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

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  • M.L. Menéndez
  • J.A. Pardo
  • L. Pardo

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.

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  • M.L. Menéndez & J.A. Pardo & L. Pardo, 2003. "Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 115-123, March.
    • Handle: RePEc:bla:anzsta:v:45:y:2003:i:1:p:115-123
    DOI: 10.1111/1467-842X.00265
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    Cited by:

    1. Martín, N. & Balakrishnan, N., 2013. "Hypothesis testing in a generic nesting framework for general distributions," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 1-23.
    2. J. A. Pardo & M. C. Pardo, 2008. "Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 357-379, September.

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