One-Way ANOVA | What I Learned Wiki - Fandom

Testing for significance in an ANOVA only reveals that at least one group (or level) is significantly different from the others. Post Hoc tests reveal the ... WhatILearnedWiki Explore MainPage AllPages Community InteractiveMaps RecentBlogPosts WikiContent RecentlyChangedPages WhatILearnedWiki BehavioralResearchMethods HypothesisTesting One-WayANOVA Two-WayANOVA Mann-WhitneyU WilcoxonTTest Organization Help Forums Policy Copyright Community Siteadministration Sitemaintenance Blogposts Ncsucase/InternetBenefits Community Help FANDOM Games Anime Movies TV Video Wikis ExploreWikis CommunityCentral StartaWiki Don'thaveanaccount? Register SignIn Advertisement One-WayANOVA Viewsource History Talk(0) ReturntoBehavioralResearchMethods ShortforOne-WayAnalysisofVariance,aOne-WayANOVAisusedtolookatthedifferencesbetweentwoormoregroups(orlevels)of oneindependentvariable.Theindependentvariableis ideallynominalbutcanbeordinal.Thedependentvariableisideallyratiobutcanbeinterval. Forexample,ifyourindependentvariableismood,thegroups(orlevels)couldbemad,sad,ok,andhappy.Apossibledependentvariablecouldbethescoreonamathtest.Thenyoucanseeiftherearedifferencesintestscoresbetweeneachlevelofmood. Thistestworksdifferentlyfromattestbecauseitdoesnotcomparethemeans,itcomparesthevariancesbetweenthegroups(orlevels).Todothis,thevarianceinthedatasetispartitionedintotwogroups:WithinandBetweensamplevariance. Whynotjustuseattest?Welliftheindependentvariableonlyhastwolevels,wecanuseattest!BUTwhentheindependentvariablehasthreeormorelevels,wehavetouseANOVA.UsingmultiplettestswouldincreaseourprobabilityofmakingaTypeIError. Contents 1IndependentandRepeatedMeasures 1.1IndependentMeasures 1.2RepeatedMeasures 2Significance 3PostHocTests 3.1PairwiseComparisons 3.2Tukey'sHonestlySignificantDifference(HSD) 3.3SchefféTest 3.4Fisher'sLeastSignificantDifference(LSD) 3.5StudentNewman-Kewls(SNK) 3.6RyanProcedure(REGW) 4One-WayANOVAinSPSS 4.1IndependentMeasuresinSPSS 4.2RepeatedMeasuresinSPSS IndependentandRepeatedMeasures SincewearecomparingsampleswithANOVAs,weneedtoknowwhowe'recomparing. IndependentMeasures Therearedifferentparticipantsineachgroup(orlevel). IndependentMeasuresANOVAexample Todeterminethepresenceofdifferences,theobservedvariabilityiscomparedtotheexpectedvariability(withindividualdifferences).Soyoucomparewhatyoufindinyoursamplestowhatwouldbeexpectedbyusingsimilarbutdifferentsamples(withnosignificantdifferences). Forexample,sayyourindependentvariableis"TypeofAnimal"withthelevels"Mammal","Bird",and"Reptile".Thenadependentvariablecouldbearatingof"Friendliness"onascaleof1(notfriendly)to10(veryfriendly). Sincetherearedifferentanimalsineachleveloftheindependentvariable,youhavetoaccountforthosedifferences.Thismakestheexpectedvariabilitybiggerwhichmeansyourobservedvariabilityneedstobeevenbigger! IndependentMeasuresANOVAneedbiggerdifferencesthanRepeatedMeasuresANVOAtobesignificant. RepeatedMeasures Thesameparticipantsareineverygroup(orlevel). RepeatedMeasuresANOVAexample Todeterminethepresenceofdifferences,theobservedvariabilityiscomparedtotheexpectedvariability(withoutindividualdifferences).Soyoucomparethemeasuredperformanceofyoursampleinallofthegroups(levels)toasituationwheretherearenodifferences. Forexample,sayyourindependentvariableis"StudySetting"withlevels"Underwater","Snow",and"Indoors".Thenadependentvariablecouldbeatestscoreonascaleof0(nocorrectanswers)to100(allcorrectanswers). Sinceyoucanhavethesamepeopletrystudyingineachconditionforeachtest,youdon'thavetoaccountforindividualdifferences.Thismakesyourvariabilitysmaller. RepeatedMeasuresANOVAsneedsmallerdifferencestofindsignificancebecausetheydonothavetoaccountforindividualdifferences. Significance