Research Article Open Access

Geometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered Categories

Tomoyuki Nakagawa1, Toshiki Takei1, Aki Ishii1 and Sadao Tomizawa1
  • 1 Tokyo University of Science, Japan
Journal of Mathematics and Statistics
Volume 16 No. 1, 2020, 170-175

DOI: https://doi.org/10.3844/jmssp.2020.170.175

Submitted On: 15 June 2020 Published On: 11 August 2020

How to Cite: Nakagawa, T., Takei, T., Ishii, A. & Tomizawa, S. (2020). Geometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered Categories. Journal of Mathematics and Statistics, 16(1), 170-175. https://doi.org/10.3844/jmssp.2020.170.175

Abstract

For square contingency tables, some studies have developed the weighted arithmetic mean type measure to represent the degree of departure from the marginal homogeneity. The present paper proposes (1) the cumulative partial marginal homogeneity model which has the weaker restriction than the marginal homogeneity model and (2) the measure to represent the degree of departure from the proposed model. The measure is expressed as a weighted geometric mean of the diversity index. Finally, numerical studies are presented.

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Keywords

  • Geometric Mean
  • Marginal Homogeneity
  • Measure
  • Square Contingency Table