Understanding "Main and Interaction Effects" in Bayesian ANOVA
I have a question on the analyses that I am currently trying to run in JASP. I will limit myself to one example which should then help me coping with the rest.
So, I have a mixed-factors design with one repeated measures factor (scenario, three levels) and one between-subjects factor (Studiennr, 6 levels). I am mostly interested in an effect of Studiennr, i.e., I expect data to show differences across the different studies, and I expect interaction effects of Studiennr and scenario. The results in JASP (default priors) give me the following:
Sorry for blurring the post-hoc tests.
I have been trying to interpret the results and find the correct reporting following https://www.cairn.info/revue-l-annee-psychologique-2020-1-page-73.htm (I understood that I can use BFincl in analysis of effects to determine whether there are significant effects of the factors scenario, Studiennr, and interaction. If BFincl >3, I would assume an effect - please correct me if I'm wrong.) .
If I understand things correctly, the Model Comparison Table indicates that the model only including scenario is the best predicting. Also, considering the Table "Analysis of Effects", it seems like while the scenario most definetely has an influence (BFincl = infinity), the posterior probability of the data decreases both for including the main effect of scenario and the interaction effect.
However, I am not sure whether I correctly interpret the data for the following reasons
a) a frequentist analysis reveals significant main effects of scenario and Studiennr and a significant interaction
b) the descriptives look very much like there is an effect of Studiennr
c) the post hoc tests indicates differences across some of the levels in Studiennr (e.g., 7th line, 14th line).
I would greatly appreciate if someone could help me understand the issues at hand - while there is lots of stuff on t-tests, I still find it hard to cope with the Bayesian ANOVA...