Waldian t tests: Sequential Bayesian t tests with controlled error probabilities.

Bayesian ests have become increasingly popular alternatives to null-hypothesis significance testing (NHST) in psychological research. In contrast to NHST, they allow for the quantification of evidence in favor of the null hypothesis and for optional stopping. A major drawback of Bayesian ests, however, is that error probabilities of statistical decisions remain uncontrolled. Previous approaches in the literature to remedy this problem require time-consuming simulations to calibrate decision thresholds. In this article, we propose a sequential probability ratio test that combines Bayesian ests with simple decision criteria developed by Abraham Wald in 1947. We discuss this sequential procedure, which we call Waldian est, in the context of three recently proposed specifications of Bayesian ests. Waldian ests preserve the key idea of Bayesian t tests by assuming a distribution for the effect size under the alternative hypothesis. At the same time, they control expected frequentist error probabilities, with the nominal Type I and Type II error probabilities serving as upper bounds to the actual expected error rates under the specified statistical models. Thus, Waldian ests are fully justified from both a Bayesian and a frequentist point of view. We highlight the relationship between Bayesian and frequentist error probabilities and critically discuss the implications of conventional stopping criteria for sequential Bayesian ests. Finally, we provide a user-friendly web application that implements the proposed procedure for interested researchers. (PsycInfo Database Record (c) 2022 APA, all rights reserved).