Interpretation and reporting of Bayes Mixed Factor ANOVA
Hello
I'm very new to Bayes, and am a little confused on the interpretation of the BF and specifically interactions. I would like to present the BF alongside the traditional ANOVA (actually it is an ANCOVA I am running - age is a covariate). I understand BF10 and BF01, but the interactions in the 'model comparison' are not analogous to the interaction effects in the traditional ANOVA since they also contain the main effects (TargetAge + Pgroup + TargetAge *Pgroup) and the BF tells a pattern that is quite different to the interaction effect in the traditional ANOVA.
I have compared with the null model which I feel makes most sense for what I need. I've also got the Analysis of Effects table, but then I'm not sure how this directly compares to the traditional ANOVA. Essentially, I'd like to report BF10 with ANOVA..
Below I report the BF10, but got stuck on what to report for the interaction. So, my question is, what should I report here? If I need to use BFinc instead, then how would I need to rephrase what I report below?
Mixed factor ANCOVA and the analogous Bayesian analysis were conducted and are reported. We report Bayes Factor 10 to demonstrate comparisons of the alternative model to the null model. The covariate for age was found to be significant, F(1, 110) = 9.63, p = 0.002, ƞp2 = 0.08, BF10 = 31.24, therefore, when participant age is controlled for, this analysis found no main effect of group, F(2, 110) = 0.70, p = 0.489, ƞp2 = 0.013, BF10 = 0.26, and no interaction between group and stimulus age, F(8, 440) = 0.40, p = 0.919, ƞp2 = 0.007 [BF10 = ????? ]. However, a main effect of stimulus age was revealed, F(4, 440) = 4.15, p = 0.003, ƞp2 = 0.036, BF10 = 2.24 x 1011.
Many thanks!
Comments
Well there are several issues here. First, the Bayesian models by default enforce the "principle of marginality", which means that when interactions are included, so are the constituent main effects. You can turn off this behavior under "Additional Options". Second, I would summarize the results using the inclusion BF from the analysis of effects table, and include the complete model comparison table as an online appendix.
EJ