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【精品】敬邀出席【慢性腎臟病防治科技研究 ..75

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【精品】敬邀出席【慢性腎臟病防治科技研究 ..75GATHERINGDATATheNonmathematicalSideofStatistics第一页,共62页。TheCentralityofDataProbabilitybeginswithaxiomsandmodels,notdata.Statisticsbeginswithdata.Afterthestatisticsreformmovementofthepastdecademostfreshmanstatisticscourses“emphasize”data.Thatis,theytrytogivethe...

【精品】敬邀出席【慢性腎臟病防治科技研究  ..75
GATHERINGDATATheNonmathematicalSideofStatistics第一页,共62页。TheCentralityofDataProbabilitybeginswithaxiomsandmodels,notdata.Statisticsbeginswithdata.Afterthestatisticsreformmovementofthepastdecademostfreshmanstatisticscourses“emphasize”data.Thatis,theytrytogivethestudentssomeexperienceworkingwithrealworlddatasets.ThesedatasetscomeprintedinthebackofthebookorinsupplementarydiskettesorCDs,sometimeswithsoftwareforperformingsimplestatisticalanalysis.第二页,共62页。TheCentralityofDataMostfreshmanstatisticstextshavelittletosayabouthowtogatherdata.Theygenerallyhaveanintroductorychapterortwotalkingabouttypesofdata(nominal/categorical,ordinal,interval,ratio),aboutthedifferencebetweenpopulationandsample,abouttypesofsamples(random,stratified,cluster,convenience),aboutthedifferencebetweenexperimentsandobservationalstudies,andaboutacoupleofwell-knownstatisticalgaffes(e.g.,DeweyDefeatsTruman).Thetreatment,however,isoftenbriefandlackingininsight.第三页,共62页。TheCentralityofDataSuchcoursesgivetheimpressionthatgatheringdataisarelativelyeasypartofstatisticalanalysis.Thecoursefocusesontheanalysisofdata,implyingthatthisiswheretherealworkofthestatisticianlies.Infact,thegatheringofgooddataistremendouslyhard.Thetechniquesofdoingsoareamajorstudyintheirownright.Whenweteachourstudentsandourselvestoreadstatisticscritically,thefirstquestionweshouldraiseis,“Howwasthedatacollected?”Itismucheasiertogetbaddatathangood,andbaddatawillproducebadresultsregardlessofwhatmathematicaltoolsweusetoanalyzeit.第四页,共62页。GoodData:TheSalkPolioVaccineThesourceforthisinformationischapters1and2ofStatistics,2e,byFreedman,Pisani,Purves,Adhikari,W.W. Norton&Company1991,ISBN0-393-96043-9.Ihighlyrecommendthisbookifyoureallywanttounderstandstatistics.Itpresentsagreatdealofgoodinformationclearlyandreadably.第五页,共62页。GoodData:TheSalkPolioVaccinePoliofirstappearedintheU.S.in1916.In1954thePublicHealthServicewasreadytoperformalarge-scalefieldtestofthevaccinedevelopedbyJonasSalk.Ithadprovedsafeandeffectiveinlaboratoryexperiments.第六页,共62页。GoodData:TheSalkPolioVaccineThegoalofthistestwastocomparetheincidenceofpolioamongvaccinatedchildren(thetreatmentgroup)withtheincidenceamongnon-vaccinatedchildren(thecontrolgroup).Thisisacommonsortofstatisticalstudy.Ifwecansomehowmakethetreatmentandcontrolgroupsidenticalinallwaysexceptwhethertheyreceivetreatment,thenwecanattributeanyobserveddifferences(e.g.,differentpoliorates)tothetreatment.Thechallengeistomakethetwogroupsidentical.第七页,共62页。GoodData:TheSalkPolioVaccineNote,bytheway,thatwedonotexpectthevaccinetoworkperfectly.Itwillprotectsomechildrenandnotothers.Itwillreducetherateofpoliobutnottozero.ThePublicHealthServicewantedtoperformatestonchildreningradesone,two,andthree,themostsusceptibleages(intheendthetestinvolvedabout750,000children).Oneplausibleapproachwastoinoculateallthechildrenandseeifthepolioratedroppedcomparedtothepreviousyear.Polio,however,isanepidemicdiseasewhoseratesvarydramaticallyfromyeartoyear.Ifratesdropped,wewouldnotknowwhetherthevaccinewaseffectiveoritwassimplyalow-incidenceyear.