Behavior Research Methods

, Volume 39, Issue 1, pp 71–81

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


    • University of Southern California
  • Chih-Ping Chou
    • University of Southern California
  • Alan W. Stacy
    • University of Southern California
  • Huiyan Ma
    • University of Southern California
  • Jennifer Unger
    • University of Southern California
  • Peggy Gallaher
    • University of Southern California

DOI: 10.3758/BF03192845

Cite this article as:
Sun, W., Chou, C., Stacy, A.W. et al. Behav Res (2007) 39: 71. doi:10.3758/BF03192845


Cronbach’s α 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 α 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 α 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 α via this method. The simulation analysis showed that Cronbach’s α from upper-bound ϕ might be appropriate for estimating the real reliability when standardized Cronbach’s α is problematic.

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© Psychonomic Society, Inc. 2007