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We provide evidence that, in certain circumstances, a root-mean-square test of goodness of fit can be significantly more powerful than state-of-the-art tests in detecting deviations from Hardy–Weinberg equilibrium. Unlike Pearson's   $\chi ^2$   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 data sets and simulations, and through asymptotic analysis.

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