McDonald's omega(t), Cronbach's alpha, and Generalized theta for Composite Reliability of Common Factors Structures

Simsek G., Noyan F.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol.42, no.9, pp.2008-2025, 2013 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 9
  • Publication Date: 2013
  • Doi Number: 10.1080/03610918.2012.689062
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2008-2025
  • Keywords: Common factors, Composite reliability, Cronbach's alpha, McDonald's omega total, Simulation, 62H25, 65C05, COEFFICIENT-ALPHA, INTERNAL CONSISTENCY, CORRELATED ERRORS, LOWER BOUNDS, SCALES, SCORE


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.