  The American Statistical Association (ASA) statement on statistical
significance and P-values \cite{wasserstein2016asa} cautioned statisticians
against making scientific decisions solely on the basis of traditional
P-values. The statement delineated key issues with P-values, including a lack
of transparency, an inability to quantify evidence in support of the null
hypothesis, and an inability to measure the size of an effect or the importance
of a result. In this article, we demonstrate that the interval null hypothesis
framework (instead of the point null hypothesis framework), when used in tandem
with Bayes factor-based tests, is instrumental in circumnavigating the key
issues of P-values. Further, we note that specifying prior densities for Bayes
factors is challenging and has been a reason for criticism of Bayesian
hypothesis testing in existing literature. We address this by adapting Bayes
factors directly based on common test statistics. We demonstrate, through
numerical experiments and real data examples, that the proposed Bayesian
interval hypothesis testing procedures can be calibrated to ensure frequentist
error control while retaining their inherent interpretability. Finally, we
illustrate the improved flexibility and applicability of the proposed methods
by providing coherent frameworks for competitive landscape analysis and
end-to-end Bayesian hypothesis tests in the context of reporting clinical trial
outcomes.
