Intro to Statistics with R: Analysis of Variance (ANOVA)

In this first chapter you will learn the basic concepts of ANOVA based on the working memory training example. The difference and benefits compared to t-tests is explained, and you will see how you can compare two or more group means by engaging in ANOVA. Furthermore, you will get a deep understanding on F-tests and the corresponding distribution.

The F-ratio you calculated in the previous chapter tells you if there is a significant effect somewhere across your groups, but it does not tell you which pairwise comparisons are significant. That is what the post-hoc tests explained in this chapter will do for you. Post-hoc tests such as Tukey’s and Bonferroni’s procedure allow for multiple comparisons without inflating the probability of a type I error.

In this final chapter on ANOVA the different concepts behind a factorial ANOVA are explained. In a Factorial ANOVA you have two independent variables and one dependent continuous variable. This allows you to look at main effects, interaction effects, and simple effects. Special attention goes to effect size, post-hoc tests, simple effects analyses and the homogeneity of variance assumption.