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Chapter 9. Analysis of variance > Two-way factorial ANOVA
9.5. Two-way factorial ANOVA
In a two-way factorial ANOVA, subjects are assigned to groups that are formed from the cross-classification of two factors. This example uses the ToothGrowth dataset in the base installation to demonstrate a two-way between-groups ANOVA. Sixty guinea pigs are randomly assigned to receive one of three levels of ascorbic acid (0.5, 1, or 2mg), and one of two delivery methods (orange juice or Vitamin C), under the restriction that each treatment combination has 10 guinea pigs. The dependent variable is tooth length. The following listing shows the code for the analysis.
Listing 9.6. Two-way ANOVA
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Show All > 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 4.46
2 VC 0.5 2.75
3 OJ 1.0 3.91
4 VC 1.0 2.52
5 OJ 2.0 2.66
6 VC 2.0 4.80
> fit <- aov(len ~ supp*dose)
> summary(fit)
Df Sum Sq Mean Sq F value Pr(>F)
supp 1 205 205 12.32 0.0009 ***
dose 1 2224 2224 133.42 <2e-16 ***
supp:dose 1 89 89 5.33 0.0246 *
Residuals 56 934 17
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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