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Robust estimation of Cronbach's alpha


  • Christmann, A.
  • Van Aelst, S.


Cronbach's alpha is a popular method to measure reliability, e.g. in quantifying the reliability of a score to summarize the information of several items in questionnaires. The alpha coefficient is known to be non-robust. We study the behavior of this coefficient in different settings to identify situations where Cronbach's alpha is extremely sensitive to violations of the classical model assumptions. Furthermore, we construct a robust version of Cronbach's alpha which is insensitive to a small proportion of data that belong to a different source. The idea is that the robust Cronbach's alpha reflects the reliability of the bulk of the data. For example, it should not be possible that some small amount of outliers makes a score look reliable if it is not.

Suggested Citation

  • Christmann, A. & Van Aelst, S., 2006. "Robust estimation of Cronbach's alpha," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1660-1674, August.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1660-1674

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    References listed on IDEAS

    1. G. Kuder & M. Richardson, 1937. "The theory of the estimation of test reliability," Psychometrika, Springer;The Psychometric Society, vol. 2(3), pages 151-160, September.
    2. Louis Guttman, 1953. "Reliability formulas that do not assume experimental independence," Psychometrika, Springer;The Psychometric Society, vol. 18(3), pages 225-239, September.
    3. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    4. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    5. Helena Kraemer, 1981. "Extension of Feldt's approach to testing homogeneity of coefficients of reliability," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 41-45, March.
    6. Leonard Feldt, 1965. "The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty," Psychometrika, Springer;The Psychometric Society, vol. 30(3), pages 357-370, September.
    7. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    8. J. Berge & Frits Zegers, 1978. "A series of lower bounds to the reliability of a test," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 575-579, December.
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    Cited by:

    1. Marcus Selart & Svein Johansen, 2011. "Ethical Decision Making in Organizations: The Role of Leadership Stress," Journal of Business Ethics, Springer, vol. 99(2), pages 129-143, March.
    2. Leontitsis, Alexandros & Pagge, Jenny, 2007. "A simulation approach on Cronbach's alpha statistical significance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 336-340.


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