广告调查（第二版）英文 指导手册 Davis-Instructors-Manual-ch16 Quantitative Data Analysis Inferential Statistics

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AdvertisingResearch:Instructor’sManual

Copyright©2012PearsonEducation,Inc.publishingasPrenticeHall

AdvertisingResearch:Instructor’sManual

Copyright©2012PearsonEducation,Inc.publishingasPrenticeHall

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16.QuantitativeDataAnalysis:InferentialStatistics

ChapterGoals

Afterreadingthischapterstudentsshouldhaveabetterunderstandingof:

• whatstatisticalsignificanceisandwhyitisimportant.

• howtoevaluatedifferentlevelsofresponsefromasinglegroupofindividuals.

• howtoevaluatethemeaningfulnessofdifferencesinlevelsofresponseamongtwoormoregroupsofindividuals.

• howtodeterminethesimultaneousandindependentinfluenceoftwoormoreexperimentalfactors.

• howtodeterminetherelationshipbetweentwoormoremeasures.NotestotheInstructor

TheChapterLectureprovidesaguidetokeytopicsandcontent.TwofilesofPowerPointslidesareprovided:davis_adresearch_ch16(part1).pptanddavis_adresearch_ch16(part2).ppt.

Levelsofsignificanceforstatisticaltestsareobtainedthroughonlinecalculators.Linkstoseveralexamplesofthesecalculatorsareprovidedwithintheslides.

ChapterLecture

Part1

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Researcherstypicallyuseinferentialstatisticstoanswertwoimportantquestions:

• HowmuchconfidencecanIhavethatthedifferencebetweentwoormoremeasuresisrealandmeaningful,andnotjust

theresultofrandomfluxuationinthedata?

• HowmuchconfidencecanIhavethattherelationshipIam

seeingbetweentwoormoremeasuresisrealandmeaning-ful?

Statisticalsignificancehelpsanswerbothquestions.

I.StatisticalSignificance

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Expressedasanumberbetween0and1.Alpha(a)representsprobabilitythatdifferenceisduetochance.Alowernumberreflectsmoreconfidencethatthedifferenceisarealone.Oncecalculated,foreaseofinterpretation,(a)isturnedintoapercentage.

• Whena=.1,forexample,thelevelofchanceis10%,soresearchercanbe90%confidentthattheresultsarereal.

When(a)is5%orlessresearcherstypicallyclaimthatfindingsarestatisticallysignificantandasaresultthatobserveddifferencesarereal.

ConsidertheexampledescribedinSlide16-5.DatashowninSlide16-6.Interpretedasfollows:

ThoseexposedtotheMustangalwayshavemorepositivescores.AresearcherlookingjustatthesescoresmightconcludethatMustang’spresenceinthegameachievedsuccessinallfouroftheareasmeasured,andasaresult,gameplacementisa

viableoptionifFordwantstochangeabroadrangeofattitudestowardMustang.Butwouldthisconclusionbecorrect?

ThetableshowninSlide16-7addsthealphavaluetoeachmeasure.

LevelsofstatisticalsignificanceshowthattheresearchercanonlyhaveconfidencethatgameplacementhelpedtochangeperceptionsofMustangasapowercar.Onlythismeasurehadan(a)levelat.05orless.Thechangesintheotherareaswerepositivebutdidnotreachthelevelofstatisticalsignificance.

Thus,basedontheresults,amorecorrectconclusionmighthave

beenthat:

PlacementinthegameworkswelltofosterpowercarperceptionsofMustangandshowssomesuccessinchangingattitudestowardMustanginotherareas.IfFordwantstofocusonimprovingpowercarperceptionsthengameplacementisanexcellentoption.IfFordwantstousegameplaytoimprove

attitudesintheremainingthreeareasthenwaysshouldbeexploredtodeterminehowcurrentMustangperceptionscanbestrengthenedwithspecificfocusonthethreeareasthatshowednearstatisticalsignificance.

