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Cronbach’s Alpha under Insufficient Effort Responding: An Analytic Approach

Author

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  • Stephen W. Carden

    (Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA)

  • Trevor R. Camper

    (Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA)

  • Nicholas S. Holtzman

    (Department of Psychology, Georgia Southern University, Statesboro, GA 30458, USA)

Abstract

Surveys commonly suffer from insufficient effort responding (IER). If not accounted for, IER can cause biases and lead to false conclusions. In particular, Cronbach’s alpha has been empirically observed to either deflate or inflate due to IER. This paper will elucidate how IER impacts Cronbach’s alpha in a variety of situations. Previous results concerning internal consistency under mixture models are extended to obtain a characterization of Cronbach’s alpha in terms of item validities, average variances, and average covariances. The characterization is then applied to contaminating distributions representing various types of IER. The discussion will provide commentary on previous simulation-based investigations, confirming some previous hypotheses for the common types of IER, but also revealing possibilities from newly considered responding patterns. Specifically, it is possible that the bias can change from negative to positive (and vice versa) as the proportion of contamination increases.

Suggested Citation

  • Stephen W. Carden & Trevor R. Camper & Nicholas S. Holtzman, 2018. "Cronbach’s Alpha under Insufficient Effort Responding: An Analytic Approach," Stats, MDPI, vol. 2(1), pages 1-14, December.
    • Handle: RePEc:gam:jstats:v:2:y:2018:i:1:p:1-14:d:191866
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    References listed on IDEAS

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    1. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    2. 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.
    3. Klaas Sijtsma, 2009. "On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 107-120, March.
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