B-Value and Empirical Equivalence Bound: A New Procedure of Hypothesis Testing

Abstract

In this study, we propose a two-stage procedure for hypothesis testing, where the first stage is conventional hypothesis testing and the second is an equivalence testing procedure using an introduced Empirical Equivalence Bound. In 2016, the American Statistical Association released a policy statement on P-values to clarify the proper use and interpretation in response to the criticism of reproducibility and replicability in scientific findings. A recent solution to improve reproducibility and transparency in statistical hypothesis testing is to integrate P-values (or confidence intervals) with practical or scientific significance. Similar ideas have been proposed via the equivalence test, where the goal is to infer equality under a presumption (null) of inequality of parameters. However, the definition of scientific significance/equivalence can sometimes be ill-justified and subjective. To circumvent this drawback, we introduce the B-value and the Empirical Equivalence Bound, which are both estimated from the data. Performing a second-stage equivalence test, our procedure offers an opportunity to improve the reproducibility of findings across studies.