Report tau or exp(tau) rather than tau-squared in random-effects meta-analyses

Abstract In random-effects meta-analysis, the between-study heterogeneity variance, $\tau ^2$ , is often reported but is not easy to interpret. For meta-analyses of differences (such as mean differences, standardized mean differences, or risk differences), the standard deviation (SD), $\tau $ , indicates the extent to which studies’ true effects vary about their average. For meta-analyses of (natural) log-transformed measures of effect (such as log risk ratios [RRs]), we explain how the geometric SD, $\exp (\tau )$ , is helpful to understand how untransformed measures (such as RRs) vary multiplicatively about their average. We recommend that authors and software developers report $\tau $ for differences and $\exp (\tau )$ for ratios, rather than $\tau ^2$ . This will facilitate the interpretation of the magnitude of heterogeneity values, for example, the interpretation of heterogeneity estimates and confidence intervals beyond simple binary statements about the presence or absence of heterogeneity.