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A Comparison of Reliability Coefficients for Ordinal Rating Scales

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  • Alexandra Raadt

    (University of Groningen)

  • Matthijs J. Warrens

    (University of Groningen)

  • Roel J. Bosker

    (University of Groningen)

  • Henk A. L. Kiers

    (University of Groningen)

Abstract

Kappa coefficients are commonly used for quantifying reliability on a categorical scale, whereas correlation coefficients are commonly applied to assess reliability on an interval scale. Both types of coefficients can be used to assess the reliability of ordinal rating scales. In this study, we compare seven reliability coefficients for ordinal rating scales: the kappa coefficients included are Cohen’s kappa, linearly weighted kappa, and quadratically weighted kappa; the correlation coefficients included are intraclass correlation ICC(3,1), Pearson’s correlation, Spearman’s rho, and Kendall’s tau-b. The primary goal is to provide a thorough understanding of these coefficients such that the applied researcher can make a sensible choice for ordinal rating scales. A second aim is to find out whether the choice of the coefficient matters. We studied to what extent we reach the same conclusions about inter-rater reliability with different coefficients, and to what extent the coefficients measure agreement in a similar way, using analytic methods, and simulated and empirical data. Using analytical methods, it is shown that differences between quadratic kappa and the Pearson and intraclass correlations increase if agreement becomes larger. Differences between the three coefficients are generally small if differences between rater means and variances are small. Furthermore, using simulated and empirical data, it is shown that differences between all reliability coefficients tend to increase if agreement between the raters increases. Moreover, for the data in this study, the same conclusion about inter-rater reliability was reached in virtually all cases with the four correlation coefficients. In addition, using quadratically weighted kappa, we reached a similar conclusion as with any correlation coefficient a great number of times. Hence, for the data in this study, it does not really matter which of these five coefficients is used. Moreover, the four correlation coefficients and quadratically weighted kappa tend to measure agreement in a similar way: their values are very highly correlated for the data in this study.

Suggested Citation

  • Alexandra Raadt & Matthijs J. Warrens & Roel J. Bosker & Henk A. L. Kiers, 2021. "A Comparison of Reliability Coefficients for Ordinal Rating Scales," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 519-543, October.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:3:d:10.1007_s00357-021-09386-5
    DOI: 10.1007/s00357-021-09386-5
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    References listed on IDEAS

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    1. Christof Schuster & David Smith, 2005. "Dispersion-weighted kappa: An integrative framework for metric and nominal scale agreement coefficients," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 135-146, March.
    2. Hauke Jan & Kossowski Tomasz, 2011. "Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data," Quaestiones Geographicae, Sciendo, vol. 30(2), pages 87-93, June.
    3. Sergio Munoz & Shrikant Bangdiwala, 1997. "Interpretation of Kappa and B statistics measures of agreement," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(1), pages 105-112.
    4. Matthijs Warrens, 2014. "Corrected Zegers-ten Berge Coefficients Are Special Cases of Cohen’s Weighted Kappa," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 179-193, July.
    5. Robert Fagot, 1993. "A generalized family of coefficients of relational agreement for numerical scales," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 357-370, June.
    6. Hubert Schouten, 1986. "Nominal scale agreement among observers," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 453-466, September.
    7. Matthijs Warrens, 2010. "Inequalities between multi-rater kappas," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 271-286, December.
    8. Matthijs Warrens, 2012. "Some Paradoxical Results for the Quadratically Weighted Kappa," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 315-323, April.
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    1. Rutger Oest, 2023. "The Dependence of Chance-Corrected Weighted Agreement Coefficients on the Power Parameter of the Weighting Scheme: Analysis and Measurement," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 554-579, June.

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