Kullback-Leibler Information type Measure of Departure from Conditional Symmetry and Decomposition of Measure from Symmetry for Contingency Tables

For the analysis of square contingency tables, Tomizawa (1994) and Tobmizawa (1995) considered the Kullback-Leibler (KL) information type measures to represent the degree of departure from symmetry (S) and from global symmetry (GS), respectively. This paper proposes a K L information type measure to represent the degree of departure from conditional symmetry (CS), being an extension of S. The proposed measure would be useful for comparing the degree of departure from CS in several tables. Also this paper gives a theorem that the value of measure from S is equal to the sum of the value of measure from GS and that from CS.