II.MakingJudgmentsAboutASingleMeasureFromOneSample

A.ComparingaSampleAveragetoAPopulationAverage

Oneoftwotestscanbeusedtocompareasamplemeantoapopulationmean.Thetestselectedisdeterminedbysamplesize.Themathunderlyingbothtestsisquitesimpleandrequiresonlyminimalmanualcomputation.

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1.LargeSampleSize

Alargesamplesizeisgenerallyconsideredtobe30ormoreindividuals.ImagineMcDonald'stestseveryproposedcommercialbeforeitisproduced.

Overtime,severalhundredtestsareconducted.McDonald'scanusepopulationofpriorteststoevaluateperformanceofproposedcommercials.Onlycommercialsthataresignificantlybetterthanaverageofpriorcommercialsonthekeymeasureof“purchaseintent”areproduced.

McDonald'stestsnewcommercial.ThedataneededtocalculatewhetherornotcommercialissignificantlybetterthantheaverageofpastcommercialsisshowninSlide16-9.

Acomparisonoftestcommercialtopopulationofcommercialsiscarriedoutinthreesteps:

1.Subtractpopulationaveragefromthesampleaverage(inthiscasethetestcommercial).Resultis.8(3.9-3.1=.8).

2.Dividepopulationstandarddeviationbysquarerootofsamplesize.Resultis.16.(Thesquarerootof100is10,sothecomputationis1.6/10=.16.)

3.DividenumberobtainedinStep1bythenumberobtainedin

Step2.Resultis5.00(calculatedas.8/.16).

ThevalueobtainedisaZ-score,whichcanbeinterpretedinoneofthreeways,allofwhichreachthesameconclusion.First,astatisticaltablecanbeused.Second,youcancompareZ-scoreobtainedtotheZ-scorerequiredfor(a)at1%and5%levelsofconfidence.Third,youcanuseanonlinecalculator.AllthreeshowthataZ-scoreof5resultsinaconfidencelevelofmuchlessthan.001,

indicatingthatthereisactuallylessthan1chancein1,000thatresultsareduetochance.ThenewMcDonald’scommercialshouldbeproduced.

2.SmallSampleSize

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Whensamplesizeislessthan30,t-test,isusedtocomparetestmeantopopulationmean.T-testisverysimilartoZtestinapproach.However,whiletheZtestusesthepopulationstandarddeviationt-testutilizesthesamplestandarddeviation.SampledatashowninSlide16-12.

Thisisthesamesituationasbefore,onlythesamplesizeislessthan30.Comparisonoftestcommercialtopopulationofcommercialsiscarriedoutinthreesteps:

1.Subtractthepopulationaveragefromthesampleaverage(inthiscasethetestcommercial).Inthisexampletheresultis-.4(3.2-

3.6=-.4).

2. Dividethetestsamplestandarddeviationbythesquarerootofthesamplesize.Inthisexampletheresultis.3(Thesquarerootof25is5,sothecomputationis1.5/5=.3.)

3.DividethenumberisobtainedinStep1bythenumberobtainedinStep2.Inthisexampletheresultis-1.33(calculatedas-.4/

.3).

Interpretationoft-valueusesdegreesoffreedomwhichisthenumberinyoursampleminusone(inthisexample24).Onceknown,thestatisticaltableoronlinecalculatorcanbeused.At-scoreof-1.33and24degreesoffreedomgivessignificancevalueof.196.Thislevelofsignificancefailstoreachthetraditionalcut-offvalues(.01or.05)andindicatesthatresearchercannotbeconfidentthatdifferencebetweentestcommercialandtheaverageofallpriorcommercialsis“real”andnotduetochance.McDonald'scannotconfidentlyconcludethattestcommercialisdifferent(eitherbetterorworse)thanaverageofpriorcommercials.

