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On the Distribution of the Maximum Likelihood Estimator of Cronbach's Alpha

Published online by Cambridge University Press:  01 January 2025

J. M. van Zyl ,
H. Neudecker  and
D. G. Nel
J. M. van Zyl*
Affiliation:
Department of Mathematical Statistics, University of the Orange Free State
H. Neudecker
Affiliation:
Cesaro, The Netherlands
D. G. Nel
Affiliation:
Statistical Research, Clover SA, South Africa
*
Requests for reprints should be sent to J.M. van Zyl, Department of Mathematical Statistics, University of the Orange Free State, P.O. Box 339, Bloemfontein 9300, SOUTH AFRICA.
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Abstract

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.

Keywords

compound symmetryCronbach's alphainternal consistencytest reliability
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 271 - 280
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

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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