Question

REPRODUCE THE ANOVA TABLE SHOWN BELOW USING R

INCLUDE ALL R COMMANDS

a O20. Containers revisited Building on the cup experiment of the Chapter 4 Step-By-Step, a student selects one type of container and designs an experiment to see whether the type of Liquid stored and the outside Environment affect the ability of a cup to maintain temperature. He randomly chooses an experimental condition and runs each twice: LiquidEnvironment Water Water Water Water Coffee Coffee Coffee Coffee Room Room Outside Outside Room Room Outside Outside Change in Temperature 13 14 31 31 27 29 After fitting a two-way ANOVA model, he obtains the fol- lowing interaction plot, ANOVA table, and effects table: 35 30 25 20 15 10 Water Outside Room Environment Sum of Mean Source DF Squares Square F-ratio P-value Liquid Environ 1 595,125 595.125 952.2 <0.0001 Interaction 1 0.125 0.125 0.2 0.6779 Error Total 1 15.125 15.125 24.2 0.0079 4 2.500 0.625 7 612.875

Answer 1

> s1=rep(x,each=4)
> s2=c(1,1,2,2,1,1,2,2)
> obs=c(13,14,31,31,11,11,27,29)
> d=data.frame(s1,s2,obs)
> liquid=factor(s1)
> env=factor(s2)
> av2=aov(obs~liquid*env)
> summary(av2)

            Df Sum Sq Mean Sq F value   Pr(>F)   
liquid       1   15.1    15.1    24.2 0.00793 **
env          1 595.1   595.1   952.2 6.57e-06 ***
liquid:env   1    0.1     0.1     0.2 0.67787   
Residuals    4    2.5     0.6                    
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1