Testing Non-Linear Ordinal Responses in L2×K Tables
Abstract
In comparative studies responses of two populations are often summarized in stratified 2 ×K tables with ordinal categories. A test, called QEt test, is proposed for testing the homogenuity of the populations against non-linear alternatives in such tables. The asymptotic distributions of proposed test are obtained both under the null and alternative hypothesis. The powers of the QEt test and extended Mantal test are compared by simulation.References
Pearson, K. (1900), On criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, Philos. Mag., series 5, 50, 157-175. (Reprinted 1948 in Karl Pearsons Early statistical papers, ed. By E. S. Pearson, Cambridge University Press.)
Nair, V. N. (1986), On Testing in Industrial Experiments with Ordered Categorical Data, Journal of American Statistical Association, 58, 690-700.
Takeuchi, K. and Hirotsu, C. (1982), The Cumulative Chi Square Method Against Ordered Alternative in Two-way Contingency Tables, Reports of Statistical Application Research, Japanese Union of Scientists and Engineers, 29, 1-13.
Hirotsu, C. (1983), Defining the pattern of association in two-way contingency tables, Biometrika, 70, 579-589.
Jayasekara, L. and Yanagawa, T. (1995) Testing ordered categorical data in 2×k Tables by the statistics with orthonormal scorollarye vectors, Bulletin of Informatics and Cybernetics, 27, 129-145.
Jayasekara, L., Nishiyama, H. and Yanagawa, T. (1999) Versatile Test for Ordinal Data in 2×k Tables,
Lindis, J.R., Heyman, E.R. and Koch, G.G. (1978), Average partial association in three way contingency tables: a review and discussion of alternative tests, International Statistical Review, 46, 237-254.
Mantel, N. (1963), Chi-square tests with one degree of freedom: extensions of the Mantel-Haenszel procedure, Journal of American Statistical Association, 58, 690-700.
Plackett, R.L. (1981). The Analysis of Categorical Data, London: Griffin.
Sinkhorn, R. (1967), Diagonal equivalence to matrices with prescribed row and column sums, Amer. Math. Month., 74, 402-5.
Wilcoxon, Frank (1945), Individual Comparisons by Ranking Methods, Biometrics 1, 80-83.
Ynagawa, T. (1986), Analysis of Discrete Multivariate Data, Tokyo: Kyoritu Shuppan.
Downloads
Published
Issue
Section
License
From Volume 7 (2016) onwards, all articles published in Ruhuna Journal of Science are Open Access articles published under the Creative Commons CC BY-NC 4.0 International License. This License permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.
Copyright on any research article published in RJS is retained by the respective author(s).
Authors who publish with this journal agree to the following terms:
a) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC-BY-NC 4.0 International, that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
b) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
c) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).