The R Book

11

Analysis of Variance

Analysis of variance is the technique we use when all the explanatory variables are categorical. The explanatory variables are called factors, and each factor has two or more levels. When there is a single factor with three or more levels we use one-way ANOVA. If we had a single factor with just two levels, we would use Student's t test (see p. 294), and this would give us exactly the same answer that we would have obtained by ANOVA (remember the rule that F = t²). Where there are two or more factors, then we use two-way or three-way ANOVA, depending on the number of explanatory variables. When there is replication at each combination of levels in a multi-way ANOVA, the experiment is called a factorial design, and this allows us to study interactions between variables, in which we test whether the response to one factor depends on the level of another factor.