chapter 25 paired samples：25章配对样本

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1、Chapter25:PairedSamplesPairedDataDataarepairedwhentheobservationsarecollectedinpairsortheobservationsinonegrouparenaturallyrelatedtoobservationsintheothergroup.·Paireddataariseinanumberofways.Perhapsthemostcommonistocomparesubjectswiththemselvesbeforeand

2、afteratreatment.oWhenpairsarisefromanexperiment,thepairingisatypeofblocking.oWhentheyarisefromanobservationalstudy,itisaformofmatching.·Howdoyouknowifthedataarepaired?oconsiderhowtheywerecollectedandwhattheymean(checktheW’s).oThereisnotesttodeterminewhet

3、herthedataarepaired.·Onceweknowthedataarepaired,wecanexaminethepairwisedifferences.·Becauseitisthedifferenceswecareabout,wetreatthemasiftheywerethedataandignoretheoriginaltwosetsofdata.·Nowthatwehaveonlyonesetofdatatoconsider,wecanreturntothesimpleone-sa

4、mplet-test.·Mechanically,apairedt-testisjustaone-samplet-testforthemeanofthepairwisedifferences.·Thesamplesizeisthenumberofpairs.AssumptionsandConditions·PairedDataAssumption:Thedatamustbepaired.·IndependenceAssumption:oIndependenceAssumption:Thedifferen

5、cesmustbeindependentofeachother.oRandomizationCondition:Randomnesscanariseinmanyways.Whatwewanttoknowusuallyfocusesourattentiononwheretherandomnessshouldbe.Forexample,ifitwasanobservationalstudy,weneedtohavearandomsampleofindividuals.Ifitwasanexperiment,

6、weneedtohaverandomassignmentofsubjectstotreatments.o10%Condition:Whenasampleisobviouslysmall,wemaynotexplicitlycheckthiscondition.·NormalPopulationAssumption:WeneedtoassumethatthepopulationofdifferencesfollowsaNormalmodel.oNearlyNormalCondition:Checkthis

7、withahistogram.Pairedt-TestWetestthehypothesisH0:md=D0,wherethed’sarethepairwisedifferencesandD0isalmostalways0.Weusetheteststatistic:wherenisthenumberofpairs.istheordinarystandarderrorforthemeanappliedtothedifferences.3ConfidenceIntervalforMatchedPairs(

8、Pairedt-interval)Theconfidenceintervalis:Example:Beforeyoutookthiscourse,youprobablyheardmanystoriesaboutstatisticscourses.Oftentimesparentsofstudentshavehadbadexperienceswithstatisticscoursesandpassontheiranxietiestotheir