Distribution of the standardized mean change effect size for meta-analysis on repeated measures

When conducting a meta-analysis on studies with repeated measures, a useful measure of effect size is Becker's (1988) standardized mean change. This paper examines the distributional properties of the standardized mean change, and discusses potential problems with the variance formulae given in Becker (1988). First, an error in the exact variance formula can lead to severe underestimation of the actual sampling variance. Second, Becker (1988) recommended the use of an approximation which is shown to underestimate the sampling variance when sample size is small. Using the approximation can decrease the accuracy of meta-analysis results: however, the degree of error is generally small.