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Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 349–356 | Cite as

Measure for Uniform Association Based on Concordant and Discordant Pairs for Cross-classifications

  • Kouji Tahata
  • Sadao Tomizawa
Article

Abstract

For cross-classifications with ordered categories, a measure is proposed to represent the degree of departure from uniform association. The measure is expressed by using the Shannon entropy or the Kullback-Leibler information, based on the probabilities for concordant and discordant adjacent pairs. It would be useful when one wants to use a single summary measure to measure the degree of departure from equality of conditional probabilities for concordant adjacent pairs and those for discordant adjacent pairs, which also represents the degree of departure from uniform association. Examples are given.

AMS Subject Classification

62H17 

Key-words

Kullback-Leibler information Local odds ratio Shannon entropy 

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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of Information Sciences, Faculty of Science and TechnologyTokyo University of ScienceNoda CityJapan

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