11_ReducedVsFull

11_ReducedVsFull - REDUCEDvs.FULLMODEL F-TEST Testsof C d =

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Unformatted text preview: REDUCEDvs.FULLMODEL F-TEST Testsof C d = leadtoFtests,butthatsnottheonlywayto anFtest 500/402:bigemphasisonmodelcomparison SSinANOVAtablesusuallyexplainedintermsofmodel comparison e.g.SSforABinteractionisthedifferenceinerrorSSbetweentwo models: Y ijk = + i + j + ij + ijk and Y ijk = + i + j + ijk AlsoleadstoFtests Thetestofnotreatmenteffectinthedairycowstudycanbe viewedasamodelcomparison Fullmodel: Y ij = + i + ij (or Y ij = i + ij Reducedmodel(expressesHo): Y ij = + ij Copyright c 2011Dept.ofStatistics(IowaStateUniversity) Statistics511 1/1 Questionsaboutmodelcomparison WhydoesmodelcomparisonleadtoFtests? IfyoutestHousinga C testorusingamodelcomparisontest, doyougetthesameanswer? Again,willanswerusingageneralsetup(NormalGMmodel) y = X + , N ( , 2 I ) Eachmodel(FullandReduced)correspondstoanXmatrix TwodifferentcolumnspacesforE ( y ) : C ( X o ) forreducedmodel, C ( X ) forfullmodel Keyrequirement: C ( X o ) C ( X ) Inwords:ReducedmodelXmatrixcanbeobtainedbyimposing constraintsonfullmodel.Hodescribesthoseconstraints. Modelcomparisoncorrespondstotesting H : E ( y ) C ( X o ) vs. H A : E ( y ) C ( X ) / C ( X o ) . Copyright c 2011Dept.ofStatistics(IowaStateUniversity) Statistics511 2/1 Thereducedmodelcorrespondstothenullhypothesisandsays that E ( y ) C ( X o ) ,aspecifiedsubspaceof C ( X ) . Thefullmodelsaysthat E ( y ) canbeanywherein C ( X ) thatisnot in C ( X o ) . Forexample,1-wayANOVAwith3groups. X o = 1 1 1 1 1 1 and X = 100 100 010 010 001 001 Copyright c 2011Dept.ofStatistics(IowaStateUniversity)2011Dept....
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11_ReducedVsFull - REDUCEDvs.FULLMODEL F-TEST Testsof C d =

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