I have two hierarchical models. Both models include 80 participants and output both a group-level posterior distribution and 80 individual-level posterior distributions for my variable of interest. The only difference in the models is that Model 1 includes data from condition A and Model 2 includes data from condition B. I want to test whether condition A and condition B are significantly different.
I now run into confusion about how to test this. I could compute HDIs for the group-level posterior distributions for models 1 and 2 and see if they are nonoverlapping. I could take the mean of every individual-level posterior distribution and then perform a frequentist paired t-test. I can get different results depending on which option I pick, though. What is the approach I should be using here?