chapter 19: sample surveys - math statistics...

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  • 1

    Chapter19:SampleSurveys

    Population

    (parameter)

    Sample

    (statistic)

    Sampling procedure

    Inference

  • 2

    Definitions Population thegroupofindividualsofinterestinthesurvey.

    Sample partofthepopulation,chosentogiveinformationaboutthepopulation.

    Parameter anumericalfactaboutthepopulation.Unknown canonlybeestimated.

    Statistic anumericalfactaboutthesample,usedtoestimatethecorrespondingfactaboutthepopulation.Known canbecomputedfromthesample.

  • 3

    Example Population USUstudentsregisteredforstat1040thissemester.

    Sample agroupofstat1040studentsselectedfromthepopulation.

    Parameter thepercentageinthepopulationwhopreferweeklyquizzesoverhomework.

    Statistic thepercentageinthesamplewhopreferweeklyquizzesoverhomework.

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    RepresentativeSamples

    Needarepresentative sample onethatislikethepopulationinthewaysthatmatter.Agoodsamplingprocedurewillbefairandimpartial.

    Estimatingpopulationparametersisonlyjustifiedwhenthesampleisrepresentative.

    Themethodofchoosingthesamplemattersalot.

    Thebestmethodsofchoosingasampleinvolvetheplanneduseofprobability.

  • 5

    WhatCangoWrong?

    Selection bias asystematictendencytoexcludesomekindsofpeople.E.g.tendencytoexcludetherich,thepoor,thehomeless,theyoung,theold,etc.

    Nonresponse bias thekindsofpeoplewhoresponddifferfromthosewhodonotrespond.E.g.peoplewhoareopinionatedabouttheissuearemorelikelytorespond.

    Ifthepeoplewhotendtobeexcludedorwhodontresponddifferinimportantwaysfromtherestofthepopulation,thesamplewillnotgivegoodestimates.

  • 6

    TheLiteraryDigestPoll

    1936,RooseveltversusLandon.

    Campaigncenteredoneconomicpolicies.

  • 7

    TheLiteraryDigestPoll

    1936,RooseveltversusLandon. Campaigncenteredoneconomicpolicies. TheLiteraryDigest tookthelargestsampleever 2.4millionpeople,andpredicted:

    Rooseveltwillonlyget43%ofthevote.

    Landonwillwin.Roosevelt won by a landslide!(Literary Digest went bankrupt)

  • 8

    Whatwentwrongin1936?

    TheLiteraryDigestsentquestionnairesto10millionpeople.

    Thenamesofthe10millioncamefromtelephonebooksandclubmembershiplists.

    SELECTIONBIAS!

    Theygotresponsesfrom2.4millionpeople. NONRESPONSEBIAS!

    Theytendedtoexcludethepoor,andforthefirsttimeinhistory,thepoortendedtovoteDemocrat.

  • 9

    Gallup:thenewkidontheblock Gallupsampled3000peopleatrandom,fromthesamelists

    theDigestused,andpredictedtheirprediction!

    Hesampled50,000peopleinaspecialwayandmadehisownprediction.

  • 10

    Biggerisbetter?

    Ifasampleisrepresentative,alargesampleisbetterthanasmallsamplebecauseitgivesmorepreciseestimatesofthepopulationparameter.

    BUT

    Ifthesamplingprocedureisbiased,takingalargesampledoesnothelp.Thisjustrepeatsthebasicmistakeonalargerscale!

  • 11

    1948:TheYearthePollsElectedDewey

  • 12

    EvenUtahvotedforTruman! Utah: Truman(Dem): 149,15154% Dewey(Rep): 124,40245%

    DeweyTruman

  • 13

  • 14

    WhatWentWrong? GallupusedQuotaSampling:

    Eachinterviewerwasassignedaquotaofsubjectstointerview.

    Theyweretoldhowmanysubjectshadtobefromcertaincategories(residence,age,sex,race,economicstatus)

    Theinterviewerscouldselectanybodytheylikedaslongastheirsubjectssatisfiedthespecifiedcriteria.

    Example: 6fromthesuburbs,7fromthecity 7men,6women ofthe7men,3hadtobeunder40,4over40 ofthe7men,6hadtobewhite,1black

  • 15

    QuotaSampling Inquotasampling,thesubjectsarehandpickedtoresemble

    thepopulationwithrespecttosomekeycharacteristics.

    QuotasamplingSEEMSreasonablebecauseitensuresthatthesamplewillresemblethepopulationwithrespecttosomeoftheimportantcharacteristicsrelatedtovotingbehavior.

    BUT:quotasamplingdoesnotworkverywellduetounintentionalbiasonthepartsoftheinterviewers.

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    QuotasamplingtendstoexcludeDemocrats!

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    ProbabilityMethods Probabilitymethodsuseobjectivechanceproceduresto

    selectsamples.Theyguardagainstbiasbecausetheyleavenodiscretiontotheinterviewer.

    Oneprobabilitymethodissimplerandomsampling.Thismeansdrawingsubjectsatrandomwithoutreplacement.

    Anotherprobabilitymethodisclustersampling.Thismeansthatclusters(eg households)areselectedatrandomandalltheindividualsintheselectedclustersaresampled.

    Astratifiedsample dividesupthepopulationintogroupsbasedonanimportantvariable(eg age)andsamplesseparatelyfromeachstratum.

    Mostlargesamplesusemultistageclustersampling.

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  • 19

    TheSuccessofProbabilityMethods

  • 20

    ProbabilityMethods

    Probabilitymethodsattempttominimizeselectionbias,buttherearestillproblemsdueto:

    nonresponsebias badlyaskedquestions interviewercontrol talkischeap

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