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

Published online by Cambridge University Press:  01 January 2022

Jan Sprenger
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Abstract

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.

Type
General Philosophy of Science
Information
Philosophy of Science , Volume 80 , Issue 5 , December 2013 , pp. 733 - 744
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

The author wishes to thank the Netherlands Organisation for Scientific Research (NWO) for support of his research through Veni grant 016.104.079, as well as José Bernardo, Cecilia Nardini, and the audience at PSA 2012, San Diego, for providing helpful input and feedback.

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