商务统计全套配套课件[美]AmirD.AczelJayavelSounderpandian著谭英平等译Chap009.ppt

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1、COMPLETEBUSINESSSTATISTICSbyAMIRD.ACZEL&JAYAVELSOUNDERPANDIAN6thedition.Chapter9AnalysisofVarianceUsingStatisticsTheHypothesisTestofAnalysisofVarianceTheTheoryandComputationsofANOVATheANOVATableandExamplesFurtherAnalysisModels,Factors,andDesignsTwo-WayAnalysisofVarianceBlockingDesignsAnalysisofV

2、ariance9ExplainthepurposeofANOVADescribethemodelandcomputationsbehindANOVAExplaintheteststatisticFConducta1-wayANOVAReportANOVAresultsinanANOVAtableApplyTukeytestforpair-wiseanalysisConducta2-wayANOVAExplainblockingdesignsApplytemplatestoconduct1-wayand2-wayANOVALEARNINGOBJECTIVES9Afterstudyingthi

3、schapteryoushouldbeableto:ANOVA(ANalysisOfVAriance)isastatisticalmethodfordeterminingtheexistenceofdifferencesamongseveralpopulationmeans.ANOVAisdesignedtodetectdifferencesamongmeansfrompopulationssubjecttodifferenttreatmentsANOVAisajointtestTheequalityofseveralpopulationmeansistestedsimultaneousl

4、yorjointly.ANOVAtestsfortheequalityofseveralpopulationmeansbylookingattwoestimatorsofthepopulationvariance(hence,analysisofvariance).9-1UsingStatisticsInananalysisofvariance:Wehaverindependentrandomsamples,eachonecorrespondingtoapopulationsubjecttoadifferenttreatment.Wehave:n=n1+n2+n3+...+nrtotalo

5、bservations.rsamplemeans:x1,x2,x3,...,xrThesersamplemeanscanbeusedtocalculateanestimatorofthepopulationvariance.Ifthepopulationmeansareequal,weexpectthevarianceamongthesamplemeanstobesmall.rsamplevariances:s12,s22,s32,...,sr2Thesesamplevariancescanbeusedtofindapooledestimatorofthepopulationvarianc

6、e.9-2TheHypothesisTestofAnalysisofVarianceWeassumeindependentrandomsamplingfromeachoftherpopulationsWeassumethattherpopulationsunderstudy:arenormallydistributed,withmeansmithatmayormaynotbeequal,butwithequalvariances,si2.m1m2m3sPopulation1Population2Population39-2TheHypothesisTestofAnalysisofVari

7、ance(continued):AssumptionsTheteststatisticofanalysisofvariance:F(r-1,n-r)=EstimateofvariancebasedonmeansfromrsamplesEstimateofvariancebasedonallsampleobservationsThatis,theteststatisticinananalysisofvarianceisba