Scale reliability, Cronbach's Coefficient Alpha, and violations of essential tau-equivalence with fixed congeneric components

The population discrepancy between Cronbach's Coefficient Alpha and scale reliability with fixed congeneric measures, uncorrelated errors, and sampling of subjects is studied. This difference is expressed in terms of individual component violations of the assumption of essential tau-equivalence that is necessary and sufficient for Alpha to equal composite reliability. An upper bound of the discrepancy is obtained and its magnitude assessed in practical contexts of informed scale development. As an alternative when the difference may be considerable, a latent variable model is recommended for estimating scale reliability.