**Instructor(s):**

Andrew Conway is a Psychology Professor in the Division of Behavioral and Organizational Sciences at Claremont Graduate University in Claremont, California. He has been teaching introduction to statistics for undergraduate students and advanced statistics for graduate students for 20 years, at a variety of institutions, including the University of South Carolina, the University of Illinois in Chicago, and Princeton University.

Analysis of Variance (ANOVA) is probably one of the most popular and commonly used statistical procedures. In this course, Professor Conway will cover the essentials of ANOVA such as one-way between groups ANOVA, post-hoc tests, and repeated measures 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.

- Introduction to ANOVA 50 xp
- Working memory experiment 100 xp
- Difference between t-tests and ANOVA 50 xp
- Exploration of the F-test 50 xp
- Generate density plot of the F-distribution 100 xp
- Why is the F-distribution always positive? 50 xp
- F-ratio 50 xp
- Between group sum of squares 100 xp
- Within groups sum of squares 100 xp
- Calculating the F-ratio 100 xp
- ANOVA table 50 xp
- A faster way: ANOVA in R 100 xp
- Significance of the F-ratio 50 xp
- Levene's test 100 xp
- Does the assumption hold? 50 xp

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.