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Results on the Standard Error of the Coefficient Alpha Index of Reliability

Author

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  • Adam Duhachek

    (Department of Marketing, Kelley School of Business, Indiana University, Bloomington, Indiana 47405)

  • Anne T. Coughlan

    (Northwestern University, Evanston, Illinois 60208)

  • Dawn Iacobucci

    (Department of Marketing, Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19428)

Abstract

In this research, we investigate the behavior of Cronbach’s coefficient alpha and its new standard error. We systematically analyze the effects of sample size, scale length, strength of item intercorrelations, and scale dimensionality. We demonstrate the beneficial effects of sample size on alpha’s standard error and of scale length and the strengths of item intercorrelations (effects that are substitutes in their benefits) on both alpha and its standard error. Our findings also speak to this adage: Heterogeneity within the item covariance matrix (e.g., through multidimensionality or poor items) negatively impacts reliability by decreasing the precision of the estimation. We also examined the question of “equilibrium” scale length, showing the conditions for which it is optimal to add no items, or one, or multiple items to a scale. In terms of “best practices,” we recommend that researchers report a confidence interval or standard error along with the coefficient alpha point estimate.

Suggested Citation

  • Adam Duhachek & Anne T. Coughlan & Dawn Iacobucci, 2005. "Results on the Standard Error of the Coefficient Alpha Index of Reliability," Marketing Science, INFORMS, vol. 24(2), pages 294-301, July.
  • Handle: RePEc:inm:ormksc:v:24:y:2005:i:2:p:294-301
    DOI: 10.1287/mksc.1040.0097
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    2. Verbeke, W.J.M.I. & Wuyts, S.H.K., 2006. "Moving in Social Circles – Social Circle Membership and Performance Implications," ERIM Report Series Research in Management ERS-2006-041-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Massimiliano Pastore & Luigi Lombardi, 2014. "The impact of faking on Cronbach’s alpha for dichotomous and ordered rating scores," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1191-1211, May.
    4. Amir T. Payandeh Najafabadi & Maryam Omidi Najafabadi, 2016. "On the Bayesian estimation for Cronbach's alpha," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2416-2441, October.
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