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

• Published in: Australian & New Zealand journal of statistics Vol. 45; no. 1; pp. 115 - 123
• Main Authors: Menéndez, M.L., Pardo, J.A., Pardo, L.
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishing Ltd 01.03.2003
• Subjects: chi-bar squared distribution; contingency table; φ-divergence measure
• ISSN: 1369-1473; 1467-842X
• DOI: 10.1111/1467-842X.00265

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.