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

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...

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Bibliographic Details
Published in:	Journal of the American Statistical Association 2019-07, Vol.114 (527), p.1105-1112
Main Authors:	Rubin-Delanchy, Patrick, Heard, Nicholas A., Lawson, Daniel J.
Format:	Article
Language:	eng
Subjects:	Computer security Convex order Cyber-security Economic models Meaning Meta-analysis Network p-Value Property Regression analysis Statistical methods Statistics Theory and Methods Uniform distribution Values
Online Access:	Get full text
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Summary:	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.
ISSN:	0162-1459 1537-274X