B.ComparingaSampleProportiontoaPopulationProportion

ThinkaboutMcDonald'stryingtoassessimpactofproposedcommercialsonconsumers’intentiontoeatatMcDonald's.Afterseeingthetestcommercial,respondentsasked:"Thenexttimeyougotoafastfoodrestaurantwherewillyougo?"Thepercentageofrespondentsanswering"McDonald's"istallied.

McDonald'scancomparetheproportionofrespondentssaying"McDonald's"afterseeingatestcommercialtotheaveragepercentagesaying"McDonald's"

withintheirpopulationofpriortests.DatashowninSlide16-16.

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Comparisonoftestcommercialtopopulationofcommercialstakesfivesteps:

1.Turnthepopulationandsampleproportionsintodecimals.Then,subtractthepopulationproportionfromthesampleproportion

(inthiscasethetestcommercial).Inthisexample,theresultis

.18(.75-.57=.18).

2.Multiplythetwopopulationproportions.Inthisexampletheresultis.25(.57*.43=.25).

3.DividethenumberfromStep2bythesamplesize.Inthisexample,theresultis.005(.25/50).

4.TakethesquarerootofthenumberobtainedinStep3.Inthisexample,thesquarerootisof.005is.071.

5.DividethenumberfromStep1bythenumberisStep4.Inthisexampletheresultis2.53(.18/.071=2.53).

ThevalueobtainedisaZ-score,whichisinterpretedsimilarlytotheZ-scorediscussedearlier.Z-scoreof2.53translatestoan(a)of.011.ThisindicatesthatMcDonald’scanbenearly99%confidentthatthedifferencesarerealandnotduetochance.Giventhataislessthanthe.05levelofsignificance,McDonald’sconcludesthattheproportionofrespondentswhosaytheyintendtotryMcDonald'safterseeingtestcommercialishigherthanaverageproportionofindividualssaying"McDonald's"inpopulationoftestcommercials.Thiscommercialissignificantlybetterthanpriorcommercials.

III.ExaminingtheInternalCharacteristicsofaSingleSample

Themostcommonapproachtoexaminingapatternofresponsestoasinglemeasureischi-square.Inthiscase,itexaminesfrequencydistributionwithinsinglesampleanddeterminesifpatternissignificantlydifferentthanchance.

Example:Anadvertiserhasfourcommercialsandwishestodeterminewhichcommercialbestcommunicatesatargetmessage.Allfourcommercialsareshowntoasampleofconsumersand,afterallareseen,eachrespondentselectsthecommercialheorshethinkswasbestthecommunicator.

PreferencedataforthisexampleisshowninSlide16-21.

Tomaketheunderlyingdatatrendmorevisible,thetableinSlide16-22expandsthepriortable:

• Countofindividualsselectingeachcommercialisturnedintopercentagedistribution(column2).

• Theexpectednumberofindividualsselectingeachcommercialhasbeenadded(column3).Thispercentageandactualnumberassumesthatifchanceselectionwasoccurringanequalpercentageofindividualswouldselecteachcommercial.Thedatainthesecondandfifthcolumnsarewhatisusedintheactualchi-squareanalysis.

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Resultsofthechi-squarecalculationanditslevelofsignificancehavealsobeenaddedtothebottomoftable,whichwereobtainedfromtypingdataintoonlinecalculator.(Notethatactualvaluesare:152,114,91,79.Expectedvalueforallcellsis109.)

Levelofsignificanceindicatesthatresultsarenotrandomorduetochance.Theprobabilityofthispatternnotbeing“real”islessthan1in1,000.Thus,McDonald’scanconcludethatconsumers’reactionstothecommercialsareindeeddifferent.

IV.MakingJudgmentsAboutASingleMeasureFromTwoorMore

IndependentSamples

Agreatdealofadvertisingresearchentailscomparingmeasuresfromtwodifferentsamples,forexample,conductinganexperimentwheretheresearcherwantstocompareresultsofcontroltoatestgrouporwherearesearcherwantstofindoutifdifferencesbetweentwosubgroups(suchasmenversuswomen)onsamesurveyarestatisticallydifferent.InthesecasesanF-testisused.

