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Some Relationships Between Cronbach’s Alpha and the Spearman-Brown Formula

Some Relationships Between Cronbach’s Alpha and the Spearman-Brown Formula Cronbach’s alpha is an estimate of the reliability of a test score if the items are essentially tau-equivalent. Several authors have derived results that provide alternative interpretations of alpha. These interpretations are also valid if essential tau-equivalency does not hold. For example, alpha is the mean of all split-half reliabilities if the test is split into two halves that are equal in size. This note presents several connections between Cronbach’s alpha and the Spearman-Brown formula. The results provide new interpretations of Cronbach’s alpha, the stepped down alpha, and standardized alpha, that are also valid in the case that essential tau-equivalency or parallel equivalency do not hold. The main result is that the stepped down alpha is a weighted average of the alphas of all subtests of a specific size, where the weights are the denominators of the subtest alphas. Thus, the stepped down alpha can be interpreted as an average subtest alpha. Furthermore, we may calculate the stepped down alpha without using the Spearman-Brown formula. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Some Relationships Between Cronbach’s Alpha and the Spearman-Brown Formula

Warrens, Matthijs
Journal of Classification , Volume 32 (1) – Mar 21, 2015
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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Classification Society of North America
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal, Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s00357-015-9168-0
Publisher site
See Article on Publisher Site

Abstract

Cronbach’s alpha is an estimate of the reliability of a test score if the items are essentially tau-equivalent. Several authors have derived results that provide alternative interpretations of alpha. These interpretations are also valid if essential tau-equivalency does not hold. For example, alpha is the mean of all split-half reliabilities if the test is split into two halves that are equal in size. This note presents several connections between Cronbach’s alpha and the Spearman-Brown formula. The results provide new interpretations of Cronbach’s alpha, the stepped down alpha, and standardized alpha, that are also valid in the case that essential tau-equivalency or parallel equivalency do not hold. The main result is that the stepped down alpha is a weighted average of the alphas of all subtests of a specific size, where the weights are the denominators of the subtest alphas. Thus, the stepped down alpha can be interpreted as an average subtest alpha. Furthermore, we may calculate the stepped down alpha without using the Spearman-Brown formula.

Journal

Journal of Classification – Springer Journals

Published: Mar 21, 2015

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