Title: Investigating the Relationship Between the Bayes Factor and the Separation of Credible Intervals.

Speaker: Farouk Nathoo, University of Victoria (https://www.math.uvic.ca/~nathoo/

Location: via zoom (https://carleton-ca.zoom.us/j/97371740556)

Date: Friday, March 17, 2023

Time: 1:00 – 2:00 pm

**Abstract: **The relationship between confidence intervals and null hypothesis significance testing is well known and is a topic taught in introductory statistics. In contrast, within the Bayesian paradigm, the relationship between the Bayes factor and credible intervals is not well known. We examined the relationship between the Bayes factor and the separation of credible intervals in between- and within-subject designs under a range of effect and sample sizes. For the within-subject case, we considered five intervals: (1) the within-subject confidence interval of Loftus and Masson (1994), (2) the within-subject Bayesian interval developed by Nathoo, Kilshaw, and Masson (2018), whose derivation conditions on estimated random effects, (3) and (4) two modifications of (2) based on a proposal by Heck (2019) to allow for shrinkage and account for uncertainty in the estimation of random effects, and (5) the standard Bayesian highest-density interval. We derived and observed through simulations a clear and consistent relationship between the Bayes factor and the separation of credible intervals. Remarkably, this relationship, for a given sample size, is well described by a simple quadratic exponential curve and is most precise in case (4). This observation is formalized through a limiting theorem for the case of between-subject designs with two conditions.