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

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 modelisequaltothesumofthemeasuresforthereverseglobalsymmetrymodelandfortheconditionalpointsymmetrymodel. © 2021 The Authors . Published by Atlantis Press B.V. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).