第八页,共62页。GoodData:TheSalkPolioVaccineThusitwasdecidedtovaccinatesomeofthechildrenandleaveothersunvaccinatedsoastobeabletocomparethegroupsduringthesameyear.Isthisunethical,however,intentionallyleavingsomechildrenunprotected?Thepointisthatwedonotyetknowhoweffectivethevaccineis,andwedonotknowwhatrisksitpresents.Inparticularwedonotknowwhetherthebenefitsoutweightherisks.第九页,共62页。GoodData:TheSalkPolioVaccineThenextquestionishowtodecidewhichchildrentovaccinate.Firstofall,wecannotvaccinatechildrenwithouttheirparents’approval.Perhapswecanjustvaccinatethechildrenwhoseparentsapproveandusethosewhoseparentsdonotapproveasourcontrolgroup.Butthispresentsaproblem:Experiencesuggeststhathigher-incomeparentsaremorelikelytogivepermissionfortheirchildrentoparticipateinsuchtests.Thisintroducesadifferencebetweenthetreatmentgroupandthecontrolgroup.第十页,共62页。GoodData:TheSalkPolioVaccineIsthisaproblem?Offhandthedifferencemayseemirrelevant,butitturnsouttobeimportant.Polioismorelikelytoaffectchildrenfromricherfamiliesthanthosefrompoorerfamilies.Why?Inpoorerfamilieshygieneisoftenworse,andchildrencatchpoliowhentheyareyoungandstillprotectedbyantibodiesfromtheirmothers.Thustheygetmildcasesofpolioandareimmunethenceforth.Inricherfamilieshygieneisbetter.Thechildrencatchpolioatanolderagewhentheyareunprotectedanditaffectsthemmoreseverely.第十一页,共62页。GoodData:TheSalkPolioVaccineThususingthechildrenwhoseparentsgivepermissionintroducesaconfoundingfactorintothestudy.Thatis,itintroducesaseconddifferencebetweenthetreatmentandcontrolgroupswhoseinfluenceontheresultsisinextricablyconfusedwiththeinfluenceofthefirst.Ifwefailtoruleoutpossibleconfoundingfactors,wecannotknowwhetherobserveddifferencesbetweenthetreatmentandcontrolgroupsaretheresultofthetreatment.Indeedtheconfoundingvariablemaycanceltheeffectsofthetreatment,makingitappearthereisnodifferencebetweenthetwogroups.Usingthechildrenwithoutpermissionasthecontrolgroupbiasestheexperimentagainstthevaccinebecausethechildreninthecontrolgroupareinherentlylesslikelytocatchpoliothanthetreatmentchildren.第十二页,共62页。GoodData:TheSalkPolioVaccineConfoundingisacommonandsometimessubtlecauseofdatabeingbad.Whenwehearastatisticalresult,weshouldbeonthelookoutforconfoundingvariables.Evenwhenwedonotseehowthesevariablesinfluencetheoutcomeofourexperiment,theycastdoubtontheusefulnessofthedata.Sometimestheconfoundingvariableshaveeffectsthatarenotobvious(likefamilyincomeonpolio).第十三页,共62页。GoodData:TheSalkPolioVaccineThusthesomeschooldistrictsdecidedtouserandomizedcontrolstodecidewhichchildrentovaccinateamongthechildrenwhoseparentsgavepermissionfortheirparticipationintheexperiment.Thatis,inessence,thedistrictsflippedacoinforeachchildwithpermission,givingthevaccineifthecoinflippedheadsandnotgivingitifthecoinflippedtails.第十四页,共62页。GoodData:TheSalkPolioVaccineThisiscounterintuitivetomanypeople.Howdoesrandomassignmentguaranteetherewillbenoconfoundingvariables?Ofcourseitdoesnotguaranteeit,butitmakesithighlyunlikely.Forinstancethenumberof“rich”childreninthetreatmentgroupisabinomialrandomvariablewithparameterp,wherepisthepercentageof“rich”childreninthepopulation.Fromourprobabilisticworkweknowthatthefractionof“rich”childreninalargesampleishighlyunlikelytodifferfrompbymuch.Thesameistrueofeveryotherconfoundingfactor.Itisunlikelytobepresentineithergroupinapercentagemuchdifferentfromitspercentageofthewholepopulation.第十五页,共62页。