Page 251 - Applied Statistics with R

12.5. TWO-WAY ANOVA 251

Factor B, Level 1 Factor B, Level 2
Factor A, Level 1 + + 1 + + 2
1
1
Factor A, Level 2 + + 1 + + 2
2
2
Factor B Only Model (One-Way): = + +

Factor B, Level 1 Factor B, Level 2
Factor A, Level 1 + 1 + 2
Factor A, Level 2 + 1 + 2

Factor A Only Model (One-Way): = + +

Factor B, Level 1 Factor B, Level 2
Factor A, Level 1 + 1 + 1
Factor A, Level 2 + 2 + 2

Null Model: = +

Factor B, Level 1 Factor B, Level 2
Factor A, Level 1
Factor A, Level 2

The question then, is which of these models should we use if we have two factors?
The most important question to consider is whether or not we should model the
interaction. Is the effect of Factor A the same for all levels of Factor B? In
the additive model, yes. In the interaction model, no. Both models would use
a different mean for each group, but in a very specific way in both cases.

Let’s discuss these comparisons by looking at some examples. We’ll first look at
the rats data from the faraway package. There are two factors here: poison
and treat. We use the levels() function to extract the levels of a factor
variable.

levels(rats$poison)

## [1] "I" "II" "III"