McDonald's ωt, Cronbach's α, and Generalized θ for Composite Reliability of Common Factors Structures

Abstract

In the common factor model for subtest scores, several reliability coefficients, including Cronbach's alpha, have been found to be biased. In this article, we introduce a new coefficient, theta(G), or Generalized theta, which is a generalized version of Armor's theta coefficient and is equal to the true reliability when the dimensions are orthogonal and the measures are parallel. We assessed the McDonald's omega(t), alpha, and theta(G) in terms of mean bias, efficiency, and precision using a Monte Carlo simulation. theta(G) outperformed omega(t) when the factors were orthogonal or nearly orthogonal with low correlations between them.