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ON THE EQUIVALENCE OF SOME INDICES OF SIMILARITY: IMPLICATION FOR BINARY PRESENCE/ABSENCE DATA

Authors

  • Ahmed N. Albatineh,

    Corresponding author
    1. Florida International University and Western Michigan University
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    • Department of Biostatistics, Robert Stemple College of Public Health and Social Work, Florida International University, Miami, Florida, U.S.A. e-mail: aalbatin@fiu.edu

  • Hafiz M.R. Khan,

    1. Florida International University and Western Michigan University
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    • Department of Biostatistics, Robert Stemple College of Public Health and Social Work, Florida International University, Miami, Florida, U.S.A. e-mail: aalbatin@fiu.edu

  • Magdalena Niewiadomska-Bugaj

    1. Florida International University and Western Michigan University
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    • Department of Statistics, Western Michigan University, Kalamazoo, Michigan, U.S.A.


  • Acknowledgements. The authors thank the editor and two anonymous referees for their valuable comments and suggestions that improved the presentation of the paper.

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Summary

Cohen’s kappa, a special case of the weighted kappa, is a chance-corrected index used extensively to quantify inter-rater agreement in validation and reliability studies. In this paper, it is shown that in inter-rater agreement for 2 × 2 tables, for two raters having the same number of opposite ratings, the weighted kappa, Cohen’s kappa, Peirce, Yule, Maxwell and Pilliner and Fleiss indices are identical. This implies that the weights in the weighted kappa are less important under such assumptions. Equivalently, it is shown that for two partitions of the same data set, resulting from two clustering algorithms having the same number of clusters with equal cluster sizes, these similarity indices are identical. Hence, an important characterisation is formulated relating equal numbers of clusters with the same cluster sizes to the presence/absence of a trait in a reliability study. Two numerical examples that exemplify the implication of this relationship are presented.

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