Understanding Bayes repeated measures ANOVA
I am trying to get a practical understanding of Bayes ANOVA by playing around with some synthetic data. I am struck however by how many relationships that do exist in frequentist ANOVA do not translate, so that i have to revise many of my prior intuitions. Could you confirm that my understanding is correct here?
- Equivalence between t-tests and ANOVA. In frequentist analyses, the p value for the difference between two factors of a level is always identical when run with ANOVA or with a paired t-test. This is not so with Bayes t-tests and Bayes-ANOVAs. I assume this is because of different priors?
- Independence of interactions and main effects. In frequentist ANOVAs, main effects and interactions are evaluated independent of each other, but not in Bayes ANOVA. In fact, typically, the Bayes ANOVA won't see an interaction at all, if the two factors don't already show main effects. I find this a bit problematic for several classical stimulus-response compatibility designs, for example, where one predicts an interaction of two factors, but no main effects (e.g. stimulus side (left, right) vs. response side (left, right)). Is there a way (in JASP) to force the ANOVA to consider the interaction by itself?
- Equivalence between main effects and interactions. In a frequentist repeated measures ANOVA, main effects are computed analogously to interactions (and all main effects and interactions are statistically independent of one another). For example, through a simple re-coding of columns (e.g. switching of columns C and d) in a 2x2, one of the main effects turns into an interaction (with identical p values) and vice versa. I find this equivalence does not exist in Bayes ANOVA, with BFs being different depending on whether something is coded as main effect or interaction. Why is that?
- Between-subjects variability seems to be coded differently. In frequentist repeated measures ANOVA, results will always be identical, if the difference between to conditions is the same for each participant, irrespective of the overall scores for the values in both conditions. Bayes t-tests show the same equivalence, but not Bayes ANOVAs. I don't understand why this is.
It would be great if you would have some advice for me here. I am trying to re-evaluate some of my old results with Bayes analyses but some of the problems above have hampered my progress somewhat. I am also wondering if there is some way of running Bayes ANOVAs in a way that retains some of the above relationships?