Meta-Analysis of Mid-p-Values: Some New Results based on the Convex Order

Patrick Rubin-Delanchy, Nicholas A. Heard and Daniel J. Lawson

Journal of the American Statistical Association, 2019, vol. 114, issue 527, 1105-1112

Abstract: The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger than a uniform distribution on the unit interval, in the usual stochastic order. The mid-p-value is not conservative. However, its null distribution is dominated by the uniform distribution in a different stochastic order, called the convex order. The property leads us to discover some new finite-sample and asymptotic bounds on functions of mid-p-values, which can be used to combine results from different hypothesis tests conservatively, yet more powerfully, using mid-p-values rather than p-values. Our methodology is demonstrated on real data from a cyber-security application.

Date: 2019
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DOI: 10.1080/01621459.2018.1469994

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