Evaluating Cronbach's Coefficient Alpha and Testing Its Identity to Scale Reliability: A Direct Bayesian Confirmatory Factor Analysis Procedure

A Bayesian statistics-based approach is discussed that can be used for direct evaluation of the popular Cronbach's coefficient alpha as an internal consistency index for multiple-component measuring instruments, as well as for testing its identity to scale reliability. The method represents an application of confirmatory factor analysis within the Bayesian inference framework and is widely applicable in empirical measurement research using popular latent variable modeling software. The procedure readily furnishes posterior median point estimates and credible intervals of coefficient alpha. The approach also permits testing a necessary and sufficient condition for population equality of the alpha and scale reliability coefficients, and under its plausibility provides in addition a dependable means for estimation of instrument reliability. The outlined procedure is illustrated using numerical data.