A Direct Method for Obtaining Approximate Standard Error and Confidence Interval of Maximal Reliability for Composites With Congeneric Measures

Unlike a substantial part of reliability literature in the past, this article is concerned with weighted combinations of a given set of congeneric measures with uncorrelated errors. The relationship between maximal coefficient alpha and maximal reliability for such composites is initially dealt with, and it is shown that the former is a lower bound of the latter. A direct method for obtaining approximate standard error and confidence interval for maximal reliability is then outlined. The procedure is based on a second-order Taylor series approximation and is readily and widely applicable in empirical research via use of covariance structure modeling. The described method is illustrated with a numerical example.