The factorial ANOVA

Now that you have tested the homogeneity of variance assumption, it is time to run the factorial ANOVA using the following notation:

aov(dependent_variable ~ independent_var1 * independent_var2)

The multiplication symbol in the formula ensures that both the main effect of the two independent variables as well as their interaction effect are taken into account in the ANOVA analysis.

This exercise is part of the course

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

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Exercise instructions

Use the function aov() to perform a factorial ANOVA on ab . Assign the result to ab_model.
Apply the summary() function to ab_model to get the ANOVA summary table. Study the table closely.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

## The data frame ab is preloaded in your workspace

# Factorial ANOVA
ab_model <- ___

# Get the summary table

Edit and Run Code

This exercise is part of the course

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

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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.

Exercise 1: Introduction to ANOVA Exercise 2: Working memory experiment Exercise 3: Difference between t-tests and ANOVA Exercise 4: Exploration of the F-test Exercise 5: Generate density plot of the F-distribution Exercise 6: Why is the F-distribution always positive?Exercise 7: F-ratio Exercise 8: Between group sum of squares Exercise 9: Within groups sum of squares Exercise 10: Calculating the F-ratio Exercise 11: ANOVA table Exercise 12: A faster way: ANOVA in R Exercise 13: Significance of the F-ratio Exercise 14: Levene's test Exercise 15: Does the assumption hold?

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.

Exercise 1: An introduction to post-hoc tests Exercise 2: The necessity of post-hoc tests Exercise 3: NHST table Exercise 4: Calculate and interpret the results of Tukey Exercise 5: Bonferroni adjusted p-values

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.

Exercise 1: Introduction to factorial ANOVA Exercise 2: Starting off Exercise 3: Data exploration with a barplot Exercise 4: Barplot interpretation Exercise 5: Hypotheses, F-ratios and effects Exercise 6: The homogeneity of variance assumption Exercise 7: Homogeneity of variance?Exercise 8: Groups and subjects Exercise 9: The factorial ANOVA

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Exercise 10: Interpreting the summary table Exercise 11: Post-hoc tests and effect sizes Exercise 12: The interaction effect (1)Exercise 13: The interaction effect (2)Exercise 14: The interaction effect (3)Exercise 15: The effect sizes Exercise 16: Interpreting etaSquared output (1)Exercise 17: Interpreting etaSquared output (2)Exercise 18: Pairwise comparisons Exercise 19: Tukey test for the easy driving simulator Exercise 20: Tukey test for the difficult driving simulator