Discrepancy between Bayesian and Frequentist Repeated Measures ANOVA
I am analyzing the effect of two different drugs on cognition. Clinically, we expect both drugs to have an effect, one possibly more than the other. Therefore, I used a 2x2 design with the within-subject factor "time" and the between-subject factor "treatment arm". The treatment arms differed in two other factors, which were included as covariates.
I'd like to use Bayes Statistics, but put the frequentist equivalent into additional material. Interestingly, the two analyses show different results: The RM ANOVA shows a significant if small interaction effect time * treatment arm (F=4.32, p=.04, partial eta² 0.06) but no simple effects of either factor. The Bayes RM ANOVA shows a very strong simple effect of time (BFincl = 1124.9), but no interaction effect.
I don't think the results are necessarily incompatible with our clinical observations but I'm confused by the difference.
I checked the forum for other discussions and found violated assumptions as possible explanation. Sphericity is met as the RM factor has only two levels, but Levene's test for homogeneity is significant. Trying to use the nonparametric addition (and thank you for that!) gave me the error message "Specified ANOVA design is not balanced". I am not sure what this means.
Are there any other possible reasons for the differences in the results? Is there some other procedure I should try?
Thank you very much!