aoctool - Interactive analysis of covariance - MathWorks

aoctool(x,y,group) fits a separate line to the column vectors, x and y , for each group defined by the values in the array group . group may be a ... Skiptocontent HelpCenterHelpCenter SearchHelpCenter HelpCenter MathWorks SearchMathWorks.com MathWorks Support CloseMobileSearch OpenMobileSearch Off-CanvasNavigationMenuToggle DocumentationHomeAI,DataScience,andStatistics StatisticsandMachineLearningToolbox ANOVAAnalysisofVarianceandCovariance aoctool Onthispage SyntaxDescriptionExamplesVersionHistorySeeAlso DocumentationExamplesFunctionsBlocksAppsVideosAnswers TrialSoftware TrialSoftware ProductUpdates ProductUpdates Resources DocumentationExamplesFunctionsBlocksAppsVideosAnswers MainContent aoctoolInteractiveanalysisofcovariance Syntaxaoctool(x,y,group) aoctool(x,y,group,alpha) aoctool(x,y,group,alpha,xname,yname,gname) aoctool(x,y,group,alpha,xname,yname,gname,displayopt) aoctool(x,y,group,alpha,xname,yname,gname,displayopt,model) h=aoctool(...) [h,atab,ctab]=aoctool(...) [h,atab,ctab,stats]=aoctool(...) Descriptionaoctool(x,y,group)fitsaseparatelinetothecolumn vectors,xandy,foreachgroupdefinedbythevalues inthearraygroup.groupmaybeacategoricalvariable, numericvector,characterarray,stringarray,orcellarrayofcharactervectors.Thesetypes ofmodelsareknownasone-wayanalysisofcovariance(ANOCOVA)models.Theoutputconsistsof threefigures:AninteractivegraphofthedataandpredictioncurvesAnANOVAtableAtableofparameterestimatesYoucanusethefigurestochangemodelsandtotestdifferent partsofthemodel.Moreinformationaboutinteractiveuseoftheaoctoolfunction appearsinAnalysisofCovarianceTool.aoctool(x,y,group,alpha) determinestheconfidencelevelsofthepredictionintervals.The confidencelevelis100(1-alpha)%.Thedefault valueofalphais0.05.aoctool(x,y,group,alpha,xname,yname,gname)specifies thenametouseforthex,y,andg variablesinthegraphandtables.Ifyouentersimplevariablenamesforthe x,y,andgarguments,the aoctoolfunctionusesthosenames.Ifyouenteranexpressionforone ofthesearguments,youcanspecifyanametouseinplaceofthatexpressionbysupplying thesearguments.Forexample,ifyouenterm(:,2)asthe xargument,youmightchoosetoenter'Col 2'as thexnameargument.aoctool(x,y,group,alpha,xname,yname,gname,displayopt)enables thegraphandtabledisplayswhendisplayoptis'on'(default) andsuppressesthosedisplayswhendisplayoptis'off'.aoctool(x,y,group,alpha,xname,yname,gname,displayopt,model)specifies theinitialmodeltofit.Thevalueofmodelcan beanyofthefollowing:'samemean'—Fitasingle mean,ignoringgrouping'separatemeans'—Fita separatemeantoeachgroup'sameline'—Fitasingle line,ignoringgrouping'parallellines'—Fita separatelinetoeachgroup,butconstrainthelinestobeparallel'separatelines'—Fita separatelinetoeachgroup,withnoconstraintsh=aoctool(...)returns avectorofhandlestothelineobjectsintheplot.[h,atab,ctab]=aoctool(...)returns cellarrayscontainingtheentriesinANOVAtable(atab) andthetableofcoefficientestimates(ctab). (Youcancopyatextversionofeithertabletotheclipboardbyusing theCopyTextitemontheEditmenu.)[h,atab,ctab,stats]=aoctool(...)returns astatsstructurethatyoucanusetoperforma follow-upmultiplecomparisontest.TheANOVAtableoutputincludes testsofthehypothesesthattheslopesorinterceptsareallthe same,againstageneralalternativethattheyarenotallthesame. Sometimesitispreferabletoperformatesttodeterminewhichpairs ofvaluesaresignificantlydifferent,andwhicharenot.Youcan usethemultcomparefunction toperformsuchtestsbysupplyingthestatsstructure asinput.Youcantesteithertheslopes,theintercepts,orpopulation marginalmeans(theheightsofthecurvesatthemeanxvalue).ExamplesThisexampleillustrateshowtofitdifferentmodelsnon-interactively. Afterloadingthesmallercardatasetandfittingaseparate-slopes model,youcanexaminethecoefficientestimates.loadcarsmall [h,a,c,s]=aoctool(Weight,MPG,Model_Year,0.05,... '','','','off','separatelines'); c(:,1:2) ans= 'Term''Estimate' 'Intercept'[45.97983716833132] '70'[-8.58050531454973] '76'[-3.89017396094922] '82'[12.47067927549897] 'Slope'[-0.00780212907455] '70'[0.00195840368824] '76'[0.00113831038418] '82'[-0.00309671407243]Roughlyspeaking,thelinesrelatingMPGtoWeighthave aninterceptcloseto45.98andaslopecloseto-0.0078.Eachgroup's coefficientsareoffsetfromthesevaluessomewhat.Forinstance, theinterceptforthecarsmadein1970is45.98-8.58=37.40.Next,tryafitusingparallellines.(TheANOVAtableshows thattheparallel-linesfitissignificantlyworsethantheseparate-lines fit.)[h,a,c,s]=aoctool(Weight,MPG,Model_Year,0.05,... '','','','off','parallellines'); c(:,1:2) ans= 'Term''Estimate' 'Intercept'[43.38984085130596] '70'[-3.27948192983761] '76'[-1.35036234809006] '82'[4.62984427792768] 'Slope'[-0.00664751826198]Again,therearedifferentinterceptsforeachgroup,butthis timetheslopesareconstrainedtobethesame.VersionHistoryIntroducedbeforeR2006aSeeAlsoanova1|multcompare|polytool × MATLABCommand YouclickedalinkthatcorrespondstothisMATLABcommand: RunthecommandbyenteringitintheMATLABCommandWindow. WebbrowsersdonotsupportMATLABcommands. Close × SelectaWebSite Chooseawebsitetogettranslatedcontentwhereavailableandseelocaleventsandoffers.Basedonyourlocation,werecommendthatyouselect:. Switzerland(English) Switzerland(Deutsch) Switzerland(Français) 中国(简体中文) 中国(English) Youcanalsoselectawebsitefromthefollowinglist: HowtoGetBestSitePerformance SelecttheChinasite(inChineseorEnglish)forbestsiteperformance.OtherMathWorkscountrysitesarenotoptimizedforvisitsfromyourlocation. 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