Bayesian testing of constrained hypotheses

Statistical hypothesis testing plays a central role in applied research to determine whether theories or expectations are supported by the data or not. Such expectations are often formulated using order constraints. For example an executive board may expect that sales representatives who wear a smart watch will respond faster to their emails than sales representatives who don't wear a smart watch. In addition it may be expected that this difference becomes more pronounced over time because representatives need to learn how to use the smart watch effectively. By translating these expectations into statistical hypotheses with equality and/or order constraints we can determine whether the expectations receive evidence from the data. In this chapter we show how a Bayesian statistical approach can effectively be used for this purpose. This Bayesian approach is more flexible than the traditional p-value test in the sense that multiple hypotheses with equality as well as order constraints can be tested against each other in a direct manner. The methodology can straightforwardly be used by practitioners using the freely downloadable software package BIEMS. An application in a human-computer interaction is used for illustration.