Hostname: page-component-7dd5485656-wxk4p Total loading time: 0 Render date: 2025-10-31T02:15:15.419Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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

Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 279–334.CrossRefGoogle Scholar
Guttman, L. A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 255–282.CrossRefGoogle ScholarPubMed
Jackson, P. H. & Agunwamba, C. Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic Lower Bounds. Psychometrika, 1977, 42, 567–578.CrossRefGoogle Scholar
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