On the Bias of Cronbach's Alpha

10.29973/JCSA.200406.0004

Hung Chen；Jia-Hui Chen

Cronbach's α ； reliability ； measurement theory ； classical test theory ； common factor model

中國統計學報

42卷2期（2004 / 06 / 01）

149 - 168

英文

Cronbach'sα is one of the most often used coefficient of reliability on establishing the validity of test instruments. Guttman (1945) showed that it is a lower bound on Ps, the reliability of any given test. In this paper, we quantify the positive bias Ps -αin terms of variability of the difference of true-scores of any two test items. In order to better understand the magnitude of the bias, we provide upper bounds on the magnitude of the bias under common factor model. These bounds reveal how the magnitude of the bias changes with the number of test items and variability of factor loadings among test items.

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