教育統(tǒng)計(jì)學(xué)課件

Session6ComparingTwoGroups1/36BetweengroupsSamplingdistributionofmeansNormaldistribution–individualscoresSamplingdistributionofmeans–classmeansCharacteristics:For30ormoresamples,itisnormallydistributedItsmeanisequaltothemeanofthepopulationItsstandarddeviation,calledstandarderrorofmeans,isequaltothestandarddeviationofthepopulationbythesquarerootofthesamplesize.Degreeoffreedom2/36Betweentwogroups–t-testSamplingdistributionofdifferencesbetweentwomeanstofindanindividualscoreinanormaldistribution,weusez-scoretoplaceasamplemeaninadistributionofmeans,weuseat-testtocomparethedifferencebetweentwomeans3/36Betweentwogroups–t-test4/36Researchhypothesis?Thereisnoeffectofgrouponlisteningcomprehension(i.e.,thereisnodifferenceinthemeansoftheexperimentalandcontrolgroups)Significancelevel?.051-or2-tailed?2-tailedDesignDependentvariable(s)?ListeningcomprehensionMeasurement?Scores(interval)Independentvariable(s)?GroupMeasurement?Nominal(experimentalvs.control)Independentorrepeated-measures?IndependentStatisticalprocedure?t-testBetweentwogroups–t-test5/36Betweentwogroups–t-testdf=n1+n2–2=36Criticalvaluefordf=36at.05is2.042t=.845,df=36,p=n.s.(*)6/36Thereareonlytwogroupsofoneindependentvariabletocompare.Youcan’tcross-comparegroups.Eachobservationisassignedtooneandonlyonegroup.Thedataaretrulycontinuous(intervalorstronglycontinuousordinalscores).Themeanandstandarddeviationarethemostappropriatemeasurestodescribethedata.Thedistributionintherespectivepopulationsfromwhichthesamplesweredrawnisnormal,andvariancesareequivalent.Assumptionsunderlyingt-test7/36Strengthofassociationeta2()ByrejectingtheH0,wecanshowthatthereisaneffectofthegroupsoftheindependentvariableonthedependentvariable.Thetwogroupsdifferintheirperformanceonthedependentvariable.Whenthesamplestatisticissignificant,oneroughwayofdetermininghowmuchoftheoverallvariabilityinthedatacanbeaccountedforbytheindependentvariableistodetermineitsstrengthofassociation.Theof.55isaverystrongassociation.Ittellsusthat55%ofthevariabilityinthissamplecanbeaccountedforbyindependentvariable.(45%ofthevariabilitycannotbeaccountedforbytheindependentvariable.Thisvarianceisyettobeexplained.)8/36MindworkKey9/36NonparametriccomparisonoftwogroupsMannWhitneyUWhenthereare‘outliers’inthesample,thedataarenotnormallydistributedandthemedianratherthanthemeanisthebestmeasureofcentraltendencyNon-intervaldata,ranks10/36NonparametriccomparisonoftwogroupsMannWhitneyUScoresforthetwogroupsarecombinedandrankedSumtheranksforeachgroupUsethefollowingformulaetocomputetheteststatisticUUisthesmallerofU1andU211/36Thefirsttablegivesthecriticalvaluesforsignificanceatthep≤0.05levelinatwo-tailed/non-directionaltest,andforthep≤0.025levelinaone-tailed/directionaltest.Thesecondtablegivesthecriticalvaluesforthep≤0.01levelinatwo-tailed/non-directionaltest,andforthep≤0.005levelinaone-tailed/directionaltest.Forsignificance,thecalculatedvalueofUmustbesmallerthanorequalto

thecriticalvalue.N1andN2

arethenumberofobservationsinthesmallerandlargergroup,respectively.12/36NonparametriccomparisonoftwogroupsIfthereareapproximately20ormoresubjectsineachgroup,thedistributionofUisrelativelynormalandthefollowingformulaeisusedwhereN=N1+N213/36McEncry,BakerandWilson(1994)describeaquestionnairewhichwascirculatedtostudentswhousedtheCyberTutorcorpus-basedgrammarteachingcomputerprogramandtostudentswhostudiedgrammarinthetraditionalclassroommanner.Thequestionshadtheformatof‘Howdifficult/interesting/usefuldidyoufindthetask?',andwereansweredonafive-pointLikertscale,

rangingfrom‘verydifficult'(1point)to‘veryeasy'(5points).Aggregatescoreswerefoundforeachsubjectinbothgroups.Thecombinedscoresarerankedandaveragescoresaregiventotiedranks.