TestingforsignificanceinanANOVAonlyrevealsthatatleastonegroup(orlevel)issignificantlydifferentfromtheothers.PostHoctestsrevealthelocationofthedifference(s).SoANOVAonlytellsyouifthereisadifference. TodeterminethesignificanceofanANOVA,wecomparetwotypesofvariance,WithinSampleVariance(varianceduetodifferenceswithingroups)andBetweenSampleVariance(varianceduetotheinteractionbetweengroups). WewanttheBetweenSampleVariancetobebiggerthantheWithinSampleVariance.Thiswouldmeanourgroupsaredifferentfromoneanotherandwearelikelytofindtheresultssignificant.SothehighertheBetweenSampleVariance,themoredifferentthegroups. WedonotwanttheBetweenSampleVariancetobeequaltoorlowerthantheWithinSampleVariance.Thiswouldmeantherearenosignificantdifferencesbetweenthegroups. Sotofindsignificantresults,wewantlargerdifferencesbetweenthegroupsandsmallerdifferenceswithinthegroups. Ifweonlyhavetwogroups(orlevels),thenweknowthedifferenceisbetweenthosetwo.However,ifwehavethreeormoregroups(orlevels)thenweonlyknowthatthereisadifferencebutwedon'tknowwhere.ThisiswhenweneedtouseaPostHoctest. PostHocTests Todeterminewherethedifferenceisbetweenthegroups(orlevels),weneedtouseaPostHoctest. Forexample,sayourlevelsweremad,sad,ok,andhappy.IfwehaveasignificantANOVAthenweknowthereisadifferencesomewhere.Itcouldbebetweenmadandhappy.Itcouldbebetweenmad,ok,andhappy.Itcouldbebetweenallofthemoods.Soitcouldbeanycombinationofdifferences! Basically,anANOVAdeterminesifthereisadifference.ThenthePostHoctestshowsthelocationofthedifference.OtherthanthePairwiseComparisons,allPostHoctestscanfindthedifferenceswithoutinflatingyouralphavalue(increasingyourchanceofhavingaTypeIError). PairwiseComparisons ThistechniquecomparesallofthemeansinanANOVA,twoatatime.Ineachcomparison,wearelookingforasignificantdifferencebetweenthemeans.It'slikeusingmultiplettests(thisisbad). EachcomparisonincreasestheriskofhavingaTypeIErrorbecauseitinflatesyouralphavalue. Tukey'sHonestlySignificantDifference(HSD) Thismethodusesonescoreandcomparesittoeachofthegroups(orlevels).Ifthegroup(orlevel)exceedstheHSDscore,thereisasignificantdifferencebetweenthosegroups(levels). ThisisaverycommonPostHoctest. SchefféTest Thismethodusesonescoretorepresenteachcomparisonofthegroups(orlevels).Ifthegroupsarethesamesize,thesamescorecanbeusedtocompareallofthegroups. Onlyusethistestifyouexpecttheretobedifferencesbetweenclustersofgroups(orlevels). Forexample,saywe'recomparingagegroups(young,teen,middle-aged,andolder)onhowmanyhourstheyspendinschoolperweek.Wewouldexpectyoungandteenagegroupstobesimilar,middle-agedandolderagegroupstobesimilar,andthetwoyoungergroupstobedifferentfromthetwooldergroups.Herewecanusethistest. ThistestisnotascommonasTukey'sHSDbutitismoreconservativethanTukey'sHSD.Thatmeansitishardertofindsignificantdifferencesbutifyoudofindasignificantdifference,itismoremeaningfulthanifyoufounditwithTukey'sHSD. Fisher'sLeastSignificantDifference(LSD) Thisisthebesttesttouseforthreegroups(orlevels). StudentNewman-Kewls(SNK) Thismethodsortsthegroups(orlevels)intosubsetsbyvariance. RyanProcedure(REGW) Requiresequalsamplesizes. One-WayANOVAinSPSS TheprocedureforconductinganSPSSanalysisdependsonthetypeofOne-WayANOVA,independentorrepeated. IndependentMeasuresinSPSS Clickon'Analyze'->'CompareMeans'->'One-WayANOVA' MovetheDVintothebox'DependentList' MovetheIVintothebox'Factor' Click'Post-Hoc'->andclickontheposthoctestyouwanttouse Click'Options'andselect'Descriptives' Click'OK' Youroutputshouldappear RepeatedMeasuresinSPSS Clickon'Analyze'->'GeneralLinearModel'->'RepeatedMeasures' WritethenameofyourIV(factor)insidetheboxlabeled'WithinSubjectsFactorName' Writethenumberoflevelsofyourfactorintheboxlabeled'NumberofLevels' Click'Add' Nextyouneedtodefinethelevelsofyourfactorbyclicking'Define' Selectyourfirstlevelinthecolumnontheleftandclickitovertothecolumnontheright Repeatstep6foreachlevelofyourfactor Clickon'Options' Moveyourfactorintotherighthandboxlabeled'DisplayMeansFor' Checktheboxfor'CompareMainEffects' Checktheboxfor'DescriptiveStatistics' Click'Continue' Click'OK' Youroutputshouldappear CommunitycontentisavailableunderCC-BY-SAunlessotherwisenoted. 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