Key points are not available for this paper at this time.
The originally proposed multivariate meta-analysis approach for correlation matrices—analyze Pearson correlations, with each study’s observed correlations replacing their population counterparts in its conditional-covariance matrix—performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better estimates of correlations in the conditional covariances. Fixed-effects methods with and without each refinement were examined in a Monte Carlo study; number of studies and the distribution of within-study sample sizes were varied. Both refinements improved element-wise point and interval estimates, as well as Type I error control for homogeneity tests, especially with many small studies. Practical recommendations and suggestions for future methodological work are offered. An appendix describes how to transform Fisher- Z (co)variances to the Pearson- r metric.
Adam R. Hafdahl (Fri,) studied this question.