2009 年 36 巻 1 号 p. 75-86
For square contingency tables, Tomizawa (1994), Tomizawa, Seo and Yamamoto (1998) and Tomizawa, Miyamoto and Hatanaka (2001) considered the power-divergence-type measures to represent the degree of departure from symmetry. These measures lie between 0 and 1, and have a characteristic that the degree of departure from symmetry is the minimum when the symmetry holds and the maximum when one of the probabilities in any two symmetric cells is zero. This paper proposes the generalization of these measures so that the degree of departure from symmetry can attain the maximum value 1 even when each of cell probabilities is not zero. Two kinds of measures are proposed. One is applied to the nominal data and the other is applied to the ordinal data. These measures would be useful for representing the degree of departure from symmetry when each of cell probabilities is not zero.
