Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables

M.L. Menéndez, J.A. Pardo and L. Pardo

Australian & New Zealand Journal of Statistics, 2003, vol. 45, issue 1, 115-123

Abstract: 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.

Date: 2003
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