A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables

Abstract

The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-dimensional index is constructed by combining two existing indexes. Although the existing indexes are constructed using power divergence, the existing two-dimensional index that can concurrently measure both symmetries is constructed using only Kullback-Leibler information, which is a special case of power divergence. Previous studies note the importance of using several indexes of divergence to compare the degrees of deviation from a model for several square contingency tables. This study, therefore, proposes a two-dimensional index based on power divergence in order to measure deviation from double symmetry for square contingency tables. Numerical examples show the utility of the proposed two-dimensional index using two datasets.

Keywords

• confidence region
• measure
• point symmetry
• power divergence
• symmetry