Cronbach's alpha 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 alpha 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 alpha for a scale with dichotomous items can be improved by using the upper bound of coefficient phi. 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 phi, might be appropriate for estimating the real reliability when standardized Cronbach's alpha is problematic.
