7.1 Introduction

This chapter explains analysis of variance (ANOVA). In traditional statistics courses, ANOVA was presented as if it represented a completely different class of statistical model from General Linear Models. This is not the case. Computing the ANOVA table is something you can do once you have fitted a General Linear Model using lm(), or Linear Mixed Model using 'lmer(). Doing so gives you an alternative way of performing null hypothesis significance tests for the various predictors in your model (via a statistic called the F-ratio, to which we will return). These tests have interpretive advantages over the tests based on parameter estimates and their standard errors that I presented in chapter 4. To motivate why ANOVA is useful, I am going to first explain the circumstances in which testing the difference of individual coefficients from zero is not the most useful test. This will lead into the explanation of what ANOVA is and how it works.