I have some questions regarding JASP's Bayesian post-hoc test for ANOVA.
How are the priors / posteriors / BFs computed?
Using the tooth-growth sample data,
I have conducted the same t-tests in R using BayesFactor and found the BFs to be the same.
`> list("500 vs 1000" = df %$% ttestBF(len[dose=="500"], len[dose=="1000"]) %>% extractBF(F,T),
- "500 vs 2000" = df %$% ttestBF(len[dose=="500"], len[dose=="2000"]) %>% extractBF(F,T),
- "1000 vs 2000" = df %$% ttestBF(len[dose=="1000"], len[dose=="2000"]) %>% extractBF(F,T))
$'500 vs 1000'
$'500 vs 2000'
$'1000 vs 2000'
Does this mean that posterior odds are calculated as BF*(prior odds)? In that case, the correction for multiple comparisons is not on the BF itself, but on the posterior odds - wouldn't we want the correction on the BFs themselves?
Also, I've tried looking up Westfal, Johnson and Utts's paper, but I still don't understand how the prior odds are calculated.
Constrained / Restricted models vs. post-hoc tests
Richard has previously detailed in his (old) blog how to calculate BFs for specific hypotheses regarding restricted / constrained models.
When should one conduct these tests as apposed to the methods used in JASP for post-hoc tests?