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

Area of Science:

• Statistics
• Hypothesis Testing
• Data Analysis

Background:

• Traditional p-values can be conservative with discrete test statistics, leading to less powerful hypothesis testing.
• The null distribution of ordinary p-values is stochastically larger than a uniform distribution.
• This conservativeness can impact the reliability and power of statistical conclusions.

Purpose of the Study:

• To introduce and evaluate the mid-p-value as an improvement over the ordinary p-value for discrete test statistics.
• To explore the properties of the mid-p-value's null distribution and its stochastic ordering.
• To develop new bounds for combining hypothesis tests using mid-p-values for increased power and conservativeness.

Main Methods:

• The study defines the mid-p-value and analyzes its null distribution properties, comparing it to the ordinary p-value.
• It investigates stochastic orders, specifically focusing on convex order for the mid-p-value.
• New finite-sample and asymptotic bounds are derived based on these properties.

Main Results:

• The mid-p-value is demonstrated to be non-conservative, unlike the ordinary p-value.
• Its null distribution is shown to be convexly ordered by the uniform distribution.
• New bounds are established for combining hypothesis tests, offering improved power and conservativeness.

Conclusions:

• The mid-p-value is a statistically advantageous alternative for hypothesis testing with discrete data.
• The derived bounds facilitate more effective combination of results from multiple hypothesis tests.
• The methodology is validated using real-world data from a cyber-security context.