Coefficients Alpha, Beta, Omega, and the glb: Comments on Sijtsma

2008/12/10 by William Revelle, Richard E. Zinbarg · 1,624 citations
Decision Sciences · Mathematics · Psychology · #Alpha (finance) #BETA (programming language) #Behavioral and Psychological Studies #Cognitive Abilities and Testing #Computer science #Cronbach's alpha #Mathematics #Omega #Philosophy #Physics #Programming language #Psychometric Methodologies and Testing #Psychometrics #Reliability (semiconductor) #Statistics #Test (biology) #Test validity #Validation test

paper · doi:10.1007/s11336-008-9102-z

published in Psychometrika 74(1), 145-154 (Springer Science+Business Media)

openalex publication_date 2008/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

There are three fundamental problems in Sijtsma (Psychometrika, 2008): (1) contrary to the name, the glb is not the greatest lower bound of reliability but rather is systematically less than ω t (McDonald, Test theory: A unified treatment, Erlbaum, Hillsdale, 1999), (2) we agree with Sijtsma that when considering how well a test measures one concept, α is not appropriate, but recommend ω t rather than the glb, and (3) the end user needs procedures that are readily available in open source software.

Citations

• The Proof and Measurement of Association between Two Things
• Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their Relations with Each Other and Two Alternative Conceptualizations of Reliability
• My Current Thoughts on Coefficient Alpha and Successor Procedures
• Coefficient Alpha and the Internal Structure of Tests
• Generalizability in Factorable Domains: "Domain Validity and Generalizability"1

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Related

• My Current Thoughts on Coefficient Alpha and Successor Procedures
• Your Coefficient Alpha Is Probably Wrong, but Which Coefficient Omega Is Right? A Tutorial on Using R to Obtain Better Reliability Estimates
• Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their Relations with Each Other and Two Alternative Conceptualizations of Reliability
• A Primer on Reliability via Coefficient Alpha and Omega
• A note on the alpha-level: Not all alphas can be justified