# 1. Two Way ANOVA.pdf - Two-way Analysis of Variance ANOVA ...

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Two-way Analysis ofVariance (ANOVA)Two-way analysis of varianceADM2304 - Davood AstarakyTelfer school of Management
Two Way Analysis of Variance (ANOVA)An extension of One Way Analysis ofVariance to Where There are Two (possibly)Interacting Factors
3Motivating examplesWhat is the effect of store locationandadvertising budget onmeanssales?What is the effect of weatherandtraffic density on cost of road repair?Are there real differences in change time for brake replacement based on the manufacturerandvehicle type?In each example, there is a strong chance of aninteractionbetween the two factors making their effect on theoutcome variable complex.
4Important questionsLet A and B represent the two factors (i.e. manufacturer and vehicle type) and suppose that the row factor A hasalevels (i.e. number of manufacturers) and column factor B hasblevels (i.e. number of vehicle types)There area*btreatmentcombinationsThus, if each treatment combination is representedrtimes in the sample then there areN = a*b*robservationsin the sample
5Important questionsLet A and B represent the two factors (i.e. manufacturer and vehicle type) and suppose that the row factor A hasalevels (i.e. number of manufacturers) and column factor B hasblevels (i.e. number of vehicle types)There area*btreatmentcombinationsThus, if each treatment combination is representedrtimes in the sample then there areN = a*b*robservationsin the sampleWe are primarily interested in two questions-1) Do both factors affect the mean response or only one?-2) If both do are the effects “additive” or do they “interact”?
6What to do?We could do a one-way ANOVA on each of the two factors separatelyBut why is that inadequate??
7Two-way ANOVAInstead we introduce you to a Two-Factor ANOVA test.A two-way ANOVAis a procedure in which we examine thesimultaneous effectthat twomain factorshave onthe observed data. The purpose is to simultaneously measure the impact of bothof the main factorsJust like a one-factor ANOVA, we create anF statisticwhere both the numerator and the denominator areestimates of the population standard deviation if the null hypothesis is trueIf it is not, then the numerator is an over-estimate of the SD and thus largeFvalues give us reason to believe thatthe null hypothesis is falseAgain, though the method of calculating theFstatistic is different,the rest of the analysis is the same
8Example: Brake ReplacementSuppose we are dealing with three manufactures (A, B and C) and twovehicle types (car and SUV)How manytreatment combinationsdo we have ?If 5 of each treatment combination are measured, what is the totalsample size?ManufacturerVehicle TypeReplacement TimeACAR56ACAR63ACAR69ACAR54ACAR59ASUV104ASUV90ASUV97ASUV102ASUV93BCAR66BCAR70BCAR55BCAR62BCAR72BSUV90BSUV98BSUV85BSUV89BSUV97CCAR80CCAR68CCAR75CCAR78CCAR72CSUV110CSUV95CSUV100CSUV97CSUV105

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