# 2X2 Bayesian Contingency tables, which sampling plan do I use?

Hello! I'm using JASP to run 2X2 Bayesian Contingency analyses on my data and I'm using Jamil et al., (2015) as a blueprint for how to interpret the resulting BF values. I am not sure which of the sampling plans to use for my analysis. I am torn between using the Poisson Sampling Scheme or the Independent Multiomial Sampling Scheme.

I have one independent categorical variable to which participants are randomly assigned, condition (1 or 2) and one dependent categorical variable, CE Risk (0 or 1), hence the 2X2 analysis. We tried to fix the number of people in each condition to about 24 each, then stop, but we ran over in participants. So had we stopped running participants at exactly 24 in each condition, our restriction would have been on row total, thus making it an Independent Multinomial Sampling Scheme. But because we had one more person in one condition compared to the other, would that now make my sampling plan a Poisson Sampling Scheme?

Additionally, while Jamil et al. provide excellent summaries and guidelines for conducting 2X2 Bayesian contingency analyses, I would love to learn more. Are there any additional articles that have used JASP to conduct 2X2 Bayesian contingency analyses that could provide me with some assistance with interpretation/analysis/write-up?

Thank you for your time!

## Comments

In my opinion, you have an independent multinomial. Participants are divided in two conditions, and the interest is in the differences in rate. We will provide more articles, tutorials, and books in the future!

Cheers,

E.J.

Thank you for your help E.J.!