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How can I report effect sizes for the Bayesian repeated measures ANOVA?
I'd advise you to use the classical estimates for that. We have one paper in review on this issue, and it will take some time before it is included in JASP. In general, you've hit on one of the missing features; we've already fixed this for linear regression (where we now offer posterior distributions for all regression coefficients) but we still need to do the same for ANOVA. Perhaps the BayesFactor package offers a way out, but it's best to PM Richard Morey about that; if he has useful advice, please let us know!