Testing a Precise Null Hypothesis: The Case of Lindley’s Paradox

The interpretation of tests of a point null hypothesis against an unspecified alternative is a classical and yet unresolved issue in statistical methodology. This paper approaches the problem from the perspective of Lindley’s Paradox: the divergence of Bayesian and frequentist inference in hypothesis tests with large sample size. I contend that the standard approaches in both frameworks fail to resolve the paradox. As an alternative, I suggest the Bayesian Reference Criterion: (i) it targets the predictive performance of the null hypothesis in future experiments; (ii) it provides a proper decision-theoretic model for testing a point null hypothesis and (iii) it convincingly accounts for Lindley’s Paradox. ∗Contact information: Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. Email: [email protected]. Webpage: www.laeuferpaar.de