A straightforward and valid correction to Nathoo et al.’s Bayesian within-subject credible interval

Abstract

The APA encourages authors to thoroughly report their results, including confidence intervals. However, considerable debate exists regarding the computation of confidence intervals in within-subject designs. Nathoo et al.’s (2018) recently proposed a Bayesian within-subject credible interval, which has faced criticism for not accounting for the uncertainty associated with estimating subject-specific effects. In this article, we show how Nathoo et al.’s within-subject credible interval can be easily corrected by utilizing the theory of degrees of freedom. This correction obviates the necessity for estimates of subject-specific effects that offer shrinkage. Instead, it involves a straightforward adjustment in degrees of freedom in both the interaction mean squares and the $t$-distribution used to compute the interval. Therefore, our proposed interval, being easily computable through a simple formula, eliminates the need for fully Bayesian approaches. It accurately represents uncertainty and offers the interpretational benefit of Bayesian intervals.