A.ComparingTwoMeans

1.TwoConditions

Example:AnadvertiserhasdevelopedtwoadsthataretobeplacedintorotationinGoogleAdwords.Whilebothadswillbeshowninresponsetothesamesearchterms,adsdifferinbenefit:thefirstadstressescustomerservicewhilethesecondadstresseslowprices.Adwordsletsyoumonitorthepurchaseamountresultingfromtheclick-throughforeachoftheads.Dataiscollected

foramonth,andisshowninSlide16-25.

F-testistheappropriatestatisticaltesttouseincircumstancessuchasthis.TableshowninSlide16-26addsresultsofF-test.

F-value(whichtakesintoaccountsamplesize,thedifferencesbetweentheaveragesandstandarddeviation)isusedtodeterminelevelofsignificance,

whichisreportedinthelastcolumn.Dataindicatesthatthedifferencebetweenthetwoadsaresignificantinfavorofthecustomerservicead.Thechancesofthesedifferencesbeingseenduetochanceislessthan1in1,000.

2.OneSurvey,TwoSubgroups

F-testcanbeusedtodetermineiftheresponsesofdifferentsubgroupsarestatisticallysignificant.

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Imaginethatanadvertiserasksthefive-pointratingquestion:“HowlikelyorunlikelyareyoupurchaseaniPhoneinthenextmonth?”Highernumbersindicateagreaterlikelihoodtopurchase.WhentheratingsofmenversuswomensurveyedarecomparedthedataappearsasthatshownonSlide16-27.

ThetableshownonSlide16-28addsresultsofF-test:

Asinthepriorexample,theF-valuedeterminesthelevelofsignificance.Itindicatesthatthereisasignificantdifferenceinpurchaseintent.Chanceofthesedifferencesbeingseenduetochanceislessthan1in1,000.

V.ComparingThreeorMoreMeans

A.ThreeorMoreConditions

Anadvertiserwantstotestthreeads:anexistingcustomerserviceadandtwoadditionalads.Firstnewadstressesquickdeliverywhilethesecondisa

revisedlowpricead.DataiscollectedforamonthandisshowninSlide16-30.

TableinSlide16-31addsresultsoftheF-test.

Whentestingthreeormoremeans,F-testindicateswhetherallofthemeansshouldbeconsideredthesameorifoneofmoremeansaresignificantlydifferentthantheothers.Inreadingthelevelofsignificancecolumn,itcanbeseenthatthereisasignificantdifferenceinaveragepurchaseamountgeneratedbyeachad.But,itisnotknownwhichoneisthe“best”untilabsolutelevelsareexaminedandtestsofpairsofmeansareconducted.

DataforthisanalysisisshowninSlide16-32.Whenthisisdone,therevisedlowpriceadisthemostsuccessfulasitissignificantlyhigherthantheothertwoads,whichinturnarenotdifferentfromeachother.

B.OneSurvey,ThreeorMoreSubgroups

Priorprocedurecanbeusedtocomparethreeormoresubgroupsrespondingtothesamesurvey.Imagine,forexample,thatnowyouwantedtoexaminethe

purchaseintentoftheiPhoneamongdifferentagegroups.Therelevantdatafromthefive-pointsurveyquestionisshowninSlide16-33.

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TableinSlide16-34addsresultsoftheF-test.

Asinthepriorexample,F-testindicateswhetherallmeansshouldbeconsideredthesameorifoneofmoremeansaresignificantlydifferentthantheothers.Here,thereissignificantdifferenceintheaveragepurchaseintent.But,itisnotknownwhicharesignificantlydifferentfromeachother.