Example14/36Computer-taughtRank Classroom-taughtRankT1=36,T2=53U1=10;

U2=34ExampleSPSS15/36StrengthofAssociation:eta2Assumewehad18Ssclassifiedasexceptionallanguagelearnersand12aspoorlanguagelearners.Weaskedteacherstonominatethebestlearnersandthelearnerswhohadthemostdifficulty.Wewanttofindoutwhethergoodvs.poorlearnersshowdifferencesinauditoryshort-termmemory.Aftertestingeachperson,weusetheirscorestorank-orderallthelearnersandperformaUtestwhichgivesusauvalueof3.8,whichshowsgoodlearnersdidsignificantlybetterthanpoorlearnersonthetestofauditoryshort-termmemory.Nowhowmuchofthevariabilityintheshort-termmemoryscoresfromalltheSscanbeassociatedwithbeinga‘good’vs.‘poor’learners?49.8%ofthevarianceintheranksofauditoryshort-termmemorymaybeattributedtolearnerclassificationtype.Oneindependentvariablehasexplainedmuchofthevariabilityinshort-termmemory,butthereisstillvariancetobeexplained.16/36ApplicationExercises–Assignment4Alinguiststudyinghumanmemorywouldliketoexaminetheprocessofforgettingwords.Onegroupofsubjectsisrequiredtomemorizealistofwordsintheeveningjustbeforegoingtobed.Theirrecallistested10hourslaterinthemorning.Subjectsinthesecondgroupmemorizethesamelistofwordsinthemorning,andthentheirmemoriesaretested10hourslaterafterbeingawakeallday.Thelinguisthypothesizesthattherewillbelessforgettingduringsleepthanduringabusyday.Theyrecallscoresfortwosamplesofcollegestudentsareasfollows:17/36Sketchafrequencydistributionpolygon/lineforthetwogroups.Justbylookingatthesetwodistributions,wouldyoupredictasignificantdifferencebetweenthetwotreatmentconditions?Statethenullhypothesisandtheresearchhypothesis.Istheresearchhypothesisrejectedoraccepted?Why?

18/3619/36RelatedsamplesArepeated-measurestudyisoneinwhichasinglesampleofindividualsismeasuredmorethanonceonthesamedependentvariable.Thesamesubjectsareusedinallofthetreatmentconditions.Inamatched-subjectsstudy,eachindividualinonesampleismatchedwithasubjectintheothersample.Thematchingisdonesothatthetwoindividualsareequivalentwithrespecttoaspecificvariablethattheresearcherwouldliketocontrol.Example20/36df=npairs–121/36RelatedsamplesStrengthofassociationeta222/36SignTestOrdinaldataAteacherwonderedwhetherinformationfromconversa-tionalanalysiscouldbeusedtoteachtheseculturalconventionsinanESLclass.Thestudyinvolvedtheconversationalopenings,closings,andturn-takingsignalsusedinphoneconversations.Theteacheraskedallstudentstocallherduringthefirstweekofclass.Eachperson'sphoneskills(theopenings,preclosings,closings,andturn-taking)werescoredona1-10pointscale.Duringtheclassaspecialphoneconversationunittheteacherhaddevelopedwaspresentedandpracticed.Attheendofthecourse,theteacheragainhadstudentscallherandagainrankedthemona10-pointscale.SPSSRelatedsamples–nonparametriccomparisons23/36Relatedsamples–nonparametriccomparisons24/36Relatedsamples–nonparametriccomparisonsTallythe+and–symbolsunder“Change”.DiscardSswhodonnotshowchange.Herewehave3–changes,5+changes,and2nochanges.AssignRtothesmallertotalofchanges.HereR=3.TurntotheSigntesttabletodiscoverwhetherwecanrejectthenullhypothesis.25/3626/36WilcoxonSigned-RanksTestIntervaldataWetabulatethenumbersoferrorsmadebyagroupof10subjectsintranslatingtwopassagesofEnglish,ofequallength,intoChinese.Wewishtotest,atthe5percentlevel,whetherthereisanysignificantdifferencebetweenthetwosetsofscores.Sincewearenotpredictingthedirectionofanysuchdifference,anon-directionaltestwillbeappropriate.Thescoresobservedareasfollows:SPSSRelatedsamples–nonparametriccomparisons27/36Relatedsamples–nonparametriccomparisonsCalculatethedifferences.Rankthem,givingameanrankinthecaseofties.Thepairwithzerodifferenceisdroppedfromtheanalysis.Sumthepositiveandnegativeranks.TakethesmallerrankastheW.Checkwhetherthenullhypothesisisrejected.28/3629/36Relatedsamples–nonparametriccomparisonsWhenthenumberexceeds25SignTestWilcoxonSigned-rankstest30/36Relatedsamples–nonparametric