Measure of Departure from Point Symmetry and Decomposition of Measure for Square Contingency Tables

Abstract

For square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present paper proposes Kullback–Leibler information type measures to represent the degree of departure from each of the models. Also this paper shows a theorem that the measure for the another point symmetry model is equal to the sum of the measures for the reverse global symmetry model and for the conditional point symmetry model.

Keywords

• Conditional symmetry
• Global symmetry
• Kullback–Leibler information
• Measure
• Point symmetry
• Square contingency table