Factorial Designs

R packages

We’ll use the following R packages in this chapter:

• arm
• cowplot
• ggplot2

Introduction

So far, we’ve learned how to conduct analyses with either continuous explanatory variables (regression) or categorical ones (ANOVA, t-tests). But what if we have an analysis with two or more explanatory variables where interactions are possible? This chapter introduces factorial designs, which combine two categorical explanatory variables in a way that allows us to look at the interactions between them.

Factorial designs

Fully factorial designs test for interactions by applying two or more treatments (factors) in all possible combinations. On the other hand, fractionally factorial designs are more complex and feature only a subset of all possible combinations. We can then estimate the effects of each treatment alone and in combination. The example dataset in the next section below contains two factors, each with two levels, and the fully factorial design contains all four possible treatment combinations.