GoodData:TheSalkPolioVaccineIncontrast,ifweactuallytrytoruleoutconfoundingfactorsexplicitly—tryingtoassignequalnumbersof“rich”childrentoeachgroup,forinstance—wearelikelytointroduceotherconfoundingfactors.Experienceshowsthathumanjudgmentfrequentlyintroducesbiasintodata,preciselywhenthatjudgmentistryingtoruleoutbias.Thesafecourseisalwaystouserandomization.第十六页,共62页。GoodData:TheSalkPolioVaccineSonowbyarandomprocesswehaveassignedhalfthechildren(withpermission)togetthevaccineandhalfnotto.Dowesimplygivethevaccinetotheonesanddonothingwiththeothers?Thisintroducesanotherconfoundingfactor:Thetreatmentgroupknowsithasbeentreatedandthecontrolgroupknowsthatithasnotbeentreated.Oddlyenoughsimplyknowingthatoneisbeingtreated,beingstudied,etc.canproduceadifferentresponseinpeople.Asthebookmentions,manypeoplesufferingpost-operativepainexperienceimmediatereliefafterbeinggivenaninertsubstance(e.g.,asugarpill)thattheyaretoldisapainreliever.Thisisknownastheplaceboeffect.第十七页,共62页。GoodData:TheSalkPolioVaccineSotheschooldistrictsgaveeverychildashot.Treatmentchildrenreceivedashotofvaccine,andcontrolchildrenreceivedashotofsaltwater(aplacebo).ThusthechildrenandtheirparentsdidnotknowwhetherthechildrenwereinthetreatmentgroupSimilarlyaschildrenfellillduringthefollowingyear,physicianshadtodeterminewhethertheillnesswaspolio.Thisisnotalwaystrivial;polioissometimesdifficulttodiagnose.Herethephysicianmightmakeadifferentdiagnosisifheknewthatthechildwasvaccinated.Thusthephysicianswerenottoldwhichchildrenwerevaccinated.第十八页,共62页。GoodData:TheSalkPolioVaccineWhenneitherthesubjects(children)northeevaluators(physicians)knowwhoisinthetreatmentgroup,theexperimentisadouble-blindexperiment.ThustheSalkpoliotestwasarandomizedcontrolled,doubleblindexperiment.Ingeneralthisisthebestwayofproducingdata(butitisnotalwayspossibletosetupsuchanexperiment).Herearetheresultsoftheexperiment.第十九页,共62页。GoodData:TheSalkPolioVaccineChildrenPolioRate(per100,000)Treatment200,00028Control200,00071NoPermission350,00046第二十页,共62页。GoodData:TheSalkPolioVaccineClearlythetreatmentproducedadramaticreductioninthepoliorate.Ofcourseitispossiblethatsuchadifferenceistheresultofrandomvariation(i.e.,justbychancethismanymorechildreninthecontrolgroupthanthetreatmentgroupcontractedpolio.Wepossessthemathematicaltools,however,toshowthatthisprobabilityisextremelylow.)Allotherpossiblesourcesofdifferenceinthepoliorates(confoundingfactors)areruledoutbytherandomizedcontrolled,double-blinddesign.Notebythewaythatthepoliorateinthe“noconsent”groupisquiteabitlowerthanthatforthecontrolgroup,aswewouldexpect.第二十一页,共62页。GoodData:TheSalkPolioVaccineSomeschooldistrictsusedadifferentmodelfortheexperiment,proposedbytheNationalFoundationforInfantileParalysis(NFIP).Theyproposedsimplyvaccinatingallsecondgradechildrenwhoseparentsgavepermissionandusingallchildreningradesoneandthreeascontrols.Ofcoursethisbiasestheexperimentagainstthevaccine:Thechildrenwithpermissionaremorelikelytocontractpoliothanchildreningeneral.Thefirstandthirdgradecontrolgroupsincludeallchildren,includingthosewhoseparentswouldnotgivepermission,makingthemlesslikelytocontractpoliooverall.第二十二页,共62页。GoodData:TheSalkPolioVaccineFurther,sincepolioisanepidemicdisease,oneexpectsittospreadwithinclasses.Itcouldeasilybemore(orless)prevalentinsecondgradethaninfirstsimplybecauseitspreadsamongchildrenwhoareincontactwitheachother.Thislastbiascouldgoineitherdirection.HereisthedatafromtheNFIPdesign.第二十三页,共62页。