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2007Thomson South Western Allrightsreserved Chapter14BasicDataAnalysis 2007Thomson South Western Allrightsreserved 14 2 LEARNINGOUTCOMES Knowthatanalysisconsistsofsummarizing rearranging ordering ormanipulatingdataCreateandinterpretsimpletabulationandcross tabulationtablesUnderstandhowcross tabulationscanrevealrelationshipsPerformbasicdatatransformationsDefinehypothesisandsignificancelevelDiscussthestepsinthehypothesis testingprocedureDescribethefactorsthatinfluencethechoiceofstatisticalmethodstouseforanalysis Afterstudyingthischapter youshouldbeableto 2007Thomson South Western Allrightsreserved 14 3 TheNatureofDescriptiveAnalysis DescriptiveAnalysisTheelementarytransformationofrawdatainawaythatdescribesthebasiccharacteristicssuchascentraltendency distribution andvariability HistogramAgraphicalwayofshowingafrequencydistributioninwhichtheheightofabarcorrespondstotheobservedfrequencyofthecategory 2007Thomson South Western Allrightsreserved 14 4 EXHIBIT14 1LevelsofScaleMeasurementandSuggestedDescriptiveStatistics 2007Thomson South Western Allrightsreserved 14 5 Tabulation TabulationTheorderlyarrangementofdatainatableorothersummaryformatshowingthenumberofresponsestoeachresponsecategory tallying FrequencyTableAtableshowingthedifferentwaysrespondentsansweredaquestion 2007Thomson South Western Allrightsreserved 14 6 Cross Tabulation Cross TabulationAddressesresearchquestionsinvolvingrelationshipsamongmultipleless thanintervalvariablesResultsinacombinedfrequencytabledisplayingonevariableinrowsandanothervariableincolumns ContingencyTableAdatamatrixthatdisplaysthefrequencyofsomecombinationofresponsestomultiplevariables MarginalsRowandcolumntotalsinacontingencytable whichareshowninitsmargins 2007Thomson South Western Allrightsreserved 14 7 EXHIBIT14 2Cross TabulationTablesfromaSurveyonEthicsinAmerica FromRogerRicklefs EthicsinAmerica TheWallStreetJournal October31 1983 p 33 42 November1 1983 p 33 November2 1983 p 33 andNovember3 1983 pp 33 37 2007Thomson South Western Allrightsreserved 14 8 EXHIBIT14 3PossibleCross TabulationsofOneQuestion 2007Thomson South Western Allrightsreserved 14 9 Cross Tabulation cont d PercentageCross TabulationsStatisticalbase thenumberofrespondentsorobservations inaroworcolumn usedasabasisforcomputingpercentages ElaborationandRefinementElaborationanalysis ananalysisofthebasiccross tabulationforeachlevelofavariablenotpreviouslyconsidered suchassubgroupsofthesample Moderatorvariable athirdvariablethatchangesthenatureofarelationshipbetweentheoriginalindependentanddependentvariables 2007Thomson South Western Allrightsreserved 14 10 EXHIBIT14 4Cross TabulationofMaritalStatus Sex andResponsestotheQuestion DoYouShopatTarget 2007Thomson South Western Allrightsreserved 14 11 Cross Tabulation cont d HowManyCross Tabulations Everypossibleresponsebecomesapossibleexplanatoryvariable Whenhypothesesinvolverelationshipsamongtwocategoricalvariables cross tabulationsaretherighttoolforthejob 2007Thomson South Western Allrightsreserved 14 12 DataTransformation DataTransformation alsoDataConversion Theprocessofchangingthedatafromtheiroriginalformtoaformatsuitableforperformingadataanalysisaddressingresearchobjectives 2007Thomson South Western Allrightsreserved 14 13 CalculatingRankOrder RankOrderRankingdatacanbesummarizedbyperformingadatatransformation Thetransformationinvolvesmultiplyingthefrequencybytherankingscoreforeachchoicetoresultinginanewscale 2007Thomson South Western Allrightsreserved 14 14 EXHIBIT14 5ExecutiveRankingsofPotentialConferenceDestinations 2007Thomson South Western Allrightsreserved 14 15 EXHIBIT14 6FrequenciesofConferenceDestinationRankings 2007Thomson South Western Allrightsreserved 14 16 TabularandGraphicMethodsofDisplayingData TablesAreusefulforpresentingnumericalinformationFacilitatesummarizationandcommunicationofdataCanincludestubheadsandbannerheadsthatallowthereadertoviewseveralcross tabulationsatonceChartsandGraphsTranslateinformationintovisualformssothatrelationshipsmaybeeasilygraspedCanincreasetheeffectivenessofawell designedpresentationCancreatestrongvisualimpressions 2007Thomson South Western Allrightsreserved 14 17 EXHIBIT14 7TableofRegionalAirlineUsageforVacation PleasurebyIncomeandEducationClass 2007Thomson South Western Allrightsreserved 14 18 EXHIBIT14 8AStubheadFormatTableAllowingSeveralCross TabulationstoBeIncludedinaSingleTable ConfidenceinChurch