161\u0137ir b\u016btiskumu maz\u0101kajai statistiskajai noz\u012bm\u012bguma sp\u0113jai, p\u0101rv\u0113r\u0161ot skait\u013cus noz\u012bm\u012bg\u0101s atzi\u0146\u0101s, kas var pal\u012bdz\u0113t veidot nozares un uzlabot dz\u012bvi.<\/p>\n\n\n\n<h2 id=\"h-statistical-power-in-post-hoc-testing\">Statistisk\u0101 jauda post-Hoc test\u0113\u0161an\u0101<\/h2>\n\n\n\n<h3 id=\"h-explanation-of-statistical-power-and-its-importance-in-post-hoc-testing-decision-making\">Statistisk\u0101s jaudas skaidrojums un t\u0101s noz\u012bme l\u0113mumu pie\u0146em\u0161an\u0101 p\u0113c test\u0113\u0161anas<\/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>Avots: <a href=\"https:\/\/pixabay.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pixabay<\/a><\/strong><\/em><\/figcaption><\/figure><\/div>\n\n\n<p>Apsprie\u017eot ANOVA rezult\u0101tu post hoc test\u0113\u0161anas nianses, ir oblig\u0101ti j\u0101izprot hipot\u0113\u017eu test\u0113\u0161anas b\u016btisk\u0101kais j\u0113dziens - statistisk\u0101 jauda. Vienk\u0101r\u0161\u0101k sakot, statistisk\u0101 jauda ir varb\u016bt\u012bba, ka p\u0113t\u012bjum\u0101 tiks atkl\u0101ta ietekme, ja t\u0101da patie\u0161\u0101m ir. Tas noz\u012bm\u0113, ka var atkl\u0101t patiesas at\u0161\u0137ir\u012bbas starp grup\u0101m, ja t\u0101das patie\u0161\u0101m past\u0101v.<\/p>\n\n\n\n<p>Liela statistisk\u0101 jauda samazina varb\u016bt\u012bbu pie\u013caut II tipa k\u013c\u016bdu, kas rodas tad, ja mums neizdodas atkl\u0101t at\u0161\u0137ir\u012bbu, kas paties\u012bb\u0101 past\u0101v. T\u0101 pasarg\u0101 m\u016bsu rezult\u0101tus no k\u013c\u016bdaini negat\u012bviem rezult\u0101tiem, palielinot m\u016bsu anal\u012bz\u0113 izdar\u012bto secin\u0101jumu ticam\u012bbu. \u0160is faktors k\u013c\u016bst \u012bpa\u0161i svar\u012bgs p\u0113c tam, kad p\u0113c ANOVA ir konstat\u0113tas b\u016btiskas at\u0161\u0137ir\u012bbas starp grup\u0101m.<\/p>\n\n\n\n<p>Praks\u0113 pan\u0101kt augstu statistisko jaudu bie\u017ei vien noz\u012bm\u0113 nodro\u0161in\u0101t, ka j\u016bsu p\u0113t\u012bjum\u0101 ir atbilsto\u0161a izlases lieluma paraugs. P\u0101r\u0101k maza izlase var prec\u012bzi neatspogu\u013cot paties\u0101s grupu at\u0161\u0137ir\u012bbas, savuk\u0101rt \u012bpa\u0161i lielas izlases var atkl\u0101t statistiski noz\u012bm\u012bgas, bet praktiski neb\u016btiskas at\u0161\u0137ir\u012bbas. T\u0101d\u0113j\u0101di \u0161o apsv\u0113rumu l\u012bdzsvaro\u0161ana ir \u013coti svar\u012bga, lai pie\u0146emtu p\u0101rliecino\u0161us l\u0113mumus jebkur\u0101 p\u0113t\u012bjum\u0101, kas ietver ANOVA p\u0113cp\u0101rbaudi.