Bayesian Repeated Measures ANOVA assumptions and prior

IrinaNC

Hello everyone,

I am re-analyzing old data to familiarize myself with Bayesian statistics and I have two questions regarding the Bayesian Repeated Measurements ANOVA.

1) My data is highly skewed and not normally distributed. Using the log transformation doesn't help much, it is still skewed. Therefore, I ran the analysis with the untransformed data but I am not sure how much I can trust the output and whether there is an alternative.

2) I am using the default prior but in the future I would like to use the results of this old data as the prior belief of my next experiment. I read the information about the coefficient prior and I have also watched videos from a JASP course, but I do not know how to translate a prior belief to specific numbers for repeated measures ANOVA.

In case you you want more information I uploaded my JASP analysis here: https://github.com/IrinaNoguer/JASP-Old-data/blob/main/STFP.jasp

Thank you in advance for your help,

Irina

EJ

Hi Irina,

I'm on vacation so cannot really delve into this, but it would be interesting to see how skewed your data really are, and why the log transform does not help.

Regarding the priors: for the ANOVA, you cannot change the location of the parameters, but only their width. An alternative option is to analyze the data together. So suppose you have data set A (upon which your prior beliefs are then based) and data set B. When you analyze A alone, and A and B together, you can divide the BFs to obtain the BF for B given the knowledge obtained from A (see https://link.springer.com/article/10.3758/s13428-018-1092-x). This does assume that A and B are exchangeable experiments, and that they do not differ in any aspect of the design, so the requirement is quite strict. What would be interesting is to generate data based on the posterior from data set A according to the design used for data B, and then use the BF-division trick. But this gets complicated and seems like a separate research project.

EJ