Repeated measures ANOVA - Model Comparison vs. Analysis of effects
I'm new to Bayesian Anova so I'm a bit lost with 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 attached results, if I look to the "Model Comparison" table it seems that Task + Load + Laterality + Task ✻ Load + Load ✻ Laterality is the best model, followed by Task + Load + Laterality + Load ✻ Laterality. If I do the math (10210000/7810000), it seems that the data is just 1.3 more likely under the first model.
Note that in the frequentist ANOVA, the three main effects are significant, and only Load ✻ Laterality interaction. So, the second model in the Bayesian ANOVA would be in line with the results from the frequentist ANOVA.
Then JASP shows the "Analysis of effects" table. Here the goal would be 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 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. Here, I compute "across all models", however the BFs 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.
Sorry to have missed this earlier. The post was repeated later and I've answered it there.