SAS and SPSS macros to calculate standardized Cronbach's alpha using the upper bound of the phi coefficient for dichotomous items

Abstract

Cronbach's a is widely used in social science research to estimate the internal consistency of reliability of a measurement scale. However, when items are not strictly parallel, the Cronbach's a coefficient provides a lower-bound estimate of true reliability, and this estimate may be further biased downward when items are dichotomous. The estimation of standardized Cronbach's a for a scale with dichotomous items can be improved by using the upper bound of coefficient φ. SAS and SPSS macros have been developed in this article to obtain standardized Cronbach's a via this method. The simulation analysis showed that Cronbach's a from upper-bound φ might be appropriate for estimating the real reliability when standardized Cronbach's a is problematic. Copyright 2007 Psychonomic Society, Inc.