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The mid-p-value is a proposed improvement on the ordinary p-value for thecase where the test statistic is partially or completely discrete. In thiscase, the ordinary p-value is conservative, meaning that its null distributionis larger than a uniform distribution on the unit interval, in the usualstochastic order. The mid-p-value is not conservative. However, its nulldistribution is dominated by the uniform distribution in a different stochasticorder, called the convex order. The property leads us to discover some newfinite-sample and asymptotic bounds on functions of mid-p-values, which can beused to combine results from different hypothesis tests conservatively, yetmore powerfully, using mid-p-values rather than p-values. Our methodology isdemonstrated on real data from a cyber-security application.

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