(部编教材)-彩虹完美版2

Chapter6

IntroductiontoInferentialStatistics

SamplingandSamplingDesignsChapter6

IntroductiontoInf1Whataresamples?Whataresamples?2

σ2Population母體Sample樣本Ѕ2Parameter參數Statistic統計量Sampling抽樣Generalization推論PopulationSampleParameterStat3誤差Differencesbetweenparametersandstatistics=errorsamplingerror抽樣誤差non-samplingerror非抽樣誤差(alsocalledmeasurementerror)誤差Differencesbetweenparamete4SamplingerrorthedegreetowhichagivensamplediffersfromthepopulationsamplingerrortendstobehighwithsmallsamplesizesandwilldecreaseassamplesizeincreasesSamplingerrorthedegreetowh5TargetPopulationgrouptowhichyouwishtogeneralizetheresultsofthestudyshouldbedefinedasspecificallyaspossibleTargetPopulationgrouptowhic6populationsamplingframesamplepopulationsamplingsample7SamplingTechniquesNonprobabilitySampling(nonrandomsampling)非隨機抽樣ProbabilitySampling(randomsampling)隨機抽樣SamplingTechniquesNonprobabil8NonprobabilitysamplingConveniencesampling方便抽樣gettingpeoplewhoaremostconvenientlyavailablefast&lowcostVolunteers自願樣本unitsareself-selectedNonprobabilitysamplingConveni9CharacteristicsofnonprobabilitysamplesmembersofthepopulationDONOThaveanequalchanceofbeingselectedresultscannotbegeneralizedbeyondthegroupbeingtestedCharacteristicsofnonprobabil10ProbabilitySamplingsampleshouldrepresentthepopulationusingrandomselectionmethodsProbabilitySamplingsamplesho11TypesofProbabilitySamplingSimplerandomsampling簡單隨機抽樣Systematicsampling系統式抽樣Stratifiedsampling分層隨機抽樣Clustersampling部落抽樣TypesofProbabilitySamplingS12SimpleRandomSamplingeveryunitinthepopulationhasanequalandknownprobabilityofbeingselectedaspartofthesample(抽籤)e.g.inobtainingasampleof10subjectsfromapopulationof1,000people,everyoneinthepopulationwouldhavea1/100chanceofbeingselected(orpof.01)SimpleRandomSamplingeveryun13亂數表123456789101494869377588744800919273238532415065413144804436372948603674604571131506538344616971702505702212419303101699568547585532476090020097979620426729283075504120184535115671230265534454654737179766600730890835456117158561487874340749860596362558288084381304336891373098418842696195387295200764746752814870596287945411205730771195989606910399506494190909994753228899202884387599301812683902162566763934295045601469324723279615255396369081954150240645051415194414501063958479448288866709665256761675709568792964907325亂數表12345678910149486937758874414CharacteristicsofsimplerandomsamplingUnbiased:母體內每一個體被抽到的機會均等Independence:母體內某一個個體被抽到不會影響其他個體被抽到的機會Characteristicsofsimplerand15LimitationsofsimplerandomsamplesnotpracticalforlargepopulationsSimplerandomsamplingbecomesdifficultwhenwedonthavealistofthepopulationLimitationsofsimplerandoms16SystematicSampling系統性抽樣atypeofprobabilitysamplinginwhicheverykthmemberofthepopulationisselectedk=N/nN=sizeofthepopulationn=samplesizeSystematicSampling系統性抽樣atype17Forexample:Youwanttoobtainasampleof200fromapopulationof10,000.Youwouldselectevery50th(orkth)personfromthelist.k=10000/200=50Forexample:18Advantages/disadvantagesofsystematicsamplingAssumingavailabilityofalistofpopulationmembersRandomnessofthesampledependsonrandomnessofthelistperiodicitybias:當母體個體排序出現某一週期性或規則時,systematicsampling會有週期性誤差(periodicitybias)Advantages/disadvantagesofsy19StratifiedRandomSample分層隨機抽樣Priortorandomsampling,thepopulationisdividedintosubgroups,calledstrata,e.g.,gender,ethnicgroups,professions,etc.依母體特性將個體分層(Strata)&每一個體只屬一層Subjectsarethenrandomlyselectedfromeachstrata再從每一層中隨機抽取樣本(usingsimplerandomsampling)StratifiedRandomSample分層隨機抽樣20第一層第二層第三層.....第K層Sample第一層第二層第三層.