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On the distribution of the maximum likelihood estimator of Cronbach's alpha


The asymptotic normal distribution of the maximum likelihood estimator of Cronbach's alpha (under normality) is derived for the case when no assumptions are made about the covariances among items. The asymptotic distribution is also considered for the special case of compound symmetry and compared to the exact distribution.

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The authors would like to thank Willem J. Heiser, an associate editor and the reviewers for valuable and helpful comments to improve the quality of this work.

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van Zyl, J.M., Neudecker, H. & Nel, D.G. On the distribution of the maximum likelihood estimator of Cronbach's alpha. Psychometrika 65, 271–280 (2000).

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Key words

  • compound symmetry
  • Cronbach's alpha
  • internal consistency
  • test reliability