Bivariate Dependence Orderings for Unordered Categorical Variables

  • A. Giovagnoli
  • J. Marzialetti
  • H. P. Wynn
Part of the Springer Optimization and Its Applications book series (SOIA, volume 28)


Interest in assessing the degree of association between two or more random variables has a long history in the statistical literature. Rather than measuring association, we want ways of comparing it. Restricting the attention in this chapter to unordered categorical random variables, we point at some possible definitions of dependence orderings which employ matrix theory and, to a lesser extent, group theory. This approach allows a unified investigation of the most common indicators in the statistical literature.

One very special type of association is the amount of agreement among different observers that classify the same group of statistical units: in the medical field this has led to widespread use of Cohen's Kappa. Starting with an axiomatic definition of agreement, we show its formal properties. Some criticism of Cohen's Kappa and other measures of agreement in use will ensue.


Order Relation Statistical Unit Permutation Matrix Stochastic Matrix Interrater Agreement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media LLC 2009

Authors and Affiliations

  1. 1.Department of Statistical Sciences, University of Bologna BolognaItaly
  2. 2.Department of Statistical Sciences, University of BolognaBolognaItaly
  3. 3.London School of Economics and Political ScienceLondonUK

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