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A Generalization of Coefficient Alpha

Published online by Cambridge University Press:  01 January 2025

Nambury S. Raju
Nambury S. Raju*
Affiliation:
Science Research Associates
*
Requests for reprints should be sent to Nambury S. Raju, Science Research Associates, 259 East Erie Street, Chicago, Illinois 60611.
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Abstract

It is well known that coefficient alpha can be used to estimate the reliability of a test even when the test is split into several parts. It is also known that alpha can severely underestimate test reliability when the several parts have an unequal number of items. A gernalization of alpha, βk, is proposed to correct this defect. Several properties of βk are also presented.

Keywords

reliabilitycoefficient alpha

Information

Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 4 , December 1977, pp. 549 - 565
Copyright
Copyright © 1977 The Psychometric Society

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Footnotes

The author gratefully acknowledges the assistance of Dr. Leonard Feldt for reviewing an earlier draft of this paper, and Ms. Rita Karwacki Bode and Mr. Dave Mansell for the analysis of the experimental data reported here. The comments of an unknown referee which contributed substantially to the clarity of the presentation are also gratefully acknowledged.

References

Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.CrossRefGoogle Scholar
Feldt, L. S. Estimation of the reliability of a test divided into two parts of unequal length. Psychometrika, 1975, 40, 557–561.CrossRefGoogle Scholar
Horst, P. Estimating total test reliability from parts of unequal length. Educational and Psychological Measurement, 1951, 11, 368–371.CrossRefGoogle Scholar
Kristof, W. Estimation of reliability and true score variance from a split of a test into three arbitrary parts. Psychometrika, 1974, 39, 491–499.CrossRefGoogle Scholar
Lord, F. M. and Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Novick, M. R. and Lewis, C. Coefficient alpha and the reliability of composite measurements. Psychometrika, 1967, 32, 1–13.CrossRefGoogle ScholarPubMed
Rajaratnam, N., Cronbach, L. J., & Gleser, G. C. Generalizability of Stratified—Parallel Tests. Psychometrika, 1975, 30, 39–56.CrossRefGoogle Scholar
Raju, N. S. New formula for estimating total test reliability from parts of unequal length, Proceedings, 78th Annual Convention, APA, 1970, 143-144.Google Scholar
Rulon, P. J. A simplified procedure for determining the reliability of a test by split-halves. Harvard Educational Review, 1939, 9, 99-103.Google Scholar