Two-way ANOVA

Sameer Mathur.

Two way ANOVA

attach(ToothGrowth)
table(supp,dose)

    dose
supp 0.5  1  2
  OJ  10 10 10
  VC  10 10 10

aggregate(len, by=list(supp,dose), FUN=mean)

  Group.1 Group.2     x
1      OJ     0.5 13.23
2      VC     0.5  7.98
3      OJ     1.0 22.70
4      VC     1.0 16.77
5      OJ     2.0 26.06
6      VC     2.0 26.14

aggregate(len, by=list(supp,dose), FUN=sd)

  Group.1 Group.2        x
1      OJ     0.5 4.459709
2      VC     0.5 2.746634
3      OJ     1.0 3.910953
4      VC     1.0 2.515309
5      OJ     2.0 2.655058
6      VC     2.0 4.797731

dose <- factor(dose)
fit <- aov(len ~ supp*dose)
summary(fit)

            Df Sum Sq Mean Sq F value   Pr(>F)    
supp         1  205.4   205.4  15.572 0.000231 ***
dose         2 2426.4  1213.2  92.000  < 2e-16 ***
supp:dose    2  108.3    54.2   4.107 0.021860 *  
Residuals   54  712.1    13.2                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plotting interactions

interaction.plot(dose, supp, len, type="b", 
                 col=c("red","blue"), pch=c(16, 18),
                 main = "Interaction between Dose and Supplement Type")

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library(gplots)
plotmeans(len ~ interaction(supp, dose, sep=" "),
          connect=list(c(1, 3, 5),c(2, 4, 6)), 
          col=c("red","darkgreen"),
          main = "Interaction Plot with 95% CIs", 
          xlab="Treatment and Dose Combination")

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library(HH)
interaction2wt(len~supp*dose)

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