Statistics in a Nutshell, 2nd Edition

Chapter 9. Factorial ANOVA and ANCOVA

Chapter 8 introduced simple regression and ANOVA. In this chapter, we present more complex types of ANOVA: factorial ANOVA (ANOVA with more than one grouping variable, or factor) and ANCOVA, which is an ANOVA design that includes a continuous covariate. Chapter 10 presents similar extensions of the simple regression model introduced in Chapter 8.

In research, most ANOVA designs include at least two grouping variables or factors; these models rely on the same basic principles as one-way ANOVA, but the additional complexity introduces additional concerns, including the evaluation of interactions between the factors. These types of analyses are nearly always done with a computer statistical package, but fortunately, there is enough commonality among those packages that generally if you can read the output from one, you can easily learn to read the output from another. We present information from the analyses as generically as possible to make it understandable no matter what computer program you are using.

Factorial ANOVA

It’s relatively rare in real-life studies that we are interested in the influence of a single factor. Instead, we are often interested in the influence of several factors and, possibly, how they interact as well. Factorial designs (ANOVAs including several factors) help us understand the combined effect of multiple factors on a dependent variable. We might be interested in both main effects—the effect of each factor considered alone—and ...