An exact, unconditional, nuisance-agnostic test for contingency tables

TL;DR

The paper introduces the m-test, an exact, unconditional, nuisance-agnostic statistical test for contingency tables that offers higher power than existing methods, with an implementation in R.

Contribution

It presents the m-test, a novel exact test for contingency tables that integrates over nuisance parameters, improving power over traditional tests.

Findings

Higher statistical power demonstrated via Monte Carlo simulations

Provides an R package for practical implementation

Applicable to low-marginal contingency table analysis

Abstract

Exact tests greatly improve the analysis of contingency tables when marginals are low. For instance, researchers often use Fisher's exact test, which is conditional, or Barnard's test, which is unconditional but needs to deal with a nuisance parameter. Here, we describe the m-test, an exact, unconditional test for the study of d x m binomial contingency tables. When comparing binomial trials, the m-test is related to Barnard's exact test. However, the nuisance parameter is integrated over all its possible values, instead of maximized or otherwise estimated. According to Monte Carlo simulations, this strategy yields a higher statistical power than other exact tests. We also provide a package to perform the m-test in R.