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1 results

  • Inequalities Between Kappa and Kappa-Like Statistics for k × k Tables

  • Matthijs J. Warrens
  • Journal:
    Psychometrika / Volume 75 / Issue 1 / March 2010
    Published online by Cambridge University Press:
    01 January 2025, pp. 176-185
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  • The paper presents inequalities between four descriptive statistics that can be expressed in the form [P − E(P)]/[1 − E(P)], where P is the observed proportion of agreement of a k × k table with identical categories, and E(P) is a function of the marginal probabilities. Scott’s π is an upper bound of Goodman and Kruskal’s λ and a lower bound of both Bennett et al. S and Cohen’s κ. We introduce a concept for the marginal probabilities of the k×k table called weak marginal symmetry. Using the rearrangement inequality, it is shown that Bennett et al. S is an upper bound of Cohen’s κ if the k×k table is weakly marginal symmetric.