# Bayesian ANOVA on raw data

I'm kinda new to Bayesian analysis, but here goes:

I'm measuring reaction times in a repeated measures design. Say I have 10 subjects and 2 conditions with 50 measurements for each condition (overall 1000 observations). Can I use Bayesian ANOVA on the raw observations (not averaged across condition per subject), and enter the subject as a random factor? it seems reasonable to do so (I think it's the same logic of mixed models), but I could not find any reference for such a method with a Bayesian analysis...

Any help would be appreciated, as well as any references to any article you know that used a similar method.

If I'm correct, the analysis should look like this:

Thanks!

Alon

## Comments

Hi Alon,

This is more the expertise of Richard Morey, so I'll attend him to this, as well as Quentin Gronau. For what it is worth, I think you are right. The Bayesian ANOVA in JASP is really a Bayesian linear mixed model. Perhaps there is a post on how BayesFactor deals with this...

Cheers,

E.J.

Hi Alon,

I agree with E.J.. The Bayesian ANOVA in JASP is implemented using the Bayesian linear mixed model framework from the BayesFactor package by Richard Morey. That is, the Bayesian repeated measures ANOVA in JASP is a Bayesian linear mixed model with random participant effects. Therefore, to me it seems reasonable to add subject as a random factor in your case. With respect to the fact that you have multiple observations for each participant in each condition: In the paper by Jeff Rouder and colleagues (https://doi.org/10.1016/j.jmp.2012.08.001) on which this Bayesian mixed model implementation is based it is mentioned in at least one sentence that multiple observations per condition can be handled within this framework:

"This term [the interaction between the random participant factor and the condition/stimulus factor] may be estimated if the design is replicated, that is, each participant yields several observations in each condition" (p. 367).

Furthermore, here are two links that provide additional information about mixed models in BayesFactor:

bayesfactorpcl.r-forge.r-project.org/#mixed

https://cran.r-project.org/web/packages/BayesFactor/vignettes/compare_lme4.html

Cheers,

Quentin

Thank you E.J. and Quentin