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Bivariate Dependence Orderings for Unordered Categorical Variables

In: Optimal Design and Related Areas in Optimization and Statistics

Author

Listed:
  • A. Giovagnoli

    (Department of Statistical Sciences, University of Bologna)

  • J. Marzialetti

    (Department of Statistical Sciences, University of Bologna)

  • H. P. Wynn

    (London School of Economics and Political Science)

Abstract

Summary 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.

Suggested Citation

  • A. Giovagnoli & J. Marzialetti & H. P. Wynn, 2009. "Bivariate Dependence Orderings for Unordered Categorical Variables," Springer Optimization and Its Applications, in: Luc Pronzato & Anatoly Zhigljavsky (ed.), Optimal Design and Related Areas in Optimization and Statistics, chapter 4, pages 81-96, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-79936-0_4
    DOI: 10.1007/978-0-387-79936-0_4
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