<\/p>\n\n\n\n<h3 id=\"h-managing-power-trade-offs-by-reducing-the-number-of-comparisons\">Kompromisa starp jaudu p\u0101rvald\u012bba, samazinot sal\u012bdzin\u0101jumu skaitu<\/h3>\n\n\n\n<p>Lai risin\u0101tu iesp\u0113jam\u0101s probl\u0113mas, kas saist\u012btas ar daudzk\u0101rt\u0113jiem sal\u012bdzin\u0101jumiem p\u0113cANOVA, p\u0113tniekiem ir sapr\u0101t\u012bgi j\u0101pan\u0101k kompromiss starp pietiekamas statistisk\u0101s jaudas saglab\u0101\u0161anu un I tipa k\u013c\u016bdu (viltus pozit\u012bvu rezult\u0101tu) riska kontroli. \u0160eit ir efekt\u012bvas strat\u0113\u0123ijas:<\/p>\n\n\n\n<ul>\n<li>Priorit\u0101\u0161u noteik\u0161ana: Nosakiet, kuri sal\u012bdzin\u0101jumi ir vissvar\u012bg\u0101kie j\u016bsu hipot\u0113z\u0113m, un pie\u0161\u0137iriet tiem priorit\u0101ti turpm\u0101kai izp\u0113tei.<\/li>\n\n\n\n<li>Konsolid\u0101cija: T\u0101 viet\u0101, lai p\u0101rbaud\u012btu visus iesp\u0113jamos p\u0101ru sal\u012bdzin\u0101jumus starp apstr\u0101des l\u012bme\u0146iem, koncentr\u0113jieties tikai uz katras apstr\u0101des grupas sal\u012bdzin\u0101\u0161anu ar kontroles grupu vai apvienojiet apstr\u0101des grupas noz\u012bm\u012bg\u0101s kategorij\u0101s.<\/li>\n<\/ul>\n\n\n\n<p>P\u0101rdom\u0101ti izv\u0113loties maz\u0101ku sal\u012bdzin\u0101jumu skaitu, p\u0113tnieki ne tikai palielina izredzes, ka vi\u0146u p\u0113t\u012bjums saglab\u0101s stabilu statistisko stiprumu, bet ar\u012b samazina eksperimenta k\u013c\u016bdu skaitu bez p\u0101rm\u0113r\u012bg\u0101m korekcijas proced\u016br\u0101m, kas samazina atkl\u0101jumu potenci\u0101lu.<\/p>\n\n\n\n<p>\u0160\u012b trausl\u0101 l\u012bdzsvara iev\u0113ro\u0161ana nodro\u0161ina, ka b\u016btiski svar\u012bgi secin\u0101jumi izce\u013cas, vienlaikus apliecinot metodolo\u0123isko stingr\u012bbu - tas ir b\u016btisks l\u012bdzsvara punkts visos p\u0113t\u012bjumos, kuros p\u0113c ANOVA sist\u0113mas tiek izmantota post hoc test\u0113\u0161ana.<\/p>\n\n\n\n<h2 id=\"h-summary-and-conclusion\">Kopsavilkums un secin\u0101jumi<\/h2>\n\n\n\n<h3 id=\"h-recap-of-key-points-covered-in-the-content-outline\">Satura izkl\u0101st\u0101 ietverto galveno punktu kopsavilkums<\/h3>\n\n\n\n<p>\u0160aj\u0101 rakst\u0101 m\u0113s esam \u0161\u0137\u0113rsoju\u0161i vari\u0101ciju anal\u012bzes (ANOVA) un t\u0101s kritiski svar\u012bg\u0101 pavado\u0161\u0101 -. <strong>ANOVA post hoc test\u0113\u0161ana<\/strong>. Lai s\u0101ktu, m\u0113s izveidoj\u0101m pamata izpratni par ANOVA, kur to izmanto, lai noteiktu, vai past\u0101v statistiski noz\u012bm\u012bgas at\u0161\u0137ir\u012bbas starp tr\u012bs vai vair\u0101ku neatkar\u012bgu grupu vid\u0113jiem lielumiem.<\/p>\n\n\n\n<p>M\u0113s iedzi\u013cin\u0101j\u0101mies post hoc test\u0113\u0161anas nians\u0113s, kas ir b\u016btiska, ja s\u0101kotn\u0113j\u0101 ANOVA dod noz\u012bm\u012bgus rezult\u0101tus. M\u0113s noskaidroj\u0101m, ka, lai gan ANOVA var pateikt, ka vismaz divas grupas at\u0161\u0137iras, t\u0101 nenor\u0101da, kuras grupas un cik grupas at\u0161\u0137iras viena no otras. Tie\u0161i \u0161eit noder post hoc testi.