Thisisdeterminedbycomparingeachpairofmeans,asshowninSlide16-35.Thispatternindicatesthatpurchaseintentof18-24yearoldsissignificantlyhigherthantheothertwoagegroupsandthatthepurchaseintentofthose25-49isgreaterthanthatofthoseaged50+.

VI.FactorialDesigns:MakingJudgmentsAbouttheSimultaneous

InfluenceofTwoorMoreVariables

Therearetimeswhenaresearcherwantstofindtheinfluenceoftwoormorevariablesatthesametime.Theadvantageofsimultaneouslymanipulatingtwoormorevariablesisthataresearcherisabletoseeifthereisaninteractionbetweenthevariables.Factorialdesignallowsyoutomanipulatetwoormorevariablesatthesametime.

Factorialdesignisdescribedintermsofitsmainfactorsandthelevelswithineachfactor.

ImagineanadvertiserwantstodevelopfourViraladsforanewcampaign.Theads,whilealldesignedtocommunicatethesamemessage,varyalongtwofactors:useofhumorandgenderofthespokesperson.AsshowninSlide16-36“Humor”and“Gender”arethefactors.Eachfactorhastwolevels:twolevels

ofhumorare“Absent”and“Present”whiletwolevelsof“Gender”are“Male”

and“Female.”

Thefollowingdiscussionlooksatthemostcommonoutcomesoffactorialdesigns.

A.NeitherFactorisSignificant,NoInteractionBetweenfactors

Thefirststepinanalysiscalculatesaveragesforeachfactorindependentlyandforeachcombinationoffactors.TheoutcomeshowninSlide16-37.

Thedataindicatesthat:

• Theoverallaverageforthetwoadswithamalespokesperson

was3.7whiletheoverallaverageforthetwoadswithafemalespokespersonwas3.9.

• Theoverallaverageforthetwoadswithhumorwas3.7whiletheoverallaverageforthetwoadswithouthumorwas3.9.

• Theaveragefor“Logo”was3.6whiletheaveragefor“Text”

was4.0.

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F-valueisthencomputedforeachfactortheinteractionbetweenthetwofactors.TheF-valueisthentranslatedintoan(a)asshowninSlide16-38.

Datainterpretedasfollows:

• Genderasmaineffecthadlittleinfluenceonratingsofcommercialrelevance.

• Humorasmaineffecthadlittleinfluenceonratingsofcommercialrelevance.

• Nosignificantinteractionbetweenthetwomaineffectsasthe(a)

fortheinteractionisgreaterthan.05.

FindingsareillustratedinthegraphshowninSlide16-39.Notehowlinesforbothmaineffectsareparalleltoeachother(indicatingnointeraction)andveryclosetogether(indicatingthatneithermaineffectissignificant).

B.OneFactorisSignificant,NoInteractionBetweenFactors

Asinthepriorexample,thefirststepcalculatesaveragesforeachfactorindependentlyandforeachcombinationoffactors,asshowninSlide16-40.

F-valuesandlevelsofsignificancearethencomputedforeachfactorandfortheinteractionbetweenthetwofactorsasshowninSlide16-41.

Datainterpretedasfollows:

•Genderasamaineffecthadaprofoundinfluenceonratingsofcommercialrelevance.

•Humorasamaineffecthadlittleinfluenceonratingsofcommercialrelevance.

•Therewasnosignificantinteractionbetweenthetwofactorsasthe(a)fortheinteractionisgreaterthan.05.

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FindingsareillustratedinSlide16-42.Notehowthelinesforbothfactorsareparalleltoeachother(indicatingnointeraction)withthespacebetweenthemquitelarge(indicatingasignificantmaineffect).Thisindicatesthatthemalespokespersonwasalwaysrespondedtoinamorepositivewayversusthefemalespokesperson.Regardlessofwhetherornothumorwaspresent,themalespokespersonreceivedhigherratingsversusfemalespokesperson.