第K層Sample21ShouldselectvariablesthatarerelatedtothedependentvariableHomogeneityisveryhighwithinthestrata.HeterogeneityisveryhighbetweenthestratasShouldselectvariablesthata22Whyusestratifiedsamples? permitsexaminationofsubgroupsbyensuringsufficientnumbersofsubjectswithinsubgroups確保樣本包含母體中各種不同特性的個體，增加樣本的代表性generallymoreconvenientthanasimplerandomsampleWhyusestratifiedsamples? p23PotentialdisadvantagesSometimestheexactcompositionofthepopulationisoftenunknownwithmultiplestratifyingvariables,samplingdesignscanbecomequitecomplexPotentialdisadvantagesSometim24TypesofStratifiedSamplingProportionateStratifiedRandomSampling比例分層隨機抽樣DisproportionateStratifiedRandomSampling非比例分層隨機抽樣TypesofStratifiedSamplingPr25ProportionateSamplingstratasamplesizesareproportionaltopopulationsubgroupsizes按母體比例抽取樣本e.g.,ifagrouprepresents25%ofthepopulation,thestratumrepresentingthatgroupwillcomprise25%ofthesampleProportionateSamplingstratas26DisproportionateSamplingstratasamplesizesarenotproportionaltopopulationsubgroupsizes每層抽出之樣本數不能與母體之特徵比例相呼應maybeusedtoachieveequalsamplesizesacrossstrataDisproportionateSamplingstrat27Forexample:SupposearesearcherplanstoconductasurveyregardingvariousattitudesofAgriculturalCollegeStudentsatTunghaiU.Hewishestocompareperceptionsacross4majorgroupsbutfindssomeofthegroupsarequitesmallrelativetotheoverallstudentpopulation.Asaresult,hedecidestoover-sampleminoritystudents.Forexample,althoughHospitalitystudentsonlyrepresent10%oftheAgriculturalstudentpopulation,heusesadisproportionalstratifiedsamplesothatHospitalitystudentswillcomprise25%ofhissample.Forexample:28ClusterSampling部落抽樣usedwhensubjectsarerandomlysampledfromwithina"cluster"orunit(e.g.,classroom,school,country,etc)將母體分為若干部落(cluster)，在自所有部落中隨機抽取若干部落樣本並對這些抽取的部落作抽查ClusterSampling部落抽樣usedwhen29Cluster1Cluster4ClusterkCluster3Cluster2Cluster5Cluster1Cluster3PopulationSampleCluster1Cluster4ClusterkClu30Example台中市民眾對薛凱莉事件看法將台中市依“里”為部落分成許多里隨機抽取3個里然後對此3個里的居民作全面性的訪問CompareusingclustersamplingtechniqueandsimplesamplingtechniqueExample台中市民眾對薛凱莉事件看法31Whyuseclustersamples?They'reeasiertoobtainthanasimplerandomorsystematicsampleofthesamesizeWhyuseclustersamples?They'r32DisadvantagesofClusterSamplingLessaccuratethanothersamplingtechniques(selectionstages,accuracy)GenerallyleadstoviolationofanassumptionthatsubjectsareindependentDisadvantagesofClusterSampl33SamplingDistribution抽樣分配SamplingDistribution抽樣分配34Forthemostpartinsocialscience,wewanttoknowaboutthepopulation.Inreality,theparametersareoftenunknown.Thebestthingwecandoisto“guess”whatourpopulationshouldbelikebasedontheinfowegetfromasampleresultsofasample=theresultsofapopulation???Forthemostpartinsocialsc35SamplingDistributions抽樣分配The“bridge”b/winformationfromthesampletothepopulationatheoretical,probabilisticdistributionofallpossiblesamplesofagivensize, 在母體中重複抽取固定大小的隨機樣本，所有隨機樣本的統計值的機率分配稱為抽樣分配SamplingDistributions抽樣分配The36PopulationSamplingdistributionSampleTherelationshipb/wpopulation,samplingdistribution,andsample.PopulationSamplingdistributio37

=100etc.forallpossiblesamplesofagivenNfromthepopulation=100etc.for38SamplingDistribution定理當母體為normaldistribution,我們重複抽取固定大小的隨機樣本時,則此一抽樣分配會趨近normaldistribution並且有一平均值及標準差SamplingDistribution定理當母體為no39以五名學生的考試成績(91,92,93,94,95)為母體,母體的mean為93。試比較從5名學生(母體)中隨機抽取2位學生作為樣本(n=2)和隨機抽取3位學生作為樣本之抽樣分配以五名學生的考試成績(91,92,93,94,95)為40Whenn=2sampleSamplemeansampleSamplemean91,9291.592,949391,939292,9593.591,9492.593,9493.591,959393,959492,9392.594,9594.5Whenn=2sampleSamplemeansampl41Whenn=3sampleSamplemeansampleSamplemean91,92,939291,94,9593.3391,92,9492.3392,93,949391,92,9592.6792,93,9593.3391,93,9492.6792,94,9593.6791,93,959393,94,9594Whenn=3sampleSamplemeansampl42SamplingdistributionofsamplemeanMeanoft