<\/p>\n\n\n\n<p>Apsprie\u017eot \u0161o t\u0113mu, m\u0113s piedz\u012bvoj\u0101m da\u017e\u0101dus l\u012bklo\u010dus un pagriezienus:<\/p>\n\n\n\n<ul>\n<li>ANOVA omnibus testa kritiskais raksturs, kas izmanto F-statistiku, lai noteiktu kop\u0113jo dispersiju.<\/li>\n\n\n\n<li>\u0160o rezult\u0101tu prec\u012bzas interpret\u0101cijas noz\u012bme pareizas statistisk\u0101s anal\u012bzes veik\u0161anai.<\/li>\n<\/ul>\n\n\n\n<p>Kad atkl\u0101j\u0101s t\u0101di ierobe\u017eojumi k\u0101 eksperimenta k\u013c\u016bdu \u012bpatsvars, m\u0113s saprat\u0101m, k\u0101p\u0113c post hoc test\u0113\u0161ana ir ne tikai noder\u012bga, bet ar\u012b nepiecie\u0161ama. T\u0101 sniedz preciz\u0113tu ieskatu, kontrol\u0113jot \u0161o k\u013c\u016bdu \u012bpatsvaru un \u013caujot veikt vair\u0101kus sal\u012bdzin\u0101jumus, nepalielinot I tipa k\u013c\u016bdu iesp\u0113jam\u012bbu.<\/p>\n\n\n\n<p>M\u016bsu eksped\u012bcij\u0101 pa da\u017e\u0101d\u0101m metod\u0113m, piem\u0113ram, Tukija, Holma un Duneta metodi, j\u016bs, iesp\u0113jams, paman\u012bj\u0101t, ka t\u0101s kalpo unik\u0101liem m\u0113r\u0137iem - vai tas b\u016btu visu iesp\u0113jamo vid\u0113jo v\u0113rt\u012bbu p\u0101ru daudzk\u0101rt\u0113js sal\u012bdzin\u0101jums, vai ar\u012b koncentr\u0113\u0161an\u0101s uz vienas kontroles grupas sal\u012bdzin\u0101jumu.<\/p>\n\n\n\n<p>Post hoc testa izv\u0113le ir r\u016bp\u012bgi j\u0101izv\u0113rt\u0113. K\u013c\u016bdu \u012bpatsvara kontrole nenotiek izol\u0113ti; veicot post hoc testus, ir j\u0101izv\u0113rt\u0113 faktori, kas saist\u012bti ar \u0123imenes k\u013c\u016bdu \u012bpatsvaru.<\/p>\n\n\n\n<p>Re\u0101lu piem\u0113ru iek\u013cau\u0161ana m\u016bsu diskusij\u0101 pal\u012bdz\u0113ja \u0161os konceptu\u0101los apsv\u0113rumus stingri saist\u012bt ar praktiskiem piem\u0113ro\u0161anas scen\u0101rijiem.<\/p>\n\n\n\n<p>Visbeidzot, tom\u0113r \u013coti svar\u012bgi, ka m\u0113s piev\u0113rs\u0101mies statistiskajai jaudai. Lai gan sal\u012bdzin\u0101jumu skaita samazin\u0101\u0161ana da\u017ek\u0101rt tiek uzskat\u012bta par jaudas kompromisa samazin\u0101\u0161anu\", strat\u0113\u0123isku l\u0113mumu pie\u0146em\u0161ana \u0161aj\u0101 gad\u012bjum\u0101 nodro\u0161ina secin\u0101jumu notur\u012bbu pat tad, ja \u0161eit tiek izmantoti vair\u0101ki post hoc testi.<\/p>\n\n\n\n<h3 id=\"h-concluding-thoughts-on-the-importance-and-significance-of-post-hoc-testing-in-anova\">Nobeiguma domas par post hoc test\u0113\u0161anas noz\u012bmi un noz\u012bm\u012bgumu ANOVA.