The Degree of Dependence Between Multiple-Treatment Effect Sizes

We examined the degree of dependence between standardized-mean-difference effect sizes in multiple-treatment studies in meta-analysis in terms of the correlation formula provided by Gleser and Olkin (1994) . To explore the impact of group size and the values of the true multiple-treatment effect sizes, we simplified the formula for the correlation in terms of the ratio of group sizes and under conditions of equality of sample and effect sizes. The results showed that the group-size ratio affects the correlation between effects much more than do the values of the effect sizes. A relatively smaller control-group size and large effect sizes of the same sign were associated with stronger dependence. We also showed that ignoring the dependence between individual standardized-mean-difference effect sizes always decreases the precision of differences in mean effects across studies in a meta-analysis. The difference in precision was largest when treatment groups were much larger than the control group, regardless of the size of the effects or the number of studies in the meta-analysis.