Two methods to test within-subject interaction using Bayesian ANOVA in JASP
I have two within-subject variables in my experiment: Condition (two levels: con1 and con2) and Position (five levels: pos1, pos2, pos3, pos4 and pos5). I plan to examine whether there is Condition x Position interaction.
In the framework of classical (Frequentist) ANOVA, there are two methods to investigate this interaction. One method (which is the most commonly used method) is to add both variables and their interactions into the repeated measures ANOVA analysis, and check the F value and p value for the interaction. The second method is to first calculate the difference between the two levels of Condition (e.g., con1 - con2) at each level of Position, through which I can create a new variable named Diff_Condition with five within-subject levels (pos1, pos2, pos3, pos4 and pos5). Then I can perform a one-way repeated measures ANOVA on Diff_Condition and check the F value and p value.
The F value and p value are the same for the two methods when I use classical ANOVA (as shown in JASP):
However, results for the two methods are quite different when I use Bayesian repeated measures ANOVA in JASP. This is the results for the first method:
which seems to support null hypothesis for the interaction term.
This is the results for the second method:
which strongly supports alternative hypothesis.
I was wondering whether results for the two methods are quite different in Bayesian ANOVA. Thank you very much!