CHPTER2多维数据的图示分析(多元统计分析课件-西安交通大学严明义)

CHPTER2ExploringMultivariateDataGraphically1.1IntroductionAccordingtoChambersetal.《GraphicalMethodsforDataAnalysis》,1983,“thereisnostatisticaltoolthatisaspowerfulasawell-chosengraph”.Certainlygraphicalpresentationhasanumberofadvantagesovertabulardisplaysofnumericalresults,notleastincreatinginterestandattractingtheattentionoftheviewer.Andgraphicalanalysisoftenprovidesthevehiclefordiscoveringtheunexpected.Duringthelasttwodecadesawidevarietyofnewmethodsfordisplayingdatagraphicallyhasbeendeveloped;thesewillhuntforspecialeffectsindata,indicateoutliers,identifypatterns,diagnosismodelsandgenerallysearchfornovelandperhapsunexpectedphenomena.Largenumbersofgraphsmayberequiredandcomputerswillgenerallybeneededtodrawthemforthesamereasonstheyareneededfornumericalanalysis,namelythattheyarefastandtheyareaccurate.So,becausethemachineisdoingtheworkthequestionisnolonger“shallweplot?”butrather“whatshallweplot?”Therearemanyexcitingpossibilitiesincluding,ofcourse,dynamicgraphics(seeCleveland,W.S.andMcGill,M.E.,1987,《DynamicGraphicsforStatistics》).Butexplorationmightbegin,atleast,withsomesimpler,well-knownmethods.Univariatemarginalviewsofmultivariatedatamight,forexample,beobtainedusingsimplehistograms,stem-and-leafplotsorbox-and-whiskerplots.Butvariable-by-variableexaminationofmultivariatedatacannotrevealanyrelationshipsamongvariables.Consequently,abetterplacetobeginourdiscussionofgraphicalmethodsforsuchdataisthesimplescatterplot.1.2TheScatterplotThesimplexyscatterplothasbeeninusesinceatleastthe18thcenturyandhasmanyvirtues–indeed,accordingtoTufte,E.R.(《TheVisualDisplayofQuantitativeInformation》,1983)Therelationalgraphic–initsbarestformthescatterplotanditsvariants–isthegreatestofallgraphicaldesigns.Itlinksatleasttwovariables,encouragingandevenimploringtheviewertoassessthepossiblecasualrelationshipsbetweentheplottedvariables.Itconfrontscasualtheoriesthatxcausesywithempiricalevidenceastotheactualrelationshipbetweenxandy.Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcouplesHusbandHusband’sWifeWife’sHusbandAgeAgeHeightAgeHeightAtFirstMarriage4918094315902525184128156019401659301620385217795715402658161652142030321695271660234317305216103347174043158026311685231610262617352515902340171339161023351736321700313517993516801935178533168024471758431630243817293515702733172032172028321810301740223817254016003129168329160025591585551550232616842515401850167445164025491724441640274216304016302833185531156022271700251580215717655115703234170031159028281721251650233718293516702256171055160044271745231610253616983516102231185328167020Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcouples(Continued)HusbandHusband’sWifeWife’sHusbandAgeAgeHeightAgeHeightAtFirstMarriage571610521510255516805315202147180943162025641580611530213115852315702835170535158025361675351590224017353916702330168624163027321768291510212017542116601945173939161025591699521440274318255215702529174026167024471731481730214317554215902054171350160023611723641490262717832616602027174932158024321710311500315417245316402037162039165021551764451620293617913315503032179532164025571738551560245116665215702450174550155022321775321600205416695416602034170032164022451804411670276417006115602455166443176031Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcouples(Continued)HusbandHusband’sWifeWife’sHusbandAgeAgeHeightAgeHeightAtFirstMarriage271753281640235517885116002641168041155022441715411570242217552115902130176428165029531793471690314217313715802331171328159028361725351510265618285516003046173545166022341760341700235516855115303444168539149027451559351580344817054515002844172344160041591700471570396416605716203234168133141022371803381560235418665915904949188446171025631705601580274817804716902264180155161037331795451660175216694716102327170824159026331691321530214618254716902354176057160023541905461670324917394216002862173663157022Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcouples(Continued)HusbandHusband’sWifeWife’sHusbandAgeAgeHeightAgeHeightAtFirstMarriage3418453217002423186824174019361765321540275917205615302453187150169025551720551590216216295816102342162438167022501653441690353717863515502151162044165030251695251540195416744316603534186431162023431643351630294317054116102258173650154032281691231610234517534316302147168049153020571724591520243416383815703357172542158052271725211550244817744215803037177135163028251815261650205715755716402040172934165026611749631520212517052316202424177423168022471658461670244417904016202452179853157025Table2.1Heights(mm)andages(years)ofbothpartnersinasampleof169marriedcouples(Continued)HusbandHusbandWifeWifeHusbandAgeAgeHeightAgeHeightAtFirstMarriage451824401660232017962215501960172560159021361685321620252517692415601825174928167021351716401650174917734814702133176033158020501725491670236316456415202857169455162024411851411710233816913815302030188031163022521835521720305117304315702246164451156027501723471650255217183215902530172333159022201786181590195116754515502564