Varying Coefficient Meta-Analytic Methods for Alpha Reliability

The conventional fixed-effects (FE) and random-effects (RE) confidence intervals that are used to assess the average alpha reliability across multiple studies have serious limitations. The FE method, which is based on a constant coefficient model, assumes equal reliability coefficients across studies and breaks down under minor violations of this assumption. The RE method, which is based on a random coefficient model, assumes that the selected studies are a random sample from a normally distributed superpopulation. The RE method performs poorly in typical meta-analytic applications where the studies have not been randomly sampled from a normally distributed superpopulation or have been randomly sampled from a nonnormal superpopulation. A new confidence interval for the average reliability coefficient of a specific measurement scale is based on a varying coefficient statistical model and is shown to perform well under realistic conditions of reliability heterogeneity and nonrandom sampling of studies. New methods are proposed for assessing reliability moderator effects. The proposed methods are especially useful in meta-analyses that involve a small number of carefully selected studies for the purpose of obtaining a more accurate reliability estimate or to detect factors that moderate the reliability of a scale.