<\/h3>\n\n\n\n<p>Nosl\u0113dzot \u0161o izzino\u0161o ekskursiju uz <strong>ANOVA post hoc test\u0113\u0161ana<\/strong>, atg\u0101din\u0101sim, k\u0101p\u0113c ir tik svar\u012bgi ienirt \u0161aj\u0101 konkr\u0113taj\u0101 statistisk\u0101s anal\u012bzes teritorij\u0101. P\u0113tniec\u012bbas kontekst\u0101, kas aptver gan vesel\u012bbas apr\u016bpes izr\u0101vienu, gan revolucion\u0101ru tehnolo\u0123iju att\u012bst\u012bbu, p\u0101rliecin\u0101\u0161an\u0101s, ka m\u016bsu secin\u0101jumi ir ne tikai statistiski noz\u012bm\u012bgi, bet ar\u012b praktiski noz\u012bm\u012bgi, var b\u016bt iz\u0161\u0137iro\u0161a.<\/p>\n\n\n\n<p>P\u0101rdom\u0101ta post hoc testu izmanto\u0161ana p\u0113c ANOVA \u013cauj mums p\u0101rsniegt vienk\u0101r\u0161u at\u0161\u0137ir\u012bbu atkl\u0101\u0161anu un s\u0101kt p\u0113t\u012bt, k\u0101das ir \u0161\u012bs at\u0161\u0137ir\u012bbas - un to lielumu - ar pietiekamu precizit\u0101ti un p\u0101rliec\u012bbu, lai ietekm\u0113tu turpm\u0101ko p\u0113t\u012bjumu virz\u012bbu vai politikas l\u0113mumus.<\/p>\n\n\n\n<p>T\u0101 k\u0101 esam dedz\u012bgi zin\u0101tnieki un m\u0113r\u0137tiec\u012bgi profesion\u0101\u013ci, kas orient\u0113jas pasaul\u0113, kur\u0101 arvien vair\u0101k izmanto datus, \u0161\u0101das pieejas ne tikai uzlabo m\u016bsu izpratni - t\u0101s papla\u0161ina iesp\u0113jas. Post hoc testi turpina tur\u0113t augstu paceltu l\u0101pu, izgaismojot nians\u0113tas deta\u013cas da\u017ek\u0101rt p\u0101rbag\u0101tu datu kopu vid\u016b - b\u0101ku, kas vada uz p\u0101rliecino\u0161\u0101m atzi\u0146\u0101m, palielinot m\u016bsu sp\u0113ju pie\u0146emt pamatotus l\u0113mumus, pamatojoties uz stabiliem anal\u012btiskiem procesiem, kas dedz\u012bgi iztur p\u0101rbaudes gan zin\u0101tnieku aprind\u0101s, gan laukos, kur tiek ieviesti novatoriski jaunin\u0101jumi, kas tiek nopietni \u012bstenoti, lai g\u016btu sabiedr\u012bbai daudzpus\u012bgu labumu, kas ir patiess un kas iedvesmo katru jaunu mekl\u0113jumu \"...neparedz\u0113tiem mode\u013ciem\".<\/p>\n\n\n\n<p>Vis\u0101 taj\u0101 laik\u0101 mana cer\u012bba paliek nelok\u0101ma: lai j\u016bsu pa\u0161u anal\u012bzes sniedz augl\u012bgu izpratni, kas mijas ar skaidr\u012bbu, kura ir peln\u012bjusi uzslavas un galu gal\u0101 uzlabo dz\u012bves, kuras skar uz pier\u0101d\u012bjumiem balst\u012bta prakse, kas ir m\u016b\u017e\u012bgi testament\u0101ra, balst\u012bta uz stingriem statistikas pamatiem, kas nosaka at\u0161\u0137ir\u012bbu, nenogursto\u0161i notur\u012bgu... cen\u0161oties sasniegt paties\u012bbu, kas ir vienm\u0113r nenotverama, bet m\u016b\u017e\u012bgi vilino\u0161a.<\/p>\n\n\n\n<h2 id=\"h-experience-the-power-of-visual-mastery-simplifying-complexity-with-mind-the-graph\"><br>Izbaudiet vizu\u0101l\u0101s meistar\u012bbas sp\u0113ku: vienk\u0101r\u0161ojiet sare\u017e\u0123\u012bt\u012bbu ar Mind the Graph!<\/h2>\n\n\n\n<p>Atkl\u0101jiet nevainojamas vizu\u0101l\u0101s komunik\u0101cijas potenci\u0101lu, jo m\u0113s no jauna noteiksim veidu, k\u0101 izprast sare\u017e\u0123\u012btus j\u0113dzienus. Laikmet\u0101, kur\u0101 domin\u0113 vizu\u0101lie att\u0113li, sare\u017e\u0123\u012btu ideju, pat tik nosl\u0113pumainu k\u0101 kvantu fizika, izpratne k\u013c\u016bst pavisam vienk\u0101r\u0161a, pateicoties grafikas efektivit\u0101tei.