A comment on sampling error in the standardized mean difference with unequal sample sizes: avoiding potential errors in meta-analytic and primary research

The authors discuss potential confusion in conducting primary studies and meta-analyses on the basis of differences between groups. First, the authors show that a formula for the sampling error of the standardized mean difference (d) that is based on equal group sample sizes can produce substantially biased results if applied with markedly unequal group sizes. Second, the authors show that the same concerns are present when primary analyses or meta-analyses are conducted with point-biserial correlations, as the point-biserial correlation (r) is a transformation of d. Third, the authors examine the practice of correcting a point-biserial r for unequal sample sizes and note that such correction would also increase the sampling error of the corrected r. Correcting rs for unequal sample sizes, but using the standard formula for sampling error in uncorrected r, can result in bias. The authors offer a set of recommendations for conducting meta-analyses of group differences.