Meta-analysis of mid-p-values: some new results based on the convex order

TL;DR

This paper explores the properties of mid-p-values, showing they are dominated by the uniform distribution in the convex order, leading to new bounds for combining hypothesis tests more effectively.

Contribution

It introduces novel finite-sample and asymptotic bounds for mid-p-values based on convex order, improving hypothesis test combination methods.

Findings

Mid-p-values are dominated by the uniform distribution in convex order.

New bounds enable more powerful and conservative test combination.

Application demonstrated on cyber-security data.

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.