<\/p>\n\n\n\n<p>Uzs\u0101ciet vizu\u0101lo ce\u013cojumu ar <a href=\"https:\/\/mindthegraph.com\/?utm_source=blog&amp;utm_medium=content\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a>, j\u016bsu galvenais pal\u012bgs, lai sare\u017e\u0123\u012btus v\u0113st\u012bjumus p\u0101rv\u0113rstu aizraujo\u0161os vizu\u0101los materi\u0101los. M\u016bsu galerij\u0101 ir vair\u0101k nek\u0101 t\u016bksto\u0161 r\u016bp\u012bgi izstr\u0101d\u0101tu ilustr\u0101ciju, t\u0101p\u0113c iesp\u0113jas ir neierobe\u017eotas. M\u016bsu modernais viedo plak\u0101tu veidot\u0101js \u013cauj jums bez piep\u016bles izveidot plak\u0101tus, kas izce\u013cas.<\/p>\n\n\n\n<p>K\u0101p\u0113c samierin\u0101ties ar parasto, ja varat izveidot piel\u0101gotu vizu\u0101lo \u0161edevru? Izmantojiet m\u016bsu talant\u012bg\u0101s komandas zin\u0101\u0161anas, lai piel\u0101gotu ilustr\u0101cijas atbilsto\u0161i j\u016bsu unik\u0101laj\u0101m vajadz\u012bb\u0101m. Mind the Graph nav tikai r\u012bks - tie ir j\u016bsu v\u0101rti uz pasauli, kur\u0101 vizu\u0101lie att\u0113li run\u0101 ska\u013c\u0101k nek\u0101 v\u0101rdi.<\/p>\n\n\n\n<p>Vai esat gatavs uzlabot savu komunik\u0101cijas sp\u0113li? Re\u0123istr\u0113jieties bez maksas un s\u0101ciet veidot jau tagad. J\u016bsu v\u0113st\u012bjums, m\u016bsu vizu\u0101lais noform\u0113jums - nevainojama kombin\u0101cija!<\/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\">S\u0101ciet veidot ar 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>Iepaz\u012bstieties ar post hoc test\u0113\u0161anas ANOVA nians\u0113m. Pilnveidojiet savu statistisko anal\u012bzi un atkl\u0101jiet savu datu kopu noz\u012bm\u012bgumu.<\/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. 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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\/lv\/author\/fabricio\/"}]}},"_links":{"self":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/50301"}],"collection":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/comments?post=50301"}],"version-history":[{"count":3,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/50301\/revisions"}],"predecessor-version":[{"id":50305,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/posts\/50301\/revisions\/50305"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/media\/50304"}],"wp:attachment":[{"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/media?parent=50301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/categories?post=50301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mindthegraph.com\/blog\/lv\/wp-json\/wp\/v2\/tags?post=50301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}