Methods for averaging alpha coefficients in reliability generalization studies

The reliability generalization (RG) approach is a kind of meta-analysis that aims to statistically integrate a set of independent reliability coefficients obtained in several applications of a test, with the purpose of characterizing the measurement error and determining which factors related to the studies and samples can explain its variability. Diverse procedures have been proposed in the literature for averaging a set of independent alpha coefficients, and there is no consensus about which methods are best. Here, we present the results of a Monte Carlo simulation study, comparing the performance of twelve procedures proposed in Feldt and Charter, in terms of bias and mean square error. These procedures differ from each other in the transformation (or not) of the coefficients, and in the application or not of a weighting scheme based on sample size. Our results recommend using weighted methods in contrast to unweighted ones, and transforming the coefficients by the Hakstian and Whalen's proposal or by the proposal based on the square root of the inverse alpha coefficient. Lastly, we discuss the relations between the diverse procedures for averaging alpha coefficients with fixed-effects, random-effects, and varying coefficients models.