# Preprint: A Tutorial on Conducting and Interpreting a Bayesian ANOVA in JASP

This post is a teaser for van den Bergh, D., van Doorn, J., Marsman, M., Draws, T., van Kesteren, E.-J., Derks, K., Dablander, F., Gronau, Q. F., Kucharsky, S., Komarlu Narendra Gupta, A. R., Sarafoglou, A., Voelkel, J. G., Stefan, A., Ly, A., Hinne, M., Matzke, D., & Wagenmakers, E.-J. (in press). A tutorial on conducting and interpreting a Bayesian ANOVA in JASP. L’Année Psychologique/Topics in Cognitive Psychology. Preprint available on PsyArXiv: https://psyarxiv.com/spreb

## Abstract

“Analysis of variance (ANOVA) is the standard procedure for statistical inference in factorial designs. Typically, ANOVAs are executed using frequentist statistics, where p-values determine statistical significance in an all-or-none fashion. In recent years, the Bayesian approach to statistics is increasingly viewed as a legitimate alternative to the p-value. However, the broad adoption of Bayesian statistics (and Bayesian ANOVA in particular) is frustrated by the fact that Bayesian concepts are rarely taught in applied statistics courses. Consequently, practitioners may be unsure how to conduct a Bayesian ANOVA and interpret the results. Here we provide a guide for executing and interpreting a Bayesian ANOVA with JASP, an open-source statistical software program with a graphical user interface. We explain the key concepts of the Bayesian ANOVA using two empirical examples.”

### Example I: A Robot’s Social Skills

“Do people take longer to switch off a robot when it displays social skills? This question was studied by Horstmann et al. (2018) and we use their data to illustrate the key concepts of a Bayesian ANOVA.”

“Horstmann et al. (2018) manipulated two variables in a between-subjects design. First, they manipulated the robots’ verbal responses to be either social (e.g., “Oh yes, pizza is great. One time I ate a pizza as big as me.”) or functional (e.g., “You prefer pizza. This worked
well. Let us continue.”). Second, either the robot protested to being turned off (e.g., “No! Please do not switch me off! I am scared that it [sic] will not brighten up again!”) or it did not. Therefore, the design of this study is a 2×2 between-subjects ANOVA.”

These are the data:

Here is the main analysis outcome (this is merely a teaser; details are presented in the article):

Next, the article discusses the model-averaged “analysis of effects”:

Finally, these are the parameter estimates:

The article presents a second example, on post-hoc test for the houses of Hogwarts — but a discussion of that example goes beyond the purpose of this teaser. We hope our article will make it a little easier to interpret the JASP output for the Bayesian ANOVA!

#### References

Van den Bergh, D., van Doorn, J., Marsman, M., Draws, T., van Kesteren, E.-J., Derks, K., Dablander, F., Gronau, Q. F., Kucharsky, S., Komarlu Narendra Gupta, A. R., Sarafoglou, A., Voelkel, J. G., Stefan, A., Ly, A., Hinne, M., Matzke, D., & Wagenmakers, E.-J. (in press). A tutorial on conducting and interpreting a Bayesian ANOVA in JASP. L’Année Psychologique/Topics in Cognitive Psychology. PsyArXiv Preprint: https://psyarxiv.com/spreb.