GoodData:TheSalkPolioVaccineChildrenPolioRate(per100,000)Treatment(grade2)225,00025Control(grades1&3)725,00054NoPermission(grade2)125,00044第二十四页,共62页。GoodData:TheSalkPolioVaccineHerethetreatmentandnopermissionratesarecomparable(28to25and46to44),butthecontrolgroupratesarequitedifferent(71to54).Thereflectsthepoorerdesignandtheconfoundingvariableswehavealreadynoted.Poorerdesignproducespoorerdata.第二十五页,共62页。GoodandPoorData:ThePortacavalShuntThisinformationalsocomesfromthesametext.Onetreatmentforcirrhosisoftheliverinvolvesadifficultsurgerytocreatea“portacavalshunt”toredirectbleeding.Herearetheresultsof50studiesinatwo-waytable.Itpartitionsthestudiesbythesortofcontrolsusedandbythedegreeofenthusiasmthestudyhadforthesurgery.第二十六页,共62页。GoodandPoorData:ThePortacavalShuntMarkedEnthusiasmModerateEnthusiasmNoEnthusiasmNoControls2471Controls,butnotrandomized1032RandomizedControlled013第二十七页,共62页。GoodandPoorData:ThePortacavalShuntThusenthusiasmforthesurgeryisquitehighinpoorlydesignedexperimentsandalmostnonexistentinwell-designedones.Whichwouldyoutrust?第二十八页,共62页。GoodandPoorData:ThePortacavalShuntItisdifficultorimpossibletociteaparticularreasonforthedifferencesintheresults,butaplausibleexplanationisthatwhenassignmentisnotrandomphysicianstendtorecommendtreatmentforpatientswhoareinbettershapetostartwith.Thismakesthetreatmentlookbetterthanitreallyis.Inallthreeofthedesigncategoriesaboveabout60%ofthepatientswhoreceivedtheportacavalshuntwerestillaliveafterthreeyears.Intherandomizedcontrolledexperimentsthethree-yearsurvivalrateofuntreatedpatientswasalsoabout60%.Intheotherexperimentsthethree-yearsurvivalrateofuntreatedpatientswasabout45%—theywereevidentlyweakertostartwith.第二十九页,共62页。MoreMedicalDataFromStatisticsbyFreedmanandPisaniAnotherfairlycommonsurgeryiscoronarybypasssurgery.Thebookreportson29studiesofthissurgery,8ofwhichusedrandomizedcontrols.Therestusedhistoricalcontrols — thatis,theycomparedsurgicalresultstothoseobtainedbythetraditionaltreatmentinpaststudies.Againthisleavesroomforconfoundingvariablestocreepin.Thedifferenttimeandplaceofthepatientsinthehistoricalcontrolsmeanmanyaspectsofthepatientstreatmentmayhavebeendifferent(e.g.,weredifferentantibioticsavailable,werethenursingpracticesthesame,wasthetypicaldietcomparable?).第三十页,共62页。MoreMedicalDataFromStatisticsbyFreedmanandPisaniAmongthe21experimentsusinghistoricalcontrols,16werepositiveabouttheeffectsofbypasssurgeryand5werenegativeaboutit.Amongthe8randomizedcontrolledexperiments1waspositiveand7werenegative.Again,gooddataleadstodramaticallydifferentconclusions.Onewonderswhetherresearcherstendtohaveabiasinfavoroftheapproachestheyarestudying.第三十一页,共62页。MoreMedicalDataFromStatisticsbyFreedmanandPisaniIn9ofthenon-randomizedexperimentsand6oftherandomizedonesthree-yearsurvivalrateswereavailable.Inthehistoricalcontrolexperiments90.9%ofthosetreatedsurvivedthreeyearsbutonly71.1%ofthoseinthecontrolgroupdid.Intherandomizedcontrolledexperiments87.6%ofthetreatedpatientssurvivedthreeyearsand83.2%ofthecontrolgroupdid.Thelowersurvivalrateinthehistoricalcontrolgroupcomparedtotherandomizedcontrolgroupsuggeststhatthetreatmentisnotthemainsourceofincreasedsurvival.第三十二页,共62页。MoreMedicalDataFromStatisticsbyFreedmanandPisaniMoretragicisthecaseofDES,adrugusedthroughthelate1960’stopreventmiscarriage.FivestudiesofDESusinghistoricalcontrolswereallpositiveaboutitseffects.Threestudiesusingrandomizedcontrolswereallnegative.NeverthelessdoctorscontinuedtogiveDESto50,000womenperyear.LateritwasdeterminedthatifawomanpregnantwithagirlreceivesDESitcancausearareformofcancerinthatdaughterwhenshegrowsup.ThustheUSbannedDESintreatmentofmiscarriagein1971.