Can we Find Evidence for the Null in a Bayesian t-Test? Not Unless we Reconsider Bayes Factor Thresholds

Within the fields of behavioural and psychological research, the use of Bayesian statistics has gathered increased interest. A statistical test commonly employed in behavioral and psychological research is the t-test. For the Bayesian t-test, a Bayes Factor (BF) can be computed which reflects evidence in favor of either the alternative hypothesis (H1) or the null hypothesis (H0). Even though the BF is a continuous measure of evidence, it is common to define specific thresholds for accepting the evidence in favor of either the H1 or the H0. Such evidence thresholds (e.g., BF 3, BF 6, BF 10) are adopted by related scientific journals to define minimum publication or preregistration requirements. However, exceeding these thresholds is not analogous when H1 is true compared to when H0 is true. In turn, this disanalogy might require scientists to invest additional time and resources when H0 is true, as opposed to when H1 is true. In this study, we simulated 200 million BFs for various effect size, sample size, and variance assumptions, to demonstrate this disanalogy. Further, we show that despite having small shifts in the sample sizes required for exceeding various BF thresholds when H1 is true, when the H0 is true the probabilities of exceeding a BF 6 or a BF 10 are close to chance. As such, we recommend the use of a BF 3 evidence threshold for the H0 independently of the evidence threshold set for H1.