The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

This note discusses the merits of coefficient alpha and their conditions in light of recent critical publications that miss out on significant research findings over the past several decades. That earlier research has demonstrated the empirical relevance and utility of coefficient alpha under certain empirical circumstances. The article highlights…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

A critical discussion of the assumption of uncorrelated errors in classical psychometric theory and its applications is provided. It is pointed out that this assumption is essential for a number of fundamental results and underlies the concept of parallel tests, the Spearman-Brown's prophecy and the correction for attenuation formulas as well as…

Outlines a correlation structures modeling approach to the study of stability in reliability of multiple, repeatedly administered measures and illustrates the method on data from a fluid intelligence study (P. Bates and others, 1986). The method is also applicable when examining relationships between model parameters across all variables.…

Studied the population discrepancy of coefficient alpha from the composite reliability coefficient for fixed congeneric measures with correlated errors and expressed it in terms of parameters of the measures. Recommends structural equation modeling for identifying cases in which the discrepancy can be large. (SLD)