McDonald's ω_t, 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 α, have been found to be biased. In this article, we introduce a new coefficient, θ_G, 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 ω_t, α, and θ_G in terms of mean bias, efficiency, and precision using a Monte Carlo simulation. θ_G outperformed ω_t when the factors were orthogonal or nearly orthogonal with low correlations between them.

Keywords:

• Common factors
• Composite reliability
• Cronbach's alpha
• McDonald's omega total
• Simulation

Mathematics Subject Classification:

• 62H25
• 65C05

Acknowledgments

The authors would like to express their gratitude to the referees, who offered extremely valuable suggestions for improvements in the earlier version of this study.