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A Series of Lower Bounds to the Reliability of a Test

Published online by Cambridge University Press:  01 January 2025

Jos. M. F. ten Berge  and
Frits E. Zegers
Jos. M. F. ten Berge*
Affiliation:
University of Groningen
Frits E. Zegers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Department of Psychology, University of Groningen, Oude Boteringestraat 34, Groningen, The Netherlands.
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Abstract

Two well-known lower bounds to the reliability in classical test theory, Guttman’s λ2 and Cronbach’s coefficient alpha, are shown to be terms of an infinite series of lower bounds. All terms of this series are equal to the reliability if and only if the test is composed of items which are essentially tau-equivalent. Some practical examples, comparing the first 7 terms of the series, are offered. It appears that the second term (λ2) is generally worth-while computing as an improvement of the first term (alpha) whereas going beyond the second term is not worth the computational effort. Possibly an exception should be made for very short tests having widely spread absolute values of covariances between items. The relationship of the series and previous work on lower bound estimates for the reliability is briefly discussed.

Keywords

internal consistencyhomogeneity

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 4 , December 1978 , pp. 575 - 579
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The authors are obliged to Henk Camstra for providing a computer program that was used in this study.

References

Cronbach, L. J.. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.CrossRefGoogle Scholar
Guttman, L.. A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 255–282.CrossRefGoogle ScholarPubMed
Jackson, P. H. & Agunwamba, C. C.. Lower bounds for the reliability of the total score on a test composed of nonhomogeneous items: I. Algebraic lower bounds. Psychometrika, 1977, 42, 567–578.CrossRefGoogle Scholar
Kuder, G. F. & Richardson, M. W.. The theory of the estimation of test reliability. Psychometrika, 1937, 2, 151–160.CrossRefGoogle Scholar
Lord, F. M. & Novick, M. R.. Statistical theories of mental test scores, 1974, Reading, Mass.: Addison-Wesley.Google Scholar
Woodhouse, B. & Jackson, P. H.. Lower bounds for the reliability of the total score on a test composed of nonhomogeneous items: II. A search procedure to locate the greatest lower bound. Psychometrika, 1977, 42, 579–591.CrossRefGoogle Scholar