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

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.