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Chapter14

BasicDataAnalysisLEARNINGOUTCOMESKnowthatanalysisconsistsofsummarizing,rearranging,ordering,ormanipulatingdataCreateandinterpretsimpletabulationandcross-tabulationtablesUnderstandhowcross-tabulationscanrevealrelationshipsPerformbasicdatatransformationsDefinehypothesisandsignificancelevelDiscussthestepsinthehypothesis-testingprocedureDescribethefactorsthatinfluencethechoiceofstatisticalmethodstouseforanalysisAfterstudyingthischapter,youshouldbeableto2TheNatureofDescriptiveAnalysisDescriptiveAnalysisTheelementarytransformationofrawdatainawaythatdescribesthebasiccharacteristicssuchascentraltendency,distribution,andvariability.HistogramAgraphicalwayofshowingafrequencydistributioninwhichtheheightofabarcorrespondstotheobservedfrequencyofthecategory.3EXHIBIT14.1

LevelsofScaleMeasurementandSuggestedDescriptiveStatistics4TabulationTabulationTheorderlyarrangementofdatainatableorothersummaryformatshowingthenumberofresponsestoeachresponsecategory;tallying.FrequencyTableAtableshowingthedifferentwaysrespondentsansweredaquestion.5Cross-TabulationCross-TabulationAddressesresearchquestionsinvolvingrelationshipsamongmultipleless-thanintervalvariablesResultsinacombinedfrequencytabledisplayingonevariableinrowsandanothervariableincolumns.ContingencyTableAdatamatrixthatdisplaysthefrequencyofsomecombinationofresponsestomultiplevariables.MarginalsRowandcolumntotalsinacontingencytable,whichareshowninitsmargins.6EXHIBIT14.2

Cross-TabulationTablesfromaSurveyonEthicsinAmericaFromRogerRicklefs,“EthicsinAmerica,”TheWallStreetJournal,October31,1983,p.33,42;November1,1983,p.33;November2,1983,p.33;andNovember3,1983,pp.33,37.7EXHIBIT14.3

PossibleCross-TabulationsofOneQuestion8Cross-Tabulation(cont’d)PercentageCross-TabulationsStatisticalbase:thenumberofrespondentsorobservations(inaroworcolumn)usedasabasisforcomputingpercentages.ElaborationandRefinementElaborationanalysis:ananalysisofthebasiccross-tabulationforeachlevelofavariablenotpreviouslyconsidered,suchassubgroupsofthesample.Moderatorvariable:athirdvariablethatchangesthenatureofarelationshipbetweentheoriginalindependentanddependentvariables.9EXHIBIT14.4

Cross-TabulationofMaritalStatus,Sex,andResponsestotheQuestion“DoYouShopatTarget?”10Cross-Tabulation(cont’d)HowManyCross-Tabulations?Everypossibleresponsebecomesapossibleexplanatoryvariable.Whenhypothesesinvolverelationshipsamongtwocategoricalvariables,cross-tabulationsaretherighttoolforthejob.11DataTransformationDataTransformation(alsoDataConversion)Theprocessofchangingthedatafromtheiroriginalformtoaformatsuitableforperformingadataanalysisaddressingresearchobjectives.Bimodal12CalculatingRankOrderRankOrderRankingdatacanbesummarizedbyperformingadatatransformation.Thetransformationinvolvesmultiplyingthefrequencybytherankingscoreforeachchoicetoresultinginanewscale.13EXHIBIT14.5ExecutiveRankingsofPotentialConferenceDestinations14EXHIBIT14.6FrequenciesofConferenceDestinationRankings15TabularandGraphicMethodsofDisplayingDataTablesAreusefulforpresentingnumericalinformationFacilitatesummarizationandcommunicationofdataCanincludestubheadsandbannerheadsthatallowthereadertoviewseveralcross-tabulationsatonceChartsandGraphsTranslateinformationintovisualformssothatrelationshipsmaybeeasilygraspedCanincreasetheeffectivenessofawell-designedpresentationCancreatestrongvisualimpressions16EXHIBIT14.7TableofRegionalAirlineUsageforVacation/PleasurebyIncomeandEducationClass17EXHIBIT14.8AStubheadFormatTableAllowingSeveralCross-TabulationstoBeIncludedinaSingleTableConfidenceinChurch/OrganizedReligionQuestion:IamgoingtoreadyoualistofinstitutionsinAmericansociety.Wouldyoutellmehowmuchconfidenceyou,yourself,haveineachone—agreatdeal,quitealot,some,orverylittle?TheChurchorOrganizedReligion*Lessthan1percent.

