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Measure of departure from marginal point-symmetry for two-way contingency tables

Author

Listed:
  • Kouji Yamamoto

    (Center of Clinical Investigation and Researc h, Osaka University Hospital - Japan)

  • Kouji Tahata

    (Department of Information Sciences, Faculty of Sciences and Technology Tokyo University of Sciences - Japan)

  • Motoko Suzuki

    (Department of Information Sciences, Faculty of Sciences and Technology Tokyo University of Sciences - Japan)

  • Sadao Tomizawa

    (Department of Information Sciences, Faculty of Sciences and Technology, Tokyo University of Sciences - Japan)

Abstract

For two-way contingency tables, Tomizawa (1985) considered the point-symmetry and marginal point-symmetry models, and omizawa, Yamamoto and Tahata (2007) proposed a measure to represent the degree of departure from point-symmetry. The present paper proposes a measure to represent the degree of departure from marginal pointsymmetry for two-way tables. The proposed measure is expressed by using Cressie-Read power-divergence or Patil-Taillie diversity index. This measure would be useful for comparing the degrees of departure from marginal point-symmetry in several tables. The relationship between the degree of departure from marginal point-symmetry and the measure is shown when it is reasonable to assume underlying bivariate normal distribution. Examples are shown.

Suggested Citation

  • Kouji Yamamoto & Kouji Tahata & Motoko Suzuki & Sadao Tomizawa, 2011. "Measure of departure from marginal point-symmetry for two-way contingency tables," Statistica, Department of Statistics, University of Bologna, vol. 71(3), pages 367-380.
    • Handle: RePEc:bot:rivsta:v:71:y:2011:i:3:p:367-380
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