9.1 Introduction

In Week 9 we talked about analyses of variance - tests for comparing means across one categorical IV/predictor (typically with at least 3 levels) on one continuous outcome. In this extension module we move to some more complex ANOVA models - specifically two-way ANOVAs, where we have two categorical predictors and one continuous outcome. The main goal is still largely the same - comparing means across groups - but becomes a bit more complex with the involvement of two variables. We’ll also briefly consider the instance of a three-way ANOVA (i.e. three predictors), but won’t spend too much time on this for good reason. We’ll also talk briefly about some statistical concepts that we haven’t covered in the main subject content, specifically about interactions and contrasts.

By the end of this module you should be able to:

• Describe what an interaction is
• Conduct and interpret an omnibus two-way ANOVA
• Distinguish between post-hoc tests, simple effects tests and planned contrasts
• Attempt to think about a three-way ANOVA (but see warnings on the relevant page)