Evaluation of various estimators for standardized mean difference in meta‐analysis

Meta-analyses of a treatment's effect compared with a control frequently calculate the meta-effect from standardized mean differences (SMDs). SMDs are usually estimated by Cohen's d or Hedges' g. Cohen's d divides the difference between sample means of a continuous response by the pooled standard deviation, but is subject to nonnegligible bias for small sample sizes. Hedges' g removes this bias with a correction factor. The current literature (including meta-analysis books and software packages) is confusingly inconsistent about methods for synthesizing SMDs, potentially making reproducibility a problem. Using conventional methods, the variance estimate of SMD is associated with the point estimate of SMD, so Hedges' g is not guaranteed to be unbiased in meta-analyses. This article comprehensively reviews and evaluates available methods for synthesizing SMDs. Their performance is compared using extensive simulation studies and analyses of actual datasets. We find that because of the intrinsic association between point estimates and standard errors, the usual version of Hedges' g can result in more biased meta-estimation than Cohen's d. We recommend using average-adjusted variance estimators to obtain an unbiased meta-estimate, and the Hartung-Knapp-Sidik-Jonkman method for accurate estimation of its confidence interval.