OrganizedReligionQuestion IamgoingtoreadyoualistofinstitutionsinAmericansociety Wouldyoutellmehowmuchconfidenceyou yourself haveineachone agreatdeal quitealot some orverylittle TheChurchorOrganizedReligion Lessthan1percent From ConfidenceinChurch OrganizedReligion TheGallupReport238 July1985 p 4 2007Thomson South Western Allrightsreserved 14 19 EXHIBIT14 9TheBasicFormsofGraphicPresentation 2007Thomson South Western Allrightsreserved 14 20 EXHIBIT14 10LineGraphsHighlightingComparisonsoverTime Americansspendninemorehoursattheofficetodaythantheydid27yearsago Reprintedfrom TimeOff AmericanDemographics March2001 p 24 2007Thomson South Western Allrightsreserved 14 21 ComputerProgramsforAnalysis StatisticalPackagesSpreadsheetsExcelStatisticalsoftware SASSPSS StatisticalPackageforSocialSciences MINITAB 2007Thomson South Western Allrightsreserved 14 22 EXHIBIT14 11TheBasicDataAnalysisWindow 2007Thomson South Western Allrightsreserved 14 23 EXHIBIT14 12SASComputerOutputofDescriptiveStatistics 2007Thomson South Western Allrightsreserved 14 24 EXHIBIT14 13SPSSHistogramOutput 2007Thomson South Western Allrightsreserved 14 25 EXHIBIT14 14ExamplesofSPSSOutputforCross Tabulation FromRealStatsRealEasy SPSSforWindows Copyright 1992 SPSS Inc 2007Thomson South Western Allrightsreserved 14 26 UnivariateStatistics StatingaHypothesis HypothesisUnprovenproposition asuppositionthattentativelyexplainscertainfactsorphenomenaAnassumptionaboutnatureoftheworld NullHypothesis Ho StatementaboutthestatusquoNodifferenceinsampleandpopulationAlternativeHypothesis H1 Statementthatindicatestheoppositeofthenullhypothesis 2007Thomson South Western Allrightsreserved 14 27 TheHypothesis TestingProcedure ProcessThespecificallystatedhypothesisisderivedfromtheresearchobjectives Asampleisobtainedandtherelevantvariableismeasured Themeasuredsamplevalueiscomparedtothevalueeitherstatedexplicitlyorimpliedinthehypothesis Ifthevalueisconsistentwiththehypothesis thehypothesisissupported Ifthevalueisnotconsistentwiththehypothesis thehypothesisisnotsupported 2007Thomson South Western Allrightsreserved 14 28 SignificanceLevelsandp Values SignificanceLevel Acriticalprobabilityassociatedwithastatisticalhypothesistestthatindicateshowlikelyaninferencesupportingadifferencebetweenanobservedvalueandsomestatisticalexpectationistrue TheacceptablelevelofTypeIerror p ValueProbabilityvalue ortheobservedorcomputedsignificancelevel p valuesarecomparedtosignificancelevelstotesthypotheses Higherp valuesequalmoresupportforanhypothesis CriticalvaluesThevaluesthatlieexactlyontheboundaryoftheregionofrejection 2007Thomson South Western Allrightsreserved 14 29 EXHIBIT14 15ASamplingDistributionoftheMeanAssuming 3 0 2007Thomson South Western Allrightsreserved 14 30 AnExampleofHypothesisTesting Thenullhypothesis themeanisequalto3 0 Thealternativehypothesis themeandoesnotequalto3 0 2007Thomson South Western Allrightsreserved 14 31 AnExampleofHypothesisTesting cont d 2007Thomson South Western Allrightsreserved 14 32 EXHIBIT14 16AHypothesisTestUsingtheSamplingDistributionofXundertheHypothesis 3 0 2007Thomson South Western Allrightsreserved 14 33 TheChi SquareTestforGoodnessofFit Chi square 2 t testTestsforstatisticalsignificanceIsparticularlyappropriatefortestinghypothesesaboutfrequenciesarrangedinafrequencyorcontingencytable Goodness of Fit GOF Ageneraltermrepresentinghowwellsomecomputedtableormatrixofvaluesmatchessomepopulationorpredeterminedtableormatrixofthesamesize 2007Thomson South Western Allrightsreserved 14 34 TheChi SquareTestforGoodnessofFit TheProcess Formulatethenullhypothesisanddeterminetheexpectedfrequencyofeachanswer Determinetheappropriatesignificancelevel Calculatethe 2value usingtheobservedfrequenciesfromthesampleandtheexpectedfrequencies Makethestatisticaldecisionbycomparingthecalculated 2valuewiththecritical 2value 2007Thomson South Western Allrightsreserved 14 35 Chi SquareFormula chi squarestatisticOi observedfrequencyintheithcellEi expectedfrequencyontheithcell Ri totalobservedfrequencyintheithrowCj totalobservedfrequencyinthejthcolumnn samplesize 2007Thomson South Western Allrightsreserved 14 36 DegreesofFreedom d f R 1 C 1 2 1 2 1 1 d f R 1 C 1 2007Thomson South Western Allrightsreserved 14 37 EXHIBIT14 17One WayFrequencyTableforBrandAwareness EXHIBIT14 18TableCalculatingtheChi SquareStatistic 2007Thomson South Western Allrightsrese
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