13 推断统计-两个样本

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1、13StatisticalInference:Two-SampleCase推断统计：两个样本Lecturer:XiaorongChengPsychologySchool1IntroductionAge;sex;personality;intelligence...Controldirectly;randomlyassignSubjectvariableManipulatevariableIntactgroupdesignTrueexperimentIfthedifferencebetweenthemeansissufficientlylarge,weassumethatthepopul

2、ationparametersfromwhichthesamplesweredrawnarealsodifferent.（如果两个样本的平均数差异足够大，我们假设两样本来自2的总体也有差异）StandarderrorofthedifferencebetweenmeansStandarderrorofthedifferencebetweenmeans（平均数差异的标准误）Asamplingdistributionofthedifferencebetweenthemeans（平均数差异的抽样分布）Iftwopopulationsareequal（如果两总体相等）,0XX12

3、X1X2Iftwopopulationsarenotequal（如果两总体不相等）,XXXX121212Standarderrorofthedifferencebetweenmeans:standarddeviationofthesamplingdistributionofthedifferencebetweenmeans.（平均数差异的标准误就是平均数差异的抽样分布的标准差）X12X3StandarderrorofthedifferencebetweenmeansIfallpopulationparametersareknown,comparetwome

4、ans（如果所有总体参数已知，比较两平均数）:()XX()1212zXX124StandarderrorofthedifferencebetweenmeansEstimatingXX1222sssBiasedestimateifn1≠n2XX12X1X2SSSS11s()12()UnbiasedestimateXX12nn2nn1212SSSS12Ifn1=n2sXX12()NN(1)22ssˆˆ12sXX12nn125StandarderrorofthedifferencebetweenmeansIndependentpopulati

5、onsfromPopulation1Population2whichsamplesaredrawn.SamplesselectedfromtheX1X2populations.sˆsˆ12Samplevarianceusedtoestimate22sss+sthevarianceofthesamplingXXnn12distribution.Thetwoestimatedvariancesare22sss12usedtoobtainthestandarderrorofX1X2nnthedifferencebetweentwomeans.12Whenthestandarderro

6、rsofthemeanfortwopopulationsarecombined,weobtainthestandarderrorofthedifferencebetweenmeans6Hypothesistesting:independentgroupst-ratio()XX()1212tsXX12df()nn212H:120012()XX12tsXX127Hypothesistesting:independentgroupst-ratioComputationalexample(incubationeffect孵化效应)SEARCHBAEOH

7、OLENEDUMRANDExamplesofrebusproblemsusedbySmithinhisresearch.(AdaptedfromR.A.Fink,T.B.Ward,&S.M.Smith(1992).Creativecognition:Theory,research,andapplications,Cambridge,MA:MITPress.)8Hypothesistesting:independentgroupst-