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Combining Correlation Matrices: Simulation Analysis of Improved Fixed-Effects Methods

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  • Adam R. Hafdahl

    (University of Missouri–Columbia)

Abstract

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.

Suggested Citation

  • Adam R. Hafdahl, 2007. "Combining Correlation Matrices: Simulation Analysis of Improved Fixed-Effects Methods," Journal of Educational and Behavioral Statistics, , vol. 32(2), pages 180-205, June.
    • Handle: RePEc:sae:jedbes:v:32:y:2007:i:2:p:180-205
    DOI: 10.3102/1076998606298041
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