Transcription of 1 Basic ANOVA concepts - Calvin University
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1 Basic ANOVA concepts - Calvin University
Math143 ANOVA1 AnalysisofVariance( ANOVA )Recall,whenwewa ntedtocompare twopopulationmeans, 'sexpandthistocomparek 3 ,wecangraphicallygetanideaofwhatis goingonbylookingatside-by-sideboxplots.( , , , ) , weare consideringa quantitativeresponsevariableasit relatestooneormore explanatoryvariables, tthissetting:(i)Whichacademicdepartmenti nthesciencesgivesoutthelowestaveragegrad es?(Explanatoryvari-able:department; Responsevariable:studentGPA's forindividualcourses)(ii)Whichkindofprom otionalcampaignleadstogreateststore incomeatChristmastime?(Explanatoryvariab le:promotiontype; Responsevariable:dailystore income)(iii)Howdothetypeofcareerandmarit alstatusofa personrelatetothetotalcostinannualclaims she/heislikelytomakeonherhealthinsurance .(Explanatoryvariables:careerandmaritals tatus;Responsevariable:healthinsurancepa youts)Eachvalueoftheexplanatoryvariable( orvalue-pair, if there is more thanoneexplanatoryvariable)repre-sentsa ' , ,there are twofactors(explanatoryvariables):aspirin (valuesare takingit or nottakingit )andbetacarotene(valuesagainare takingit or nottakingit ),andthisdividesthesubjectsintofourgroup scorrespondingtothefourcellsofFigure ( ).
treatments is large relative to the variation within treatments, and we reject the null hypothesis of equal means. If F is small, the variability between treatments is small relative to the variation within treatments, and we do not reject the null hypothesis of equal means. (In this case, the sample data is consistent with
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