Methods for the integrated meta-analysis of mean and variation effects

Alistair M Senior, Tim Dodgson, Malgorzata Lagisz , Yefeng Yang, Shinichi Nakagawa

Meta-analyses in ecology and evolution typically focus on population means via effect sizes such as the log response ratio. Recently, there has been interest in quantifying effects on variability using the log variability ratio and the log coefficient of variation ratio. Until now, testing for the effects on group means and variabilities has necessitated two separate models. We present a workflow for one integrated meta-analysis of mean and variation effects, or ‘IMAMV’. In a worked example, using data from the diet-mixing literature we show how the focal parameters from IMAMV match those from the equivalent two-model analysis. A common limitation to meta-analysis of variation, is unreported variance values in the primary literature. IMAMV can increase the power to detect effects on variation in meta-analytics datasets with missing variance values through ‘borrowing of strength’. We show, for example, that in a dataset with 20% missing variance values, IMAMV increased the precision of the meta-analytic estimate on the variation effect by 10% compared to the conventional two-model approach. IMAMV can be implemented in commonly used software and requires no additional data beyond that used in the analysis of group means.