Bayesian repeated measures ANOVA - Model Comparison vs. Analysis of effects
I posted this question a few weeks ago (see the thread below) but apparently went unnoticed. So I just re-post it just in case I get luckier this time.
Anyway, I'm quite new to Bayesian Anova so I'm a having a bit of a difficult time interpreting the JASP output. I've run a 2 (Task) x 2 (Load) x 2 (Laterality) model for which I get the following output:
In the results output above, the "Model Comparison" table suggests that Task + Load + Laterality + Task ✻ Load + Load ✻ Laterality is the best model, followed by Task + Load + Laterality + Load ✻ Laterality. However if I do the math (10210000/7810000), it seems that the data is just 1.3 more likely under the first model.
In the "frequentist" ANOVA, the three main effects are significant together with Load ✻ Laterality interaction (no further significant interactions). So, the second model in the Bayesian ANOVA would be in line with the results from the frequentist ANOVA, but not the first one.
Then JASP shows the "Analysis of effects" table. Here the goal is to retain model selection uncertainty by averaging the conclusions from each candidate model, weighted by that model’s posterior plausibility (according to Wagenmakers et al., 2018, Bayesian inference for psychology. Part II). If I look to the BF inclusion values in this table, the results are also in line with the frequentist ANOVA, showing strong evidence in favour of the three main effects and the Load ✻ Laterality interaction. Note that this values are computed "across all models", however the BF values are lower if I compute "across matched models".
In sum, my question refers to how to best interpret these results. Should I look to the "Analysis of effects" table or to the "Model Comparison" output? It would seem that the results are different whether I look to one or the other.
Any help would be very much appreciated.