A New Effect Size for Meta‐Analysis of Magnitude: lnM

Abstract

Meta‐analyses in ecology and evolution sometimes target the magnitude of differences between groups rather than their direction, for example, when the question concerns deviation from a biological optimum or divergence from a reference state. A common practice is to convert signed effects into magnitudes by taking absolute values, but this can induce upward distortion and non‐normal sampling distributions under standard meta‐analytic models. Here we introduce lnM, a log‐ratio effect size for the magnitude of difference between two groups, defined from one‐way ANOVA components. lnM is asymptotically normal, supports standard multilevel meta‐analysis and meta‐regression and applies to both ratio‐ and interval‐scale traits. Using theory, simulations and worked examples, we show when delta‐method and single‐fit bootstrap estimators perform well, and how lnM can be used to assess publication bias.

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