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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 ( ).

1.3 Basic Idea of ANOVA Analysis of variance is a perfectly descriptive name of what is actually done to analyze sample data ac-quired to answer problems such as those described in Section 1.1. Take a look at Figures 12.2(a) and 12.2(b) (p. 746) in your text. Side-by-side boxplots like these in both gur es reveal differences between samples

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