【复旦大学首批FIST项目传播学研究方法讲义】3-统计推断和t-检验-方差分析

3、统计推断、卡方检验、t检验和方差分析WinsonPeng彭泰权复旦大学2013年FIST课程·传播研究方法OutlineInferentialStatisticsSignificanceTestCrosstabulation/Chi-squareTestt-TestF-Test/ANOVA3I.WhatDoesBivariateAnalysisDo?1.EstimateandtestthesignificanceofthedifferenceinanintervalDVbetween/amonggroups(Comparemeansbasedont-testorF-test)2.EstimateandtestthesignificanceofthedifferenceinanominalDVbetween/amonggroups(Crosstabulationsbasedon2test)3.EstimateandtestthesignificanceofthecorrelationsbetweenanintervalIVandanintervalDV(CorrelationorRegressionbasedont-testorF-test)4StatisticalTechniquesforBivariateAnalysisIVDVDichotomousMultinomialContinuousDichotomous2TestofCrosstabulationAnalysisLogisticRegressionMultinomialMultinomialLogisticRegressionContinuoust-TestANOVA(F-Test)Correlation/OLSRegression5StatisticalTechniquesforMulti-IVsandSingleDVIVsDVDichotomousMultinomialContinuousMixedDichotomousLog-linearModelingLogisticRegressionMultinomialMultinomialLogisticRegressionContinuousANOVAOLSRegression/ANCOVA6StatisticalTechniquesforMulti-IVsandMulti-DVsIVsDVsDichotomousMultinomialContinuousMixedDichotomousLatentCategoricalAnalysis(LCA)Notavailable;convertcontinuousIVstocategoricalandthenuseLCAMultinomialContinuousGeneralLinearModeling(GLM)/MANCOVAMANCOVA/StructuralEquationModeling(SEM)ProbabilityTheory,SamplingDistributions,andEstimatesofSamplingErrorSamplingDistributionoSinglemostimportantconceptininferentialstatisticsoDefinition:Thetheoretical,probabilisticdistributionofastatisticforallpossiblesamplesofagivensize(N).oThesamplingdistributionisatheoreticaldistribution.Everyapplicationofinferentialstatisticsinvolvesthreedifferentdistributions.oPopulation:empirical;unknownoSamplingDistribution:theoretical;knownoSample:empirical;knownInformationfromsampleislinkedtopopulationviasamplingdistributionFigure7.4TheSamplingDistributionofTenCasesFigures7.5&7.6Figure7.7SamplingDistribution:Properties1.Normalinshape.2.Hasameanequaltothepopulationmean.3.Hasastandarddeviation(standarderror)equaltothepopulationstandarddeviationdividedbythesquarerootofN.CentralLimitTheorem:KeyIfrepeatedrandomsamplesofsizeNaredrawnfromanypopulationwithmeanµandstandarddeviationσ,then,asNbecomeslarge,thesamplingdistributionofsamplemeanswillapproachnormality,withameanµandstandarddeviationofoForanytraitorvariable,eventhosethatarenotnormallydistributedinthepopulation,assamplesizegrowslarger,thesamplingdistributionofsamplemeanswillbecomenormalinshape.ImportanceofCentralLimitTheorem:removesconstraintofnormalityinthepopulation./N13StepsinSignificanceTest1.FormulatenullandalternativehypothesesoNullhypothesis(H0):oAlternativehypothesis(Ha):oOne-tailedvs.two-tailedtests2.Chooseappropriateteststatistic:z,t,F,or23.Specifysignificancelevelandcriticalvalue:oSignificancelevel:=.05(or.01,.001)oCriticalvalue:specificZ-,t-,F-,or2valuecorrespondingtothechosen-level212114StepsinSignificanceTest(2)4.Estimatethechosenteststatistic,e.g.,,or5.Comparetheestimatedstatisticagainstthespecifiedcriticalvalue()todecideiftheevidenceisstrongevidencetorejectH0,e.g.,:oifzZa,acceptH0;oifzZa,rejectH0.2121xxsexxz2121xxsexxt15221Za/2-Za/2RegionofRejectionRegionofRejectionRegionofAcceptanceSignificanceLevel()&CriticalValue(Za)16SignificanceLevel()vs.ProbabilityLevel(p)isacriticalvalue(commonlyas.05,.01,or.001)forsamplingdistributionprescribedinadvance;pisanobservedprobabilitybasedonthesampledata;ifp,H0isrejected;otherwise,H0cannotberejected.17TypeIvs.TypeIIErrorsTypeIError:rejectanullhypothesiswhenitisinfacttrue.TypeIIError:acceptanullhypothesiswhenitisactuallyfalse.Sinceitisimpossible/impracticaltoknowifthenullhypothesisistrueorfalse,rejectionofanH0alwaysinvolvesmakingaTypeIErrorwhereasacceptanceofanH0alwaysrunstheriskofaTypeIIError.18ErrorsinSignificanceTestH0isactuallyDecisionTrueFalseRejectH0TypeIErrorCorrectDecisionAcceptH0CorrectDecisionTypeIIError19CalculationofTypeI&IIErrorsProbability(TypeIError)=Probability(TypeIIError)=bPowerofTest=1-b20ConcludingRemarksaboutStatisticalSignificanceStatisticalsignificanceisonlyvalidfordatabasedonrandomsampleorrandomizedexperiment;Statisticalsignificanceisnotthesameaspracticalsignificance;Statisticalsignificanceisonlyasmallpartofarelationshipunderstudy;Otheraspectsofarelationshipinvolvedirection(positiveornegative),strength(strong,moderate,orweak),andform(linearornonlinear).21TestSignificant?YesCheckTypeIError:NoCheckTypeIIError:Causedbyoutliers?Causedbyoutliers?Wrongdirection?Smalleffectsize?Practicalsignificant?Measurementerrors?Smallsamplesize?Wrongfunctionalform?LifeaftertheSignificanceTest22StatisticalSignificancevs.StrengthofRelationshiprSignificantNon-significantr=1YesImpossible1r≥.7StrongTrivial.7r≥.3ModerateTrivial.3r0WeakTrivialr=0ImpossibleTrivialCaution:readKozak,M.(2009).Whatisstrongcorrelation?TeachingStatistics,31,85-86.23ii.CrosstabulationAnalysisUsedforbivariateanalysisbetweentwocategoricalvariablesConstructionofacrosstabulation:oColumns:IV(i.e.,eachcategoryofIVforacolumn)oRows:DV(i.e.,eachcategoryofDVforarow)oCe