ABSTRACT
This chapter extends the previous discussion of analysis of variance (ANOVA; see Chapter 9) to factorial ANOVA. The chapter begins with a discussion of when it is appropriate to conduct a factorial ANOVA. In this section, the three main outcomes of a factorial ANOVA with two categorical, independent variables are introduced: Main effects for each of the independent variables and an interaction effect. Next, a brief discussion of potential problems with factorial ANOVA is presented, such as small group sizes or unequal variances across groups. The bulk of the chapter involves an in-depth discussion of factorial ANOVA. This includes an introduction to the idea of partial or controlled effects, interpreting main effects and interaction effects, and how to interpret graphical representations of factorial ANOVA results. A brief discussion of how to interpret main effects in the presence of a significant interaction is followed by a discussion of simple effects. Next, the concept of analysis of covariance (ANCOVA) is introduced and it is noted that a covariate, or covariates, can be added to any ANOVA model. Most of the remainder of the chapter (before the “Writing It Up” and “Work Problems” sections that appear in most of the chapters) is devoted to presenting examples that illustrate how factorial ANOVA works, including interpretations of published research and explanations of Statistical Package for the Social Sciences (SPSS) output.
