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A Note on the Relation between Coefficient Alpha and Guttman’s “split-half” Lower Bounds

Published online by Cambridge University Press:  01 January 2025

Paul H. Jackson
Paul H. Jackson*
Affiliation:
University College of Wales, Aberystwyth
*
Requests for reprints should be sent to P. H. Jackson, Department of Statistics, University College of Wales, Aberystwyth, Dyfed, Wales, U.K.
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Abstract

Use of the same term “split-half” for division of an n-item test into two subtests containing equal [Cronbach], and possibly unequal [Guttman], numbers of items sometimes leads to a misunderstanding about the relation between Guttman’s maximum split-half bound and Cronbach’s coefficient alpha.

Coefficient alpha is the average of split-half bounds in the Cronbach sense and so is not larger than the maximum split-half bound in either sense when n is even. When n is odd, however, splithalf bounds exist only in the Guttman sense and the largest of these may be smaller than coefficient alpha.

Keywords

reliability boundscoefficient alphasplit-half bounds
Type
Notes And Comments
Information
Psychometrika , Volume 44 , Issue 2 , June 1979 , pp. 251 - 252
Copyright
Copyright © 1979 The Psychometric Society

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References

Reference Note

Bentler, P. M. & Woodward, J. A. Inequalities among lower-bounds to reliability, 1977, Chapel Hill: University of North Carolina.Google Scholar

References

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Guttman, L. A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 255–282.CrossRefGoogle ScholarPubMed
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Rozeboom, W. W. Foundations of the theory of prediction, 1966, Homewood, Illinois: Dorsey Press.Google Scholar
Woodhouse, B. & Jackson, P. H. Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A Search Procedure to locate the Greatest Lower Bound. Psychometrika, 1977, 42, 579–591.CrossRefGoogle Scholar