InferentialConfidenceIntervalsandEquivalenceTesting推理的置信区间和等价测试

Differences,Equivalence,IndeterminacyInferentialConfidenceIntervalsandtheirApplicationtoEquivalenceTestingConfidenceintervalapproachAssuggestedbymanyleadingquantitativepsychguys,usingconfidenceintervalsinlieuofemphasizingp-valuesmaymakeforabetterapproachforevaluatinggroupdifferencesetc.ConfidenceintervalscanprovidealltherelevantNHSTinfoaswellasameansofgraphicallydisplayingstaticallysignificantdifferencesOneapproachistosimplyseeifourintervalforthestatisticofinterestcontainstheH0value.Ifnot,rejectH0

GroupCIsThisishowCIsareoftendisplayedNotehowusingindividualCIsshowsoverlap,leadingonetothinkthatthereisnostatisticaldifferenceTheerrortermforeachgroupisnotthesameasthatusedintheactualt-testConfidenceIntervalsWithmeandifferencescoreswewouldloseindividualgroupdata(notthatwecouldn’tadditintableform)However,mighttherebeawaytoretaintheindividualgroupmeanintervalsandshowstatisticaldifference?InferentialCIsTryon,2001;Goldstein&Healy,1995ProvideatechniqueforgivingCIsinwhichnon-overlapsuggestsstatisticalsignificanceatthelevelspecifiedbythecriticalvalueused.Notethatfortheonesamplecasewe’djustgoaboutbusinessasusual,andseeiftheH0valuefallswithintheinterval.i.e.nothingwouldchange.InferentialCIsForgroupdifferencesallthatisrequiredisacorrection(reduction)toourCIequationSpecificallythecriticalvalueReductiontermTheratioofthestandarderrorofthedifferencebetweenmeanstothesumoftherespectivegroupstandarderrorsHoldsforunequalsamplesizesasiscomputedindividuallyforeachsampleInferentialCIsWhatitboilsdowntoInferentialCIsSonowwecancomputethegroupmeanCIsas:Andnownon-overlapsuggestsstatisticalsignificanceatthespecifiedlevelGraphicallyNowwehavenooverlapandcanclearlydiscernstatisticaldifference(previousandnewinferentialCIs)DependentsamplesWithdependentsampleswemusttakeintoaccountthecorrelationbetweenthetwosamplesNewreductiontermICIsNotethattheICIforeachgroupisnolongera95%confidenceintervalforthegroupmeanWhatitwouldbeaCIforiswhateverpercentilethereducedcriticalvalueisassociatedwithE.g.ifE=.65andt.95(30)=2.04,thentx=1.33,whichwouldcreateaboutan80%regularCIThekeyismaintainingthetypeIerrorratefortheactualinferencetestinquestion(regardingthedifferencebetweenmeans),andthisispreservedat.05.TestsofEquivalenceAshasbeenmentioned,thetypicalmethodofNHSTappliedtolookingfordifferencesbetweengroupsdoesnottechnicallyallowustoconcludeequivalencejustbecausewedonotrejectnullpisameasureofevidenceagainstthenull,notforitHavingasmallsamplewouldallowustotheretainthenullOftenthisconclusionisreachedanywayStateddifferently,absenceofevidencedoesnotimplyevidenceofabsenceAltman&Bland,1995Examplesofusage:genericdrugvsestablisheddrugefficacyofcounsellingtherapiesTestsofEquivalenceToconcludethereisasubstantialdifferenceyoumustobserveadifferencelargeenoughtoconcludeitisnotduetosamplingerrorToconcludethere’snosubstantialdifferenceyoumustobserveadifferencesmallenoughtorejectthatclosenessisduetosamplingerrorTestsofEquivalenceTestsofEquivalenceThebasicapproach:Specifyarangeofvaluesthatwouldconstituteequivalencyamonggroups()DeterminetheappropriateconfidenceintervalforthemeandifferenceSeeiftheCIforthedifferencescorefallsentirelywithintherangeofequivalencyTestsofEquivalenceSpecifyarange?Isn’tthatsubjective?Baseiton:PreviousresearchPracticalconsiderationsYourknowledgeofthescaleofmeasurementTryonapproachDecideonarangedestimatethatreflectsyourestimationofequivalence()Inotherwords,ifmyrangedestimateissmallerthanthis,IwillconcludeequivalenceEstablishinferentialCIsforeachvariable’smeanCreateanewrangethatincludesthelowerboundfromthesmallermean,andtheupperboundfromthelargermeanSeeifthisCIrange(Rg)issmallerthanthespecifiedmaximumamountofdifferenceallowedtostillclaimequivalence()EquivalenceTestingWhichmethod?Tryon’sproposalusingICIshasseveraladvantages:EmphasisoneffectsizeNHSTisimplicitratherthanexplicitCoversbothtestsofdifferenceandequivalenceProvidesforathirdoutcomeStatisticalindeterminancySaywhat??IndeterminancyNeitherstatisticallydifferentorequivalent(orbothdifferentandequivalent)Judgmentmustbesuspendedasthereisnoevidencefororagainstanyhypothesis(orboth)Mayhelpinwardingoffinterpretationof‘marginallysignificant’findingsastrendsNoteonsamplesizeItwasmentionedhowwecouldn’tconcludeequivalencefromadifferencetestbecausesmallsamplescouldeasilybeusedtoshownonsignificancePowerisnotnecessarilythesamefortestsofequivalenceanddifferenceHowevertheideaisthesame,inthatwithlargersampleswewillbemorelikelytoconcludeequivalence

SummaryConfidenceintervalsarean