C.OneFactorisSignificant,thereisanInteractionBetweenFactors

Thefirststepintheanalysiscalculatestheaveragesforeachfactorindependentlyandforeachcombinationoffactors,asshowninSlide16-2.

TheF-valuesandlevelsofsignificancearethencomputedforeachfactorandfortheinteractionbetweenfactorsasshowninSlide16-3.

Datainterpretedasfollows:

• Therewasasignificantinteractionbetweenthetwofactorsas(a)fortheinteractionislessthan.05.Indicatesthatweneedtobecautiousininterpretingthedatarelevanttothemaineffects.

• Genderasamaineffecthadasignificant,independentinfluenceonratingsofcommercialrelevance.However,thesignificantinteractiontermindicatesthatitisnecessarytoexaminethescoresofindividualadspriortodrawingafinalconclusion.Whendone,canbeseenthatsignificanceofthismaineffectisalmostentirelyduetothedifferencebetween“Guitars”and“Text”ads.

• Humorasamaineffecthadnoindependentinfluenceonratingsofcommercialrelevance.

FindingsareillustratedinthegraphshowninSlide16-4.Notehowlinesnowrunatanangletoeachother,ratherthenrunningparallel.Thispatternisavisualindicationofaninteraction.Thelines’closenesswhenhumorispresentanddistancewhenhumorisabsentindicatesthathumoronlyexertsaninfluenceonrelevanceratingswhenitisabsentandonlyresultsinhigherratingswhenamalespokespersonisused.

D.TwoFactorsareSignificant,NoInteractionBetweenFactors

Thefirststepcalculatestheaveragesforeachfactorindependentlyandforeachcombinationoffactors,asshowninSlide16-5.

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F-valuesandlevelsofsignificancearecomputedforeachfactorandforinteractionbetweenthetwofactorsasshowninSlide16-6.

Datainterpretedasfollows:

• Genderexertedanindependentinfluenceonratingsofcommercialrelevance.Relevancewasratedhigherwhenthespokespersonwasfemaleversusmale.

• Humorexertedindependentinfluenceonratingsofcommercialrelevance.Therewasasignificantdifferencewhenhumorwaspresentversusabsent.Relevancewasratedhigherwhenhumorwaspresent.

• Therewasnosignificantinteractionbetweenthetwofactors.FindingsareillustratedinthegraphshowninSlide16-7.Notehowlinesfor

bothfactorsareparalleltoeachother(indicatingnointeraction)withthespace

betweenthemquitelarge.

E.NeitherFactorisSignificant,thereisanInteractionBetweenFactors

Thefirststepintheanalysiscalculatesaveragesforeachfactorindependentlyandforeachcombinationoffactors,asshowninSlide16-8.

F-valuesandlevelsofsignificancearecomputedforeachfactorandfortheinteractionbetweenthetwofactorsasshowninSlide16-9.

Dataindicates:

• Therewasasignificantinteractionbetweenthetwofactorsasthe

(a)fortheinteractionisgreaterthan.05.Indicatesthatweneed

tobecautiousininterpretingthedatarelevanttothemaineffects.

• Genderasamaineffecthadnosignificantinfluenceonratingsofcommercialrelevance.Therewasnosignificantdifferencewhenthegenderofthespokespersonwasvaried.Examinationoftheindividualad’smeansindicatesthattherewasalargedifferencebetweenadswithafemalespokespersonandtheadswithamalespokesperson.

• Humorasamaineffecthadnosignificantinfluenceonratingsofcommercialrelevance.Therewasnosignificantdifferencewhenhumorwaspresentorabsent.Examinationofindividualad’s

meansshowsalargedifferencebetweenadswithhumorandtheadswithouthumor.

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FindingsareillustratedinthegraphshowninSlide16-10.Notehowlinesrunatanangletoeachother,ratherthenrunningparallel.Graphindicatesthatfemalespokespeoplearebes