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Measure of departure from symmetry for the analysis of collapsed square contingency tables with ordered categories

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  • Kouji Yamamoto
  • Fumika Shimada
  • Sadao Tomizawa

Abstract

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers the symmetry model for collapsed square contingency tables and proposes a measure to represent the degree of departure from symmetry. The proposed measure is defined as the arithmetic mean of submeasures each of which represents the degree of departure from symmetry for each collapsed 3×3 table. Each submeasure also represents the mean of power-divergence or diversity index for each collapsed table. Examples are given.

Suggested Citation

  • Kouji Yamamoto & Fumika Shimada & Sadao Tomizawa, 2015. "Measure of departure from symmetry for the analysis of collapsed square contingency tables with ordered categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(4), pages 866-875, April.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:4:p:866-875
    DOI: 10.1080/02664763.2014.993362
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    References listed on IDEAS

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    1. Sadao Tomizawa & Takashi Seo & Hideharu Yamamoto, 1998. "Power-divergence-type measure of departure from symmetry for square contingency tables that have nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(3), pages 387-398.
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