Weighting by inverse variance or by sample size in meta-analysis: A simulation study

In meta-analysis, a weighted average effect size is usually obtained to summarize the global magnitude through a set of primary studies. The optimal weight to obtain the unbiased and minimum variance estimator is the inverse variance of each effect-size estimate. In practice, it is not possible to compute the optimal inverse variance because the population effect size is unknown. Hedges and Olkin and Hunter and Schmidt proposed two alternative estimators of optimal weights. In this article, the bias and relative efficiency of both estimators are assessed via Monte Carlo simulation, defining the standardized mean difference as the effect-size index. The number of studies, sample size, magnitude of population effect size, and discrepancy between two population effect sizes were manipulated. Hedges and Olkin's estimator was more efficient, although more biased, than Hunter and Schmidt's estimator. The consequences of applying both alternatives in meta-analyses are discussed.