From“ConfidenceinChurch/OrganizedReligion,””TheGallupReport238,July1985,p.4.18EXHIBIT14.9TheBasicFormsofGraphicPresentation19EXHIBIT14.10LineGraphsHighlightingComparisonsoverTimeAmericansspendninemorehoursattheofficetodaythantheydid27yearsago.Reprintedfrom“TimeOff””AmericanDemographics,March2001,p.24.20ComputerProgramsforAnalysisStatisticalPackagesSpreadsheetsExcelStatisticalsoftware:SASSPSS(StatisticalPackageforSocialSciences)MINITAB21EXHIBIT14.11TheBasicDataAnalysisWindow22EXHIBIT14.12SASComputerOutputofDescriptiveStatistics23EXHIBIT14.13SPSSHistogramOutput24EXHIBIT14.14ExamplesofSPSSOutputforCross-TabulationFromRealStatsRealEasy:SPSSforWindows.Copyright©©1992,SPSS,Inc.25UnivariateStatistics:StatingaHypothesisHypothesisUnprovenproposition:asuppositionthattentativelyexplainscertainfactsorphenomenaAnassumptionaboutnatureoftheworld.NullHypothesis(Ho)StatementaboutthestatusquoNodifferenceinsampleandpopulationAlternativeHypothesis(H1)Statementthatindicatestheoppositeofthenullhypothesis26TheHypothesis-TestingProcedureProcessThespecificallystatedhypothesisisderivedfromtheresearchobjectives.Asampleisobtainedandtherelevantvariableismeasured.Themeasuredsamplevalueiscomparedtothevalueeitherstatedexplicitlyorimpliedinthehypothesis.Ifthevalueisconsistentwiththehypothesis,thehypothesisissupported.Ifthevalueisnotconsistentwiththehypothesis,thehypothesisisnotsupported.27SignificanceLevelsandp-ValuesSignificanceLevel(α)Acriticalprobabilityassociatedwithastatisticalhypothesistestthatindicateshowlikelyaninferencesupportingadifferencebetweenanobservedvalueandsomestatisticalexpectationistrue.TheacceptablelevelofTypeIerror.p-ValueProbabilityvalue,ortheobservedorcomputedsignificancelevel;p-valuesarecomparedtosignificancelevelstotesthypotheses.Higherp-valuesequalmoresupportforanhypothesis.CriticalvaluesThevaluesthatlieexactlyontheboundaryoftheregionofrejection.28EXHIBIT14.15ASamplingDistributionoftheMeanAssumingµ=3.029AnExampleofHypothesisTestingThenullhypothesis:themeanisequalto3.0:Thealternativehypothesis:themeandoesnotequalto3.0:30AnExampleofHypothesisTesting(cont’d)31EXHIBIT14.16AHypothesisTestUsingtheSamplingDistributionofXundertheHypothesisµ=3.0—32TheChi-SquareTestforGoodnessofFitChi-square(χ2)t-testTestsforstatisticalsignificanceIsparticularlyappropriatefortestinghypothesesaboutfrequenciesarrangedinafrequencyorcontingencytable.Goodness-of-Fit(GOF)Ageneraltermrepresentinghowwellsomecomputedtableormatrixofvaluesmatchessomepopulationorpredeterminedtableormatrixofthesamesize.33TheChi-SquareTestforGoodnessofFit:TheProcessFormulatethenullhypothesisanddeterminetheexpectedfrequencyofeachanswer.Determinetheappropriatesignificancelevel.Calculatetheχ2value,usingtheobservedfrequenciesfromthesampleandtheexpectedfrequencies.Makethestatisticaldecisionbycomparingthecalculatedχ2valuewiththecriticalχ2value.34Chi-SquareFormulaχ²=chi-squarestatisticOi=observedfrequencyintheithcellEi=expectedfrequencyontheithcellRi=totalobservedfrequencyintheithrowCj=totalobservedfrequencyinthejthcolumnn=samplesize35DegreesofFreedom(d.f.)(R-1)(C-1)=(2-1)(2-1)=1d.f.=(R-1)(C-1)36EXHIBIT14.17One-WayFrequencyTableforBrandAwarenessEXHIBIT14.18TableCalculatingtheChi-SquareStatistic37ChoosingtheAppropriateStatisticalTechniqueChoosingthecorrectstatisticaltechniquerequiresconsidering:ThenumberofvariablesinvolvedThelevelofscalemeasurementThetypeofquestiontobeansweredChoiceofstatisticaltechniqueinfluences:TheresearchdesignThetypeofdatacollected38EXHIBIT14.19DescriptiveStatisticsPermissiblewithDifferentTypesofMeasurementAllstatisticsappropriateforlower-orderscales(nominalisthelowest)areappropriateforhigher-orderscales(ratioisthehighest).39EXHIBIT14.20ExamplesofSelectingtheAppropriateUnivariateStatisticalMethod40KeyTermsandConceptsDescriptiveanalysisHistogramTabulationFrequencytableCross-tabulationContingencytableMarginalsStatisticalbaseElaborationanalysisModeratorvariableDatatransformationHypothesisNullhypothesisAlternativehypothesisSignificancelevelCriticalvaluesChi-square(χ2)test419、静静夜夜四四无无邻邻,,荒荒居居旧旧业业贫贫。。。。12月月-2212月月-22Saturday,December31,202210、雨中中黄叶叶树,,灯下下白头头人。。。09:07:4809:07:4809:0712/31/20229:07:48AM11、以我独沈沈久,愧君君相见频。。。12月-2209:07:4809:07Dec-2231-Dec-2212、故人江海海别,几度度隔山川。。。09:07:4809:07:4809:07Saturday,December31,202213、乍见翻翻疑梦,,相悲各各问年。。。12月-2212月-2209:07:4809:07:48December31,202214、他乡生白发发,旧国见青青山。。31十二月月20229:07:48上午09:07:4812月-2215、比不不了得得就不不比,,得不不到的的就不不要。。。。十二月月229:07上上午午12月月-2209:07December31,202216、行行动动出出成成果果,,工工作作出出财财富富。。。。2022/12/319:07:4809:07:4831December202217、做做前前,,能能够够环环视视四四周周;;做做时时,,你你只只能能或或者者最最好好沿沿着着以以脚脚为为起起点点的的射射线线向向前前。。。。9:07:48上上午午9:07上上午午09:07:4812月月-229、没有失失败,只只有暂时时停止成成功!。。12月-2212月-22Saturday,December31,202210、很多多事情情努力力了未未必有有结果果,但但是不不努力力却什什么改改变也也没有有。。。09:07:4809:07:4809:0712/31/20229:07:48AM11、成功就是是日复一日日那一点点点小小努力力的积累。。。12月-2209:07:4809:07Dec-2231-Dec-2212、世世间间成成事事,,不不求求其其绝绝对对圆圆满满,,留留一一份份不不足足,,可可得得无无限限完完美美。。。。09:07:4809:07:4809:07Saturday,December31,202213、不知香积寺寺,数里入云云峰。。12月-2212月-2209:07:4909:07:49December31,202214、意志坚强强的人能把把世界放在在手中像泥泥块一样任任意揉捏。。31十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