多重比較Multiple comparisons @ 凝視、散記 - 隨意窩

如果要作post hoc comparisons (有人叫posteriori test) ，有許多選擇：1) Fisher's Least Significant Difference (又稱為LSD)；2) Tukey's Test；3) The Ryan Procedure ... 凝視、散記【散點透視】APersonalCasualNotesconsistofScatteredPerspectivesforLearning,ThinkingandPractices日誌相簿影音好友名片 202011081030多重比較Multiplecomparisons?Insight&Algorithm在用ANOVA時，會得到一個F-test，這個test 只能告訴你整個model是否顯著(i.e.,總體平均數不相同或不完全相同)，並不能告訴你特定的組與組之間是否有差異。

有很多種方法可以比較組間的平均值是否有差異，這些方式就稱作多重比較(multiplecomparisons)   如果要作posthoccomparisons(有人叫posterioritest)，有許多選擇：1)Fisher’sLeastSignificantDifference(又稱為LSD)；2)Tukey’sTest；3)TheRyanProcedure(REGWQ)；4)TheSchefféTest；5)Dunnett’stestforcomparingalltreatmentswithacontrol。

  會產生這麼多方法，主要是比較的方式不同。

有的方法是與均值作比較 (i.e.,所有組別的平均皆相同)，有的方法是配對比較 (pairwisecomparison)(i.e.,與控制組比較、與最佳組比較)，有的是contrast(特定兩組比較)。

比較表 (出自StatisticalmethodsforPsychologybyDavidC.Howell，第六版，頁375)：    Test Errorrate Comparison Type 事前/事後 備註 Individual t tests PCa Pairwise t 事前   Linearcontrast PC Anycontrasts F 事前   Bonferroni t FWb Anycontrasts t** 事前   Holm:Larzelere&Mulaik FWb Anycontrasts t** 兩者   Fisher’sLSD FW* Pairwise t 事後   Newman-Keulstest FW* Pairwise Range 事後 爭議性大 Ryan(REGWQ) FW Pairwise Range 事後   TukeyHSD FW Pairwise*** Range 事後 只想測試某兩組時 SchefféTest FW Anycontrasts F** 事後 想測試所有差異時 Dunnett’stest FW Withcontrol F** 事後     Note:a:Errorratepercomparison.b:Familyerrorrate(FW). FW*:againstcompletenullhypothesis.t** :modified t test.F*:modified.Pairwise***:TukeyHSDcanbeusedforallcontrasts,butispoorforthispurpose. ---------------------- AfteryouhaverunANOVAandgotasignificantF-statistic(i.e.youhaverejectedthenullhypothesisthatthemeansarethesame),thenyourunSheffe’stesttofindoutwhichpairsofmeansaresignificant.TheScheffetestcorrectsalphaforsimpleandcomplexmeancomparisons.Complexmeancomparisonsinvolvecomparingmorethanonepairofmeanssimultaneously. Outofthethreemeancomparisonstestyoucanrun(theothertwoareFisher’sLSDandTukey’sHSD).TheScheffetestisthemostflexible,butitisalsothetestwiththeloweststatisticalpower.Decidingwhichtesttorunlargelydependsonwhatcomparisonsyou’reinterestedin:   Ifyouonlywanttomakepairwisecomparisons,runtheTukeyprocedurebecauseitwillhaveanarrowerconfidenceinterval.Ifyouwanttocompareallpossiblesimpleandcomplexpairsofmeans,runtheScheffetestasitwillhaveanarrowerconfidenceinterval. UnderstandingScheffé'sTest WhileScheffé'stesthastheadvantageofgivingtheexperimentertheflexibilitytotestanycomparisonsthatappearinteresting,thedrawbackofthisflexibilityisthatthetesthasrelativelylowerstatisticalpowerthanteststhataredesignedforpre-plannedcomparisons. TheScheffétestisoneoftheoldestmultiplecomparisonproceduresinusetoday.ItisimportanttorecognizethatitisafrequentlymisusedprocedureandthatitisalsoavaluabletestwhenusedasHenrySchefféintendedit.UnlikecompetitorssuchasTukey'sHonestlySignificantDifferencetest,theScheffétestisspecificallydesignedforthesituationinwhichposthoccomparisonsinvolvemorethanpairwisedifferences.Forexample,itcouldbeusedtocomparethemeanoftwogroupstothemeanoftwoothergroupsonthebasisofinterestingdifferencesthatappearedafterthedatahadbeencollected.  SchefféTest(雪費檢定；同步檢定法) post-hoctest 同時測試所有可能的contrast，並視是否其中之一為0。

臨界值最大，最不容易顯著(也表示較不容易犯TypeIIerror)。

可用於各組人數不同、非常態分配上。

  Whatarethemajordifferencesbetweenscheffeandtukeyposthoctests? Whatarethekeyconditionsthatnecessitatetheuseofeitherscheffeandtukeyposthoctest?     Generally,TukeyandScheffétestsaremoreconservative.Theyfindithardertoseedifferencesandgenerallygivethesameresult.Inrelationtothedifferences:-Inpairwisecomparisons,TukeytestisbasedonstudentizedrangedistributionwhileScheffeisbasedinFdistribution.-Tukey'stestisveryrigorous,controllingthetypeIerrorverywell,butfavorsthetypeIIerror.-TheScheffetestallowscomparinganycontrastbetweenmeansandallowsdifferentnumberofobservationspertreatment. OR Wewouldpositthattherearenomajordifferences.Huberty,C.J,&Morris,J.D.(1988).Asinglecontrasttestprocedure.EducationalandPsychologicalMeasurement,48,567-578.   【出處】 https://researcher20.com/2010/05/27/%E5%A4%9A%E9%87%8D%E6%AF%94%E8%BC%83-multiple-comparisons/ https://www.statisticshowto.com/scheffe-test/ https://www.investopedia.com/terms/s/scheffes-test.asp https://www.researchgate.net/post/What_are_the_major_differences_between_scheffe_and_tukey_post_hoc_testsJason/Xuite日誌/回應(0)/引用(0)Whatisthedif...|日誌首頁|Journey-Don't...上一篇Whatisthedifferencebetweenlexicalandsemantic?...下一篇Journey-Don'tStopBelievin'(整晚只為一笑，不顧一切賭一把)...回應 全部展開|全部收合 全部展開|全部收合 累積|今日loading...... 關鍵字 即時新台幣匯率 匯率 COMMODITIES