The Least Difference in Means: A Statistic for Effect Size Strength and Practical Significance

With limited resources, scientific inquiries must be prioritized for further study, funding, and translation based on their practical significance: whether the effect size is large enough to be meaningful in the real world. Doing so must evaluate a result's effect strength, defined as a conservative assessment of practical significance. We propose the least difference in means ($δ_L$) as a two-sample statistic that can quantify effect strength and perform a hypothesis test to determine if a result has a meaningful effect size. To facilitate consensus, $δ_L$ allows scientists to compare effect strength between related results and choose different thresholds for hypothesis testing without recalculation. Both $δ_L$ and the relative $δ_L$ outperform other candidate statistics in identifying results with higher effect strength. We use real data to demonstrate how the relative $δ_L$ compares effect strength across broadly related experiments. The relative $δ_L$ can prioritize research based on the strength of their results.

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