第三十三页,共62页。ObservationalStudiesvs.ExperimentsThedifferencebetweenanexperimentandanobservationalstudyiswhodecideswhichpatientsgointothetreatmentgroup.Inanexperimenttheresearcherdecides.Inanobservationalstudythesubjectsdecide.Thedifferencebetweenthesetwosortsofstudycannotbeoverstated.Sincesubjectsinanobservationalstudydecidewhichgrouptheyarein,therearelimitlessopportunitiesforconfoundingfactorstocreepin.Thetreatmentandcontrolgroupsautomaticallydifferfromeachotherbytheveryfactofhavingmadedifferentchoices.第三十四页,共62页。ObservationalStudiesvs.ExperimentsWhyuseobservationalstudies?Inmanycasesexperimentationisimpossibleormorallyunthinkable.Forinstancestudiesofthelinkbetweensmokingandlungcancerarenecessarilyobservational.Researcherscannotrandomlyassignpeopletosmokeornot;peoplemakethatchoicethemselves.第三十五页,共62页。ObservationalStudiesvs.ExperimentsItwasonthisbasisthatthetobaccocompaniessolongarguedtherewasnoproofthatsmokingcausedcancer,onlythattherewasanassociationbetweensmokingandcancer.Thatis,itisclearfromobservationthatsmokershavehigherratesoflungcancer,butthisdoesnotshowthesmokingcausesthecancer.Forinstance,cigarettesmokingmaybemoreprevalentamongpeoplewithlesseducation,andthosepeoplemaytendtohavejobsthatexposethemtomoreenvironmentalhazards.Ortheymayliveinhousingthatislesslikelytohaveairconditioning,andtheairconditioningmaysomehowreducecancer.第三十六页,共62页。ObservationalStudiesvs.ExperimentsAsimplerconfoundingfactoristhatsmokersarepredominantlymale,andmendieyoungeronaveragethanwomen.第三十七页,共62页。ObservationalStudiesvs.ExperimentsForasillyexample,thereispresumablyastrongassociationbetweenthenumberofchurchesinacityandthenumberofcriminalsinacity.Why?Couldwesafelyconcludethatchurchescausecriminalactivity(orviceversa)?第三十八页,共62页。ObservationalStudiesvs.ExperimentsInthecaseofcigarettesmoking,however,researchersranmanyobservationalstudiescarefullycontrollingforplausibleconfoundingfactors(e.g.,comparingsmokersandnonsmokersofthesamesex,withthesameincomelevel,thesameeducationallevel,thesamesortsofhousingandjob).Manypeoplebelievethismakesastrongcasethatsmokingdoes,infact,causelungcancerandothermedicalproblems.第三十九页,共62页。ObservationalStudiesvs.ExperimentsThatbeingsaid,onemustalwaysbeonthelookoutforconfoundingvariablesinobservationalstudies.Evenwhenthesearecontrolledfororotherwisedealtwith,wemayalwaysbesuspiciousthatobservationalstudiesfailto“prove”whattheresearchersclaimtheydo.第四十页,共62页。ObservationalStudiesvs.ExperimentsThebook(StatisticsbyFreedmanandPisani,again),givesanintriguingexampleofthetrialofacholesterol-reducingdrugcalledClofibrate.Inarandomizedcontrolleddouble-blinkexperiment20%oftheclofibrategroupand21%ofthecontrolgroupdied,soitappearedclofibratemadenodifference.However,manyoftheclofibrategroupfailedtotaketheirmedicine,andsomepeoplethoughtthatthisconfoundingfactoraccountedfortheapparentineffectivenessofclofibrate.第四十一页,共62页。ObservationalStudiesvs.ExperimentsResearchersthenlookedattheclofibrategroupaccordingtowhethersubjects“adhered”totheexperiment(took80%ormoreofthedrug)ornot.Theyfound15%oftheadherersdied,but25%ofthenon-adherersdied.Thisappearstoshowthatclofibrateisindeedeffective.Howeverthestudyhasnowbecomeobservationalsincethesubjectsdecidewhethertoadhereornot.Weshouldlookforproblems.第四十二页,共62页。