Fast Sample Size Determination for Bayesian Equivalence Tests

Equivalence testing allows one to conclude that two characteristics are practically equivalent. We propose a framework for fast sample size determination with Bayesian equivalence tests facilitated via posterior probabilities. We assume that data are generated using statistical models with fixed parameters for the purposes of sample size determination. Our framework defines a distribution for the sample size that controls the length of posterior highest density intervals, where targets for the interval length are calibrated to yield desired power for the equivalence test. We prove the normality of the limiting distribution for the sample size and introduce a two-stage approach for estimating this distribution in the nonlimiting case. This approach is much faster than traditional power calculations for Bayesian equivalence tests, and it requires users to make fewer choices than traditional simulation-based methods for Bayesian sample size determination.