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: it targets the predictive performance of the null hypothesis in future experiments; it provides a proper decision-theoretic model for testing a point null hypothesis and it convincingly accounts for Lindley's Paradox
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DOI 10.1086/673730
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Edward Erwin (1998). The Logic of Null Hypothesis Testing. Behavioral and Brain Sciences 21 (2):197-198.

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