# Bayesian Analysis of Categorical Data with Three Groups

A labmate of mine is currently designing an experiment where three groups take part in a task and they are interested in whether they are interested in whether is any difference in the number of participants that solve the task between groups. Specifically, they are predicting that more participants in group 1 will solve the task than in either group 2 or group 3 and that there won't be any differences between group 2 and 3.

I was just wondering if there are any bayesian ways to carry out such analysis, and if so, whether they are possible to do via either Jasp or the Bayes Factor package? Would it be feasible to simply carry out a Bayesian contingency test between Group 1/Group 2, Group 1/Group 3, and Group 2/Group 3 or would that lead to multiple comparison issues?

Many Thanks!

## Comments

Hi PDN,

This is an interesting issue. I assume you are interested in a Bayesian analysis. One way would be to use contingency tables (or log-linear analyses) for the full 2x3 situation, and include order constraints. These order constraints you can't do in JASP (yet). But it seems to me that your labmate has different hypotheses:

1. group 1 > group 2 & group 3

2. group 2 = group 3

In the Bayesian framework, the principled way to deal with multiplicity is to consider the prior model odds. If the hypotheses involved are all plausible (hence: not just "discovered" after inspecting the data) then you don't need to correct and you can test them separately. You might want to test group 1 vs group 2 and group 1 vs group 3 separately, but if the theory is confirmed that these are the same than you could also analyze them together. Hopefully it does not matter (which you can then report).

Cheers,

E.J.