Reliability generalization meta-analysis: comparing different statistical methods

Reliability generalization (RG) is a kind of meta-analysis that aims to characterize how reliability varies from one test application to the next. A wide variety of statistical methods have typically been applied in RG meta-analyses, regarding statistical model (ordinary least squares, fixed-effect, random effects, varying-coefficient models), weighting scheme (inverse variance, sample size, not weighting), and transformation method (raw, Fisher's Z, Hakstian and Whalen's and Bonett's transformation) of reliability coefficients. This variety of methods compromise the comparability of RG meta-analyses results and their reproducibility. With the purpose of examining the influence of the different statistical methods applied, a methodological review was conducted on 138 published RG meta-analyses of psychological tests, amounting to a total of 4,350 internal consistency coefficients. Among all combinations of procedures that made theoretical sense, we compared thirteen strategies for calculating the average coefficient, eighteen for calculating the confidence intervals of the average coefficient and calculated the heterogeneity indices for the different transformations of the coefficients. Our findings showed that transformation methods of the reliability coefficients improved the normality adjustment of the coefficient distribution. Regarding the average reliability coefficient and the width of confidence intervals, clear differences among methods were found. The largest discrepancies were found between the different strategies for calculating confidence intervals. Our findings point towards the need for the meta-analyst to justify the statistical model assumed, as well as the transformation method of the reliability coefficients and the weighting scheme.