Experimental_Design_and_the_Analysis_of_Variance.pptVIP免费

ExperimentalDesignandtheAnalysisofVarianceComparingt>2Groups-NumericResponses•ExtensionofMethodsusedtoCompare2Groups•IndependentSamplesandPairedDataDesigns•Normalandnon-normaldatadistributionsDataDesignNormalNon-normalIndependentSamples(CRD)F-Test1-WayANOVAKruskal-WallisTestPairedData(RBD)F-Test2-WayANOVAFriedman’sTestCompletelyRandomizedDesign(CRD)•ControlledExperiments-Subjectsassignedatrandomtooneofthettreatmentstobecompared•ObservationalStudies-Subjectsaresampledfromtexistinggroups•Statisticalmodelyijismeasurementfromthejthsubjectfromgroupi:ijiijiijywhereistheoverallmean,iistheeffectoftreatmenti,ijisarandomerror,andiisthepopulationmeanforgroupi1-WayANOVAforNormalData(CRD)•Foreachgroupobtainthemean,standarddeviation,andsamplesize:1)(2..ijiijiijijinyysnyy•ObtaintheoverallmeanandsamplesizeNyNynynynnNijijttt..11..1......AnalysisofVariance-SumsofSquares•TotalVariation1)(112..NdfyyTSSTotalkinjiji•BetweenGroup(Sample)VariationtinjtiTiiiitdfyynyySST1112...2...1)()(•WithinGroup(Sample)VariationETTotalEtiiitinjiijdfdfdfSSESSTTSStNdfsnyySSEi12112.)1()(AnalysisofVarianceTableandF-TestSourceofVariationSumofSquaresDegrresofFreedomMeanSquareFTreatmentsSSTt-1MST=SST/(t-1)F=MST/MSEErrorSSEN-tMSE=SSE/(N-t)TotalTSSN-1•Assumption:Alldistributionsnormalwithcommonvariance•H0:NodifferencesamongGroupMeans(t=0)•HA:Groupmeansarenotallequal(Notalliare0))(:)9(:..:..,1,obstNtobsobsFFPvalPTableFFRRMSEMSTFSTExpectedMeanSquares•Model:yij=+i+ijwithij~N(0,2),i=0:1)()(true),is(otherwise1)()(true,is0:When)1(11)()(1)()(1021221221222MSEEMSTEHMSEEMSTEHtntnMSEEMSTEtnMSTEMSEEattiiitiiitiiiExpectedMeanSquares•3FactorseffectmagnitudeofF-statistic(forfixedt)–Truegroupeffects(1,…,t)–Groupsamplesizes(n1,…,nt)–Withingroupvariance(...