Inequalities Between Kappa and Kappa-Like Statistics for k×k Tables
By Matthijs J. Warrens. 2010
47 citations recorded by the source corpus.
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.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4e488bc054af033d99c7cbac3f3bb0fa972afb31
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In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Cohen's kappa is a weighted average (2011, unknown): “is the proportion of chance–expected agreement if it is assumed that the frequency distribution underlying the two nominal variables is the same for both variables [34,11,28].”
- Five ways to look at Cohen's kappa (2015, methodology): “However, since kappa has several useful interpretations, it is likely that it continues to be a standard tool for summarizing inter-rater agreement on a nominal scale in the near future [1,3,4,11,12].”
- Conditional inequalities between Cohen's kappa and weighted kappas (2013, methodology): “Popular descriptive statistics for summarizing the agreement between two raters are Cohen’s unweighted kappa, denoted by κ [7,19,22,27,30–35], and Cohen’s weighted kappa, denoted by κw [4,8,28].”