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On Robusiness of the Normal-Theory Based Asymptotic Distributions of Three Reliability Coefficient Estimates

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan  and
Peter M. Bentler
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Peter M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Ke-Hai Yuan, Department of Psychology, University of Notre Dame, Notre Dame, IN 46556. E-Mail: [email protected]
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Abstract

This paper studies the asymptotic distributions of three reliability coefficient estimates: Sample coefficient alpha, the reliability estimate of a composite score following a factor analysis, and the estimate of the maximal reliability of a linear combination of item scores following a factor analysis. Results indicate that the asymptotic distribution for each of the coefficient estimates, obtained based on a normal sampling distribution, is still valid within a large class of nonnormal distributions. Therefore, a formula for calculating the standard error of the sample coefficient alpha, recently obtained by van Zyl, Neudecker and Nel, applies to other reliability coefficients and can still be used even with skewed and kurtotic data such as are typical in the social and behavioral sciences.

Keywords

asymptotic distributionCronbach's alphakurtosismaximal reliabilitypseudo normal distributionsskewness
Type
Articles
Information
Psychometrika , Volume 67 , Issue 2 , June 2002 , pp. 251 - 259
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.

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