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

In the common factor model for subtest scores, several reliability coefficients, including Cronbach's α, have been found to be biased. In this article, we introduce a new coefficient, θG, or Generalized θ, which is a generalized version of Armor's θ coefficient and is equal to the true reliability when the dimensions are orthogonal and the measures are parallel. We assessed the McDonald's ωt, α, and θG in terms of mean bias, efficiency, and precision using a Monte Carlo simulation. θG outperformed ωt when the factors were orthogonal or nearly orthogonal with low correlations between them.