A note on testing for homogeneity among effect sizes sharing a common control group

L. V. Hedges and I. Olkin (1985) presented a statistic to test for homogeneity among correlated effect sizes and L. J. Gleser and I. Olkin (1994) presented a large-sample approximation to the covariance matrix of the correlated effect sizes. This article presents a more exact expression for this covariance matrix, assuming normally distributed data but not large samples, for the situation where effect sizes are correlated because a single control group was compared with more than one treatment group. After the correlation between effect sizes has been estimated, the standard Q statistic for correlated effect sizes can be used to test for homogeneity. This method is illustrated using results from schizophrenia research.