chapter  9
Factorial ANOVA
Models with Multiple Categorical Predictors and Product Terms
ByCharles M. Judd, Gary H. McClelland, Carey S. Ryan
Pages 24

In this chapter, the authors’ demonstrate classical analysis of variance with two or more categorical predictors is nothing more than a simple one-way analysis of variance (ANOVA) with a specific, clever set of contrast codes. The generalization of models with one categorical predictor to models with two categorical predictors and to models with more than two categorical predictors is straightforward. The one new difficulty introduced by the generalization of one-way ANOVA to two-way and higher ANOVA is the interpretation of the coefficients. In all other details factorial ANOVA with two or more categorical variables is exactly the same as one-way ANOVA with one categorical variable. The authors’ provide additional details on two issues—asking other questions and assessing statistical power—in order to highlight some issues that frequently arise in factorial ANOVA. The proliferation of interaction contrasts in factorial designs makes testing and interpreting individual contrasts unwieldy.