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ID:33583927
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时间:2019-02-27
《13 推断统计-两个样本》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、13StatisticalInference:Two-SampleCase推断统计:两个样本Lecturer:XiaorongChengPsychologySchool1IntroductionAge;sex;personality;intelligence...Controldirectly;randomlyassignSubjectvariableManipulatevariableIntactgroupdesignTrueexperimentIfthedifferencebetweenthemeansissufficientlylarge,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)StandarderrorofthedifferencebetweenmeansStandarderrorofthedifferencebetweenmeans(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、X1X2Iftwopopulationsarenotequal(如果两总体不相等),XXXX121212Standarderrorofthedifferencebetweenmeans: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)X12X3StandarderrorofthedifferencebetweenmeansIfallpopulationparametersareknown,comparetwome
4、ans(如果所有总体参数已知,比较两平均数):()XX()1212zXX124StandarderrorofthedifferencebetweenmeansEstimatingXX1222sssBiasedestimateifn1≠n2XX12X1X2SSSS11s()12()UnbiasedestimateXX12nn2nn1212SSSS12Ifn1=n2sXX12()NN(1)22ssˆˆ12sXX12nn125StandarderrorofthedifferencebetweenmeansIndependentpopulati
5、onsfromPopulation1Population2whichsamplesaredrawn.SamplesselectedfromtheX1X2populations.sˆsˆ12Samplevarianceusedtoestimate22sss+sthevarianceofthesamplingXXnn12distribution.Thetwoestimatedvariancesare22sss12usedtoobtainthestandarderrorofX1X2nnthedifferencebetweentwomeans.12Whenthestandarderro
6、rsofthemeanfortwopopulationsarecombined,weobtainthestandarderrorofthedifferencebetweenmeans6Hypothesistesting:independentgroupst-ratio()XX()1212tsXX12df()nn212H:120012()XX12tsXX127Hypothesistesting:independentgroupst-ratioComputationalexample(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-
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