ObservationalStudiesvs.ExperimentsAnaturalcheckistolookatthesurvivalratesofadherersandnon-adherersintheplacebo(control)group.Itturnsoutthatinthisgroup15%oftheadherersand28%ofthenon-adherersdied.Surprise!Whattheresearchershavediscoveredisthatthereisafundamentaldifferencebetweenadherersandnon-adherers(whileclofibratemakesnodifference).Suchunanticipatedconfoundingvariablesariseeasilyinobservationalstudies.第四十三页,共62页。ObservationalStudiesvs.ExperimentsStatisticsoffersseveralotherintriguingexamples.Oneobservationalstudyofultrasoundfoundanassociationbetweenuseofultrasoundduringpregnancyandlowbirthweight.Thequestionis,doesultrasoundcauselowbirthweight.Researchersfoundseveralconfoundingvariablesandcontrolledforthem,buttheassociationremained.Researcherssuspectedthereallinkwasproblempregnancies:obstetriciansprescribeultrasoundwhentheythinksomethingmaybewrong.Laterarandomizedcontrolledexperimentdemonstratedthatultrasounddoesnotcauselowbirthweights.Ifanythingitwasprotective.第四十四页,共62页。ObservationalStudiesvs.ExperimentsObservationalstudiesfoundanassociationbetweencircumcisionofmenandlowerratesofcervicalcanceramongwomen.SpecificallycervicalcancerrateswerelowamongJewsandMoslemsinthe1950’s.Someresearchersconcludedthatcircumcisionlowerstherateofcervicalcancer.Onceagain,however,therealstoryappearstolieelsewhere.Cervicalcancerisasexuallytransmitteddiseaseandtakesalongtimetodevelop.Thuspromiscuitypromotesitsoccurrencebutpotentiallymanyyearsafterward.Inthe1930’sand40’spromiscuitywasevidentlylesscommonamongJewsandMoslemsthanitwasinthegeneralpopulace.This,ratherthancircumcision,appearstoexplainthedifferingratesofcervicalcancer.第四十五页,共62页。OtherExamplesThesearefromStatisticsConceptsandControversies,4e,byDavidS.Moore,W.H. FreemanandCompany,ISBN0-7167-2863-X,theothertrulysuperbintroductiontostatisticsthatIhavefound.第四十六页,共62页。OtherExamplesAnnLandersoncepublishedinhercolumn,“Ifyouhadtodoitoveragain,wouldyouhavechildren.”Shegotnearly10,000responses,70%ofwhichsaidno.Thisisoneoftheworstsortsofobservationalstudies,avoluntaryresponsesurvey.Suchdatacollectionisgenerallyworthless.(ThisisthetechniqueusedbySherryHiteinherinfamousreportsonsexintheUS).AnationalrandomsampleconductedbyNewsdayasked1373thesamequestionandfoundthat91%wouldhavechildrenagain.Notehowdramaticthedifferenceisbetweenpoordataandgooddata.第四十七页,共62页。OtherExamplesSurveysoftensufferfromnonresponseerror.Thatis,someofthepeopleyouwanttocontactareunavailableorrefusetoparticipate.Ifthesepeoplesharesomecommonqualities,thismaybiasyourdata.Forinstancehomelesspeopleandblackpeopleweredisproportionatelymissedinthe1990census.Randomdigitdialingschemesmisspeoplewithoutphones(about6%ofhouseholdsin1997),andthisincludesdisproportionatelylargenumbersofsouthernersandpeoplelivingalone.Alsowomenaremuchmorelikelythanmentoanswerthephoneinahousehold(accordingtoonepoll,only37%ofthepeoplewhoanswercallsaremen),sosimplyspeakingwiththepersonwhoanswersoverrepresentswomen.第四十八页,共62页。OtherExamplesSurveysalsosufferfromresponseerror.Thatissubjectsmaygiveinaccurateorflatlydishonestanswers,particularlyifthesubjectisasensitiveone.Imaginearandomtelephonesurveywiththequestion,“Haveyouusedillegaldrugsinthepastsixmonths?”第四十九页,共62页。OtherExamplesWordingofquestionsmakesahugedifference.In1992theAmericanJewishCommitteetookapollwiththequestion,“DoesitseempossibleordoesitseemimpossibletoyouthattheNaziexterminationoftheJewsneverhappene
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