Abstract: Two kinds of measures are proposed to represent the degree of departure from symmetry about the main diagonal of square contingency tables having the same nominal row and column classifications. One measure is expressed by using the Kullback-Leibler information (or the average of conditional Shannon entropy), and the other is expressed by using the Pearson's chi-squared type discrepancy (or the average of conditional Gauss discrepancy). These measures would be useful for comparing the degree of departure from symmetry in several tables.
Key words and phrases: Gauss discrepancy, Kullback-Leibler information, Pearson's chi-squared type discrepancy, Shannon entropy.