Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables - Menéndez, M.L.; Pardo, J.A.; Pardo, L. (Australian & New Zealand journal of statistics, 2003)
Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let pij= Pr(X = i, Y = j). This paper introduces a family of tests based on φ–divergence measures for testing H0: pij = pji against H1: pij ≥ pji (I≥ j); and for testing H1 against H2: pij unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test.