Skip to main content
Log in

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

  • Theory and Methods
  • Published:
Psychometrika Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Bentler, P., & Woodward, J. (1980). Inequalities among lower bounds to reliability: With applications to test construction and factor analysis. Psychometrika, 45(2), 249–267.

    Article  Google Scholar 

  • Brown, W. (1910). Some experimental results in the correlation of mental abilities. British Journal of Psychology, 3(3), 296–322.

    Google Scholar 

  • Cronbach, L.J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334.

    Article  Google Scholar 

  • Cronbach, L.J. (1988). Internal consistency of tests: Analyses old and new. Psychometrika, 53(1), 63–70.

    Article  Google Scholar 

  • Cronbach, L.J., & Shavelson, R.J. (2004). My current thoughts on coefficient alpha and successor procedures. Educational and Psychological Measurement, 64(3), 391–418.

    Article  Google Scholar 

  • De Leeuw, J. (1983). Models and methods for the analysis of correlation coefficients. Journal of Econometrics, 22(1–2), 113–137.

    Article  Google Scholar 

  • Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10(4), 255–282.

    Article  Google Scholar 

  • Jackson, P., & Agunwamba, C. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic lower bounds. Psychometrika, 42(4), 567–578.

    Article  Google Scholar 

  • Lord, F.M. (1955). Sampling fluctuations resulting from the sampling of test items. Psychometrika, 20(1), 1–22.

    Article  Google Scholar 

  • Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley.

    Google Scholar 

  • McDonald, R.P. (1978). Generalizability in factorable domains: “domain validity and generalizability” 1. Educational and Psychological Measurement, 38(1), 75–79.

    Article  Google Scholar 

  • McDonald, R.P. (1999). Test theory: A unified treatment. Hillsdale: Erlbaum.

    Google Scholar 

  • McNemar, Q. (1946). Opinion-attitude methodology. Psychological Bulletin, 43(4), 289–374.

    Article  Google Scholar 

  • R Development Core Team. (2008). R: A language and environment for statistical computing. Vienna, Austria (ISBN 3-900051-07-0).

  • Rafaeli, E., & Revelle, W. (2006). A premature consensus: Are happiness and sadness truly opposite affects? Motivation and Emotion, 30(1), 1–12.

    Article  Google Scholar 

  • Raykov, T., & Shrout, P.E. (2002). Reliability of scales with general structure: Point and interval estimation using a structural equation modeling approach. Structural Equation Modeling, 9(2), 195–212.

    Article  Google Scholar 

  • Revelle, W. (1979). Hierarchical cluster-analysis and the internal structure of tests. Multivariate Behavioral Research, 14(1), 57–74.

    Article  Google Scholar 

  • Revelle, W. (2008). psych: Procedures for personality and psychological research (R package version 1.0-51).

  • Schmid, J.J., & Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22(1), 83–90.

    Article  Google Scholar 

  • Sijtsma, K. (2008). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika.

  • Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72–101.

    Article  Google Scholar 

  • Spearman, C. (1910). Correlation calculated from faulty data. British Journal of Psychology, 3(3), 271–295.

    Google Scholar 

  • Ten Berge, J.M.F., & Hofstee, W.K.B. (1999). Coefficients alpha and reliabilities of unrotated and rotated components. Psychometrika, 64(1), 83–90.

    Article  Google Scholar 

  • Ten Berge, J.M.F., & Socan, G. (2004). The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika, 69(4), 613–625.

    Article  Google Scholar 

  • Ten Berge, J.M.F., & Zegers, F.E. (1978). A series of lower bounds to the reliability of a test. Psychometrika, 43(4), 575–579.

    Article  Google Scholar 

  • Warner, W.L. (1960). Social class in America: a manual of procedure for the measurement of social status. New York: Harper.

    Google Scholar 

  • Woodhouse, B., & Jackson, P. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound. Psychometrika, 42(4), 579–591.

    Article  Google Scholar 

  • Zinbarg, R.E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω H : Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 123–133.

    Article  Google Scholar 

  • Zinbarg, R.E., Yovel, I., Revelle, W., & McDonald, R.P. (2006). Estimating generalizability to a latent variable common to all of a scale’s indicators: A comparison of estimators for ω h . Applied Psychological Measurement, 30(2), 121–144.

    Article  Google Scholar 

  • Zinbarg, R.E., Revelle, W., & Yovel, I. (2007). Estimating ω h for structures containing two group factors: Perils and prospects. Applied Psychological Measurement, 31(2), 135–157.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to William Revelle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Revelle, W., Zinbarg, R.E. Coefficients Alpha, Beta, Omega, and the glb: Comments on Sijtsma. Psychometrika 74, 145–154 (2009).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: