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ChapterFourteen14-1
Census:Populationcanvas-notreallya“sample”AskingtheentirepopulationBudgetAvailable:Avalidfactor–howmuchcanweafford?RuleofThumb:Istheresomeconventionwecanapply?Whatmightmakeanadequatesamplesize?SampleSizeforProbabilitySampling14-2KeyTerms&Definitions
NumberofSubgroupsAnalyzed:Inanysamplesizedeterminationproblem,considerationmustbegiventothenumberandanticipatedsizeofvarioussubgroupsofthetotalsamplethatmustbeanalyzed.TraditionalStatisticalMethods:Variance,standarddeviation,andconfidenceintervalplayakeyrole.SampleSizeforProbabilitySampling14-3KeyTerms&Definitions
Judgment:Bestguessof“experts”DrawonyourexperiencetodeterminesamplesizeConventional:Whathaveothersdone?SeewhatthesamplesizehasbeenforsimilarstudiesSampleSizeforNonprobabilitySampling14-4KeyTerms&Definitions
CentralLimitTheorem:Theideathatadistributionofalargenumberofsamplemeansorsampleproportionswillapproximateanormaldistribution-regardlessofthedistributionofthepopulationfromwhichtheyweredrawn.NormalDistribution:Thecontinuousdistributionthatisbellshapedandsymmetricalaboutthemean.Themean,median,andmodeareequal.Finally,about68%oftheobservationsarewithinonestandarddeviationplus/minusofthemean,96%arewithintwostandarddeviations,and99+%arewithinthreestandarddeviationsofthemeanrespectively.TheNormalDistribution14-5KeyTerms&Definitions
ProportionatePropertiesoftheNormalDistribution:Afeaturethatthenumberofobservationsfallingbetweenthemeanandagivennumberofstandarddeviationsfromthemeanisthesameforallnormaldistributions.StandardNormalDistribution:Normaldistributionwithameanofzeroandastandarddeviationofone.TheNormalDistribution14-6KeyTerms&Definitions
StandardDeviation:Themeasureofdispersioncalculatedbysubtractingthemeanoftheseriesfromeachvalueinaseries,squaringeachresult,summingtheresults,dividingthesumbythenumberofobservationsminus1andfinallytakingthesquarerootofthisvalue.TheNormalDistribution14-7KeyTerms&Definitions
ImportantCharacteristicsofaNormalDistribution14-8KeyTerms&DefinitionsBell-shapedandhasonlyonemode.SymmetricaboutitsmeanUniquelydefinedbyitsmeanandstandarddeviationThetotalareaunderanormalcurveisequaltooneTheareaofaregionunderthenormaldistributioncurvebetweenanytwovaluesofavariableequalstheprobabilityofobservingavalueinthatrangewhenanobservationisrandomlyselectedfromthedistribution.Theareabetweenthemeanandagivennumberofstandarddeviationsfromthemeanisthesameforallnormaldistributions.
PopulationDistribution:Thefrequencydistributionofalltheelementsofapopulation.SamplingDistribution:Thefrequencydistributionofalltheelementsofanindividualsample.PopulationandSamplingDistribution14-9KeyTerms&Definitions
SamplingDistributionoftheMean:Thetheoreticalfrequencydistributionofthemeansofallpossiblesamplesofagivensizedrawnfromaparticularpopulation;itisnormallydistributed.SamplingDistributionoftheMean14-10KeyTerms&Definitions
StandardErroroftheMean:Standarddeviationofadistributionofsamplemeans.StandardErroroftheMean14-11KeyTerms&Definitions
RelationshipsoftheThreeBasicTypesofDistribution14-12KeyTerms&Definitions
PointEstimate:Theparticularestimateofapopulationvalue.IntervalEstimate:Theintervalorrangeofvalueswithinwhichthetruepopulationvalueisestimatedtofall.PointandIntervalEstimations14-13KeyTerms&Definitions
ConfidenceLevel:Theprobabilitythataparticularintervalwillincludethetruepopulationvalue;alsocalledtheconfidencecoefficient.ConfidenceInterval:Theintervalthat,atthespecifiedconfidencelevel,includesthetruepopulationvalue.ConfidenceLevelandInterval14-14KeyTerms&Definitions
SamplingDistributionoftheProportion:Therelativefrequencydistributionofthesampleproportionsofmanyrandomsamplesofagivensizedrawnfromaparticularpopulation;itisnormallydistributed.SamplingDistributionoftheProportion14-15KeyTerms&Definitions
ProblemsInvolvingMean:DeterminingtheSamplingSize14-16KeyTerms&Definitions
DeterminingtheSamplingSizeAllowableSamplingError:Amountofsamplingerrortheresearcheriswillingtoaccept,E.2.TheAcceptableLevelofConfidence:Howconfidentdoestheresearcherwanttobethatanintervalincludesthepopulationmean,Z.3.PopulationStandardDeviation:Standarddeviationofavariablefortheentirepopulation,σ.14-17KeyTerms&Definitions
ProblemsInvolvingProportions:DeterminingtheSamplingSize14-18KeyTerms&Definitions
PopulationSizeandSamplingSizeIndependenceAssumption:Assumptionthatsampleelementsaredrawnindependently.14-19KeyTerms&Definitions
FinitePopulationCorrectionFactor(FPC)StatisticalPower:TheprobabilityofnotmakingatypeIIerror.14-20KeyTerms&Definitions
Youneedtocontactmorethann,sinceit’sunlikelythateveryoneyoucontactwillagreetoanswerthequestionnaire.Ifyoudeterminethatyouneed800respondentsandatypicalresponserateforyourtypeofsurveyis30%,thenyouwouldactuallyhavetocontact2,667peopletoget800completedsurveys.HowManyContacts?14-21KeyTerms&DefinitionsNumberofContacts=n/.30Or800/.3NumberofContacts=2,667Youmustcontactapproximately2,667people(with30%responserate),soyoucanexpect800peopletorespond(thefinalsamplesize).
TimetoGeneratetheSampleScopeoftheResearchBudgetAvailableExperiencewithSamplingLevelofAccuracyDesiredYourKnowledgeofthePopulationSamplingIssuesToConsider14-22
14-23KeyTerms&DefinitionsCentralLimitTheoremNormalDistributionProportionalPropertyoftheNormalDistributionStandardNormalDistributionSampleSizeforNonprobabilitySamplingStandardDeviationPopulationDistributionSampleDistributionSamplingDistributionoftheMeanLinksandbuttonareactivewhenin“SlideShowMode”KeyTerms&DefinitionsStandardErroroftheMeanPointEstimateIntervalEstimateConfidenceLevelConfidenceIntervalSamplingDistributionoftheProportionAllowableSamplingErrorPopulationStandardDeviationFinitePopulationCorrectionFactor(FPC)StatisticalPower