# Testing assumptions for Bayesian Repeated Measure ANOVA

Dear E.J. plus everyone in the forum,

If I run the classical RM ANOVA in SPSS, by default it produces a table of Mauchley's Test for Sphericity, thus allowing one to check for assumptions and where it is violated, to apply Greenhouse-Geisser corrections for instance. When I run Bayesian RM Anova in JASP, I do not get this assumption displayed in the output and there is no option for checking this assumption. My question is, does Bayesian RM Anova make assumption for sphericity? If it does, how can this be tested? Secondly, does it make assumptions for normality? It will be interesting to point out what assumptions are there for using Bayesian tests (e.g., ANOVA, T-test, etc..). My colleagues have asked me including my students and I have no answer for this or where to refer them to. I truly love JASP an have been encouraging them to use Bayesian statistics as opposed to frequentist statistics.

Thanks for your response.

Tom

## Comments

Hi Tom,

The Bayesian ANOVA (it is really a linear mixed model, see the BayesFactor documentation) makes the same assumptions as the classical ANOVA. We just have not developed the Bayesian echoes for those assumption tests (yet). We will do this in the future, but until that's done you can take a pragmatic approach and use the frequentist tests. There is of course an immediate practical problem -- suppose you do want to correct, how would you do it? In the Bayesian framework, instead of issuing a correction you would apply a more complicated model that can account for the misspecification. But that is work for the future. In general, we hope to give the Bayesian ANOVA some more love in the future.

Cheers,

E.J.

Dear E.J.,

Many thanks for responding quick to my questions. Much appreciated. I have noted all that you said and will do as suggested. Please one other question: in terms of reporting effect size for the Bayesian ANOVA, how do I go about this? I know for the classical ANOVA, you can obtain partial eta squared, which is also an option in JASP when using the classical RM ANOVA. Lastly, the advanced options for the prior, do I leave the default values as they are or do I have to alter them? I understand the complexities with setting priors and that JASP uses default priors. And what do these represent: r-scale fixed effect, r-scale random effects, r-scale covariates?

Thank you once again as I look forward to hearing from you.

Cheers,

Tom

Re effect size: this is not straightforward (I think). There's a paper with Maarten Marsman that is currently somewhere in the review system. We need to polish the Bayesian ANOVA anyway in order to show parameter estimates. We'll take the effect size issue on board then as well. For now, I'd just report the frequentist effect size measure.

Re priors for ANOVA: I'd leave them as is. The r-scales refer to the width of the prior distribution on the relevant effects. You can check the Rouder and Morey 2012 JMP paper if you feel brave enough. Maybe the BayesFactor documentation offers help as well.

Cheers,

E.J.