# chapter 19: sample surveys - math statistics...

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Chapter19:SampleSurveys

Population

(parameter)

Sample

(statistic)

Sampling procedure

Inference

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Definitions Population thegroupofindividualsofinterestinthesurvey.

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Example Population USUstudentsregisteredforstat1040thissemester.

Sample agroupofstat1040studentsselectedfromthepopulation.

Parameter thepercentageinthepopulationwhopreferweeklyquizzesoverhomework.

Statistic thepercentageinthesamplewhopreferweeklyquizzesoverhomework.

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RepresentativeSamples

Needarepresentative sample onethatislikethepopulationinthewaysthatmatter.Agoodsamplingprocedurewillbefairandimpartial.

Estimatingpopulationparametersisonlyjustifiedwhenthesampleisrepresentative.

Themethodofchoosingthesamplemattersalot.

Thebestmethodsofchoosingasampleinvolvetheplanneduseofprobability.

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WhatCangoWrong?

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

Ifthepeoplewhotendtobeexcludedorwhodontresponddifferinimportantwaysfromtherestofthepopulation,thesamplewillnotgivegoodestimates.

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TheLiteraryDigestPoll

1936,RooseveltversusLandon.

Campaigncenteredoneconomicpolicies.

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TheLiteraryDigestPoll

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

Rooseveltwillonlyget43%ofthevote.

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

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Whatwentwrongin1936?

TheLiteraryDigestsentquestionnairesto10millionpeople.

Thenamesofthe10millioncamefromtelephonebooksandclubmembershiplists.

SELECTIONBIAS!

Theygotresponsesfrom2.4millionpeople. NONRESPONSEBIAS!

Theytendedtoexcludethepoor,andforthefirsttimeinhistory,thepoortendedtovoteDemocrat.

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Gallup:thenewkidontheblock Gallupsampled3000peopleatrandom,fromthesamelists

theDigestused,andpredictedtheirprediction!

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Biggerisbetter?

Ifasampleisrepresentative,alargesampleisbetterthanasmallsamplebecauseitgivesmorepreciseestimatesofthepopulationparameter.

BUT

Ifthesamplingprocedureisbiased,takingalargesampledoesnothelp.Thisjustrepeatsthebasicmistakeonalargerscale!

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1948:TheYearthePollsElectedDewey

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

DeweyTruman

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WhatWentWrong? GallupusedQuotaSampling:

Eachinterviewerwasassignedaquotaofsubjectstointerview.

Theinterviewerscouldselectanybodytheylikedaslongastheirsubjectssatisfiedthespecifiedcriteria.

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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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TheSuccessofProbabilityMethods

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ProbabilityMethods

Probabilitymethodsattempttominimizeselectionbias,buttherearestillproblemsdueto: