Testing Hardy-Weinberg equilibrium with a simple root-mean-square statistic

TL;DR

This paper introduces a root-mean-square goodness-of-fit test for Hardy-Weinberg equilibrium that is more powerful than traditional tests, especially in detecting absolute discrepancies, supported by theoretical analysis and benchmark data.

Contribution

The paper presents a novel root-mean-square test for Hardy-Weinberg equilibrium that outperforms existing methods in power and is easy to implement with available code.

Findings

Root-mean-square test shows higher power than traditional tests.

The test detects deviations based on absolute discrepancies.

Exact P-values can be computed efficiently with software.

Abstract

We provide evidence that a root-mean-square test of goodness-of-fit can be significantly more powerful than state-of-the-art exact tests in detecting deviations from Hardy-Weinberg equilibrium. Unlike Pearson's chi-square test, the log--likelihood-ratio test, and Fisher's exact test, which are sensitive to relative discrepancies between genotypic frequencies, the root-mean-square test is sensitive to absolute discrepancies. This can increase statistical power, as we demonstrate using benchmark datasets and through asymptotic analysis. With the aid of computers, exact P-values for the root-mean-square statistic can be calculated eeffortlessly, and can be easily implemented using the author's freely available code.