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  3. Intro to Statistics with R: Analysis of Variance (ANOVA)
  • 1

    An introduction to ANOVA

    Free

    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.

  • 2

    Post-hoc analysis

    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.

  • 3

    Between groups factorial ANOVA

    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.

Initializing

Exercise

Levene's test

The assumptions of ANOVA are relatively simple. Similar to an independent t-test, we have a continuous dependent variable, which we assume to be normally distributed. Furthermore, we assume homogeneity of variance, which can be tested with Levene's test.

It's good practice to check both assumptions before you do ANOVA, but here we'll focus on the latter. If the assumptions don't hold, then the ANOVA results won't be valid.

Instructions

100 XP
  • Perform Levene's test for the working memory data wm. Use leveneTest from the car package with the dependent and independent variables as first and second arguments, respectively.
  • If you don't specify additional arguments, the deviation scores are calculated by comparing each score to its group median. This is the default behavior, even though they are typically calculated by comparing each score to its group mean. If you want to use means and not medians, add an argument center = mean. Do this now and compare the results to the first test.