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Bayesian test of homogenity in small areas: A discretization approach
Journal of the Korean Data & Information Science Society 2017;28:1547-55
Published online November 30, 2017
© 2017 Korean Data & Information Science Society.

MinSup Kim1 · Balgobin Nandram2 · Dal Ho Kim3

13Department of Statistics, Kyungpook National University
2Department of Mathematical Sciences, Worcester Polytechnic Institute
Correspondence to: Dal Ho Kim
Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: dalkim@knu.ac.kr
Received September 29, 2017; Revised October 30, 2017; Accepted November 1, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper studies Bayesian test of homogeneity in contingency tables made by discretizing a continuous variable. Sometimes when we are considering events of interest in small area setup, we can think of discretization approaches about the continuous variable. If we properly discretize the continuous variable, we can find invisible relationships between areas (groups) and a continuous variable of interest. The proper discretization of the continuous variable can support the alternative hypothesis of the homogeneity test in contingency tables even if the null hypothesis was not rejected through k-sample tests involving one-way ANOVA. In other words, the proportions of variables with a particular level can vary from group to group by the discretization. If we discretize the the continuous variable, it can be treated as an analysis of the contingency table. In this case, the chi-squared test is the most commonly employed method. However, further discretization gives rise to more cells in the table. As a result, the count in the cells becomes smaller and the accuracy of the test becomes lower. To prevent this, we can consider the Bayesian approach and apply it to the setup of the homogeneity test.
Keywords : Contingency table, Dirichlet prior, discretization, hierarchical Bayesian model, test of homogeneity