comparing two means or two proportions比较两个或两个比例

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1、Sociology601Class8:September24,20096.6:Small-sampleinferenceforaproportion7.1:Largesamplecomparisonsfortwoindependentsamplemeans.7.2:Differencebetweentwolargesampleproportions.17.1LargesamplecomparisonsfortwoindependentmeansSofar,wehavebeenmakingestima

2、tesandinferencesaboutasinglesamplestatisticNow,wewillbeginmakingestimatesandinferencesfortwosamplestatisticsatonce.manyreal-lifeproblemsinvolvesuchcomparisonstwo-groupproblemsoftenserveasastartingpointformoreinvolvedstatistics,asweshallseeinthisclass.2

3、IndependentanddependentsamplesTwoindependentrandomsamples:Twosubsamples,eachwithameanscoreforsomeothervariableexample:Comparisonsofworkhoursbyraceorsexexample:ComparisonofearningsbymaritalstatusTwodependentrandomsamples:Twoobservationsarebeingcomparedf

4、oreach“unit”inthesampleexample:before-and-aftermeasurementsofthesamepersonattwotimepointsexample:earningsbeforeandaftermarriagehusband-wifedifferences3Comparisonoftwolarge-samplemeansforindependentgroupsHypothesistestingaswehavedoneitsofar:Teststatist

5、ic:z=(Ybar-o)/(s/SQRT(n))Whatcanwedowhenwemakeinferencesaboutadifferencebetweenpopulationmeans(2-1)?Treatonesamplemeanasifitwereo?(NO:toomuchtypeIerror)Calculateaconfidenceintervalforeachsamplemeanandseeiftheyoverlap?(NO:toomuchtypeIIerror)4Figurin

6、goutateststatisticforacomparisonoftwomeansIsY2–Y1anappropriatewaytoevaluate2-1?Answer:Yes.Wecanappropriatelydefine(2-1)asaparameterofinterestandestimateitinanunbiasedwaywith(Y2–Y1)justaswewouldestimatewithY.Thislineofargumentmayseemtrivial,butitb

7、ecomesimportantwhenweworkwithvarianceandstandarddeviations.5FiguringoutastandarderrorforacomparisonoftwomeansComparingstandarderrors:A&F213:formulawithoutderivationIss2Ybar2-s2Ybar1anappropriatewaytoestimate2(Ybar2-Ybar1)?No!2(Ybar2-Ybar1)=2(Ybar2)-

8、2(Ybar2,Ybar1)+2(Ybar1)Where2(Ybar2,Ybar1)reflectshowmuchtheobservationsforthetwogroupsaredependent.Forindependentgroups,2(Ybar2,Ybar1)=0,so2(Ybar2-Ybar1)=2(Ybar2)+2(Ybar1)6Step1:Significancetestfor2-1Theparameterofinterestis2