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

Philosophy of Science 80 (5):733-744 (2014)
Testing a point null hypothesis is a classical but controversial issue in statistical methodology. A prominent illustration is Lindley’s Paradox, which emerges in hypothesis tests with large sample size and exposes a salient divergence between Bayesian and frequentist inference. A close analysis of the paradox reveals that both Bayesians and frequentists fail to satisfactorily resolve it. As an alternative, I suggest Bernardo’s 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; (iii) it convincingly addresses Lindley’s Paradox
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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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