Table of Contents
Advances in Statistics
Volume 2014 (2014), Article ID 742863, 5 pages
http://dx.doi.org/10.1155/2014/742863
Research Article

On Cronbach’s Alpha as the Mean of All Possible -Split Alphas

Institute of Psychology, Unit of Methodology and Statistics, Leiden University, P.O. Box 9555, 2300 RB Leiden, The Netherlands

Received 13 July 2014; Accepted 17 September 2014; Published 30 September 2014

Academic Editor: Steve Su

Copyright © 2014 Matthijs J. Warrens. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Coefficient alpha is the most commonly used internal consistency reliability coefficient. Alpha is the mean of all possible -split alphas if the items are divided into parts of equal size. This result gives proper interpretations of alpha: interpretations that also hold if (some of) its assumptions are not valid. Here we consider the cases where the items cannot be split into parts of equal size. It is shown that if a -split is made such that the items are divided as evenly as possible, the difference between alpha and the mean of all possible -split alphas can be made arbitrarily small by increasing the number of items.