A SAS Macro to Calculate Standardized Cronbach’s alpha using Upper Bound phi Coefficient for Dichotomous Items

Cronbach’s alpha is widely used in social science research to estimate the internal consistency 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. 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. A SAS macro, M_UB_Alpha, has been developed in this paper to obtain standardized Cronbach’s alpha based on this method. The simulation analysis showed that Cronbach’s alpha from up-bound phi might be appropriate to estimate the real reliability when standardized Cronbach’s alpha is problematic.