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1.1ChapterFiveDataCollectionandSampling5.2Recall…Statisticsisatoolforconvertingdataintoinformation:DataStatisticsInformationButwherethendoesdatacomefrom?Howisitgathered?Howdoweensureitsaccurate?Isthedatareliable?Isitrepresentativeofthepopulationfromwhichitwasdrawn?Thischapterexploressomeoftheseissues.5.3MethodsofCollectingData…Therearemanymethodsusedtocollectorobtaindataforstatisticalanalysis.Threeofthemostpopularmethodsare: •Directobservation(E.g.Numberofcustomers enteringabankperhour) •
Experiments(E.g.newwaystoproducethingsto minimizecosts) •Surveys5.4Surveys…Asurveysolicitsinformationfrompeople;e.g.Galluppolls;pre-electionpolls;marketingsurveys.TheResponseRate(i.e.theproportionofallpeopleselectedwhocompletethesurvey)isakeysurveyparameter.Surveysmaybeadministeredinavarietyofways,e.g.Personalinterview,TelephoneinterviewSelf-administeredquestionnaire5.5QuestionnaireDesign…Overtheyears,alotofthoughthasbeenputintothescienceofthedesignofsurveyquestions.Keydesignprinciples:Keepthequestionnaireasshortaspossible.Askshort,simple,andclearlywordedquestions.Startwithdemographicquestionstohelprespondentsgetstartedcomfortably.Usedichotomous(yes|no)andmultiplechoicequestions.Useopen-endedquestionscautiously.Avoidusingleading-questions.Pretestaquestionnaireonasmallnumberofpeople.Thinkaboutthewayyouintendtousethecollecteddatawhenpreparingthequestionnaire.5.6Sampling…Recallthatstatisticalinferencepermitsustodrawconclusionsaboutapopulationbasedonasample.Sampling(i.e.selectingasub-setofawholepopulation)isoftendoneforreasonsofcost(it’slessexpensivetosample1,000televisionviewersthan100millionTVviewers)andpracticality(e.g.performingacrashtestoneveryautomobileproducedisimpractical).Inanycase,thesampledpopulationandthetargetpopulationshouldbesimilartooneanother.5.7SamplingPlans…Asamplingplanisjustamethodorprocedureforspecifyinghowasamplewillbetakenfromapopulation.Wewillfocusourattentiononthesethreemethods:Simplerandomsampling,StratifiedrandomsamplingClustersampling5.8SimpleRandomSampling…Asimplerandomsampleisasampleselectedinsuchawaythateverypossiblesampleofthesamesizeisequallylikelytobechosen.Drawingthreenamesfromahatcontainingallthenamesofthestudentsintheclassisanexampleofasimplerandomsample:anygroupofthreenamesisasequallylikelyaspickinganyothergroupofthreenames.5.9SimpleRandomSampling…Example5.1:Agovernmentincometaxauditormustchooseasampleof40of1,000returnstoaudit…Extra#’smaybeusedifduplicaterandomnumbersaregenerated5.10StratifiedRandomSampling…Astratifiedrandomsampleisobtainedbyseparatingthepopulationintomutuallyexclusivesets,orstrata,andthendrawingsimplerandomsamplesfromeachstratum.Strata1:GenderMaleFemaleStrata2:Age<2020-3031-4041-5051-60>60Strata3:OccupationprofessionalclericalbluecollarotherWecanacquireaboutthetotalpopulation,makeinferenceswithinastratumormakecomparisonsacrossstrata5.11StratifiedRandomSampling…Afterthepopulationhasbeenstratified,wecanusesimplerandomsamplingtogeneratethecompletesample:Ifweonlyhavesufficientresourcestosample400peopletotal,wewoulddraw100ofthemfromthelowincomegroup……ifwearesampling1000people,we’ddraw50ofthemfromthehighincomegroup.5.12ClusterSampling…Aclustersampleisasimplerandomsampleofgroupsorclustersofelements(vs.asimplerandomsampleofindividualobjects).Thismethodisusefulwhenitisdifficultorcostlytodevelopacompletelistofthepopulationmembersorwhenthepopulationelementsarewidelydispersedgeographically.5.13SampleSize…Numericaltechniquesfordeterminingsamplesizeswillbedescribedlater,butsufficeittosaythatthelargerthesamplesizeis,themoreaccuratewecanexpectthesampleestimatestobe.5.14SamplingandNon-SamplingErrors…Twomajortypesoferrorcanarisewhenasampleofobservationsistakenfromapopulation:samplingerrorandnonsamplingerror.Samplingerrorreferstodifferencesbetweenthesampleandthepopulationthatexistonlybecauseoftheobservationsthathappenedtobeselectedforthesample.Increasingthesamplesizewillreducethiserror.5.15NonsamplingError…Nonsamplingerrorsaremoreseriousandareduetomistakesmadeintheacquisitionofdataorduetothesampleobservationsbeingselectedimproperly.Threetypesofnonsamplingerrors:ErrorsindataacquisitionNonresponseerrorsSelectionbiasNote:increasingthesamplesizewillnotreducethistypeoferror.5.16Errorsindataacquisition……arisesfromtherecordingofincorrectresponses,dueto:—incorrectmeasurementsbeingtakenbecauseoffaultyequipment,—mistakesmadeduringtranscriptionfromprimarysources,—inaccuraterecordingofdataduetomisinterpretationofterms,or—inaccurateresponsestoquestionsconcerningsensitiveissues.5.17NonresponseError
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