I have what is probably a simple question, but I need some advice. We have a simple study that has 2 conditions, and 2 groups. We predict a group x condition interaction, as shown below. That is, the difference bewteen conditions in Group 1 is larger than the difference bewteen conditions in Group 2. (In fact we would explicitly predict a crossover interaction, as shown.)
Each condition is a list of 20 items, and each item can be correct, or not. (Due to stimuli constraints we can't have more items per condition.)
What is the best Bayesian approach for testing this? We have not yet collected the data, and are planning on preregistering using Bayes Factor Design Analysis (Schönbrodt & Wagenmakers, 2016) to specify a stopping rule for data collection.
One basic approach would be to express each participant's data as a difference score, which simplifies the above plot.
I could imagine doing a t-test in JASP that would give me a Bayes Factor. However, I could also imagine there are better ways to do this.
Any suggestions, via comments or via email, would be much appreciated! This is our first attempt at both preregistration and Bayesian analysis, and we'd like to do it right.
Schönbrodt FD, Wagenmakers E-J. Bayes Factor Design Analysis: Planning for Compelling Evidence (August 9, 2016). Available at SSRN: http://ssrn.com/abstract=2722435 or http://dx.doi.org/10.2139/ssrn.2722435
Cyril Pernet suggested doing BIC model comparison with vs. without the interaction in JASP.