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Testing stochastic orders in tails of contingency tables

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  • Chi Tim Ng
  • Johan Lim
  • Kyu S. Hahn

Abstract

Testing for the difference in the strength of bivariate association in two independent contingency tables is an important issue that finds applications in various disciplines. Currently, many of the commonly used tests are based on single-index measures of association. More specifically, one obtains single-index measurements of association from two tables and compares them based on asymptotic theory. Although they are usually easy to understand and use, often much of the information contained in the data is lost with single-index measures. Accordingly, they fail to fully capture the association in the data. To remedy this shortcoming, we introduce a new summary statistic measuring various types of association in a contingency table. Based on this new summary statistic, we propose a likelihood ratio test comparing the strength of association in two independent contingency tables. The proposed test examines the stochastic order between summary statistics. We derive its asymptotic null distribution and demonstrate that the least favorable distributions are chi-bar distributions. We numerically compare the power of the proposed test to that of the tests based on single-index measures. Finally, we provide two examples illustrating the new summary statistics and the related tests.

Suggested Citation

  • Chi Tim Ng & Johan Lim & Kyu S. Hahn, 2011. "Testing stochastic orders in tails of contingency tables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1133-1149, March.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:6:p:1133-1149
    DOI: 10.1080/02664763.2010.484487
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    References listed on IDEAS

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    1. Blaug, Mark, 1985. "Where are we now in the economics of education?," Economics of Education Review, Elsevier, vol. 4(1), pages 17-28, February.
    2. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    3. Bartolucci, F. & Scaccia, L., 2004. "Testing for positive association in contingency tables with fixed margins," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 195-210, August.
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    1. Jeremy E. Reynolds, 2014. "Prevailing Preferences," ILR Review, Cornell University, ILR School, vol. 67(3), pages 1017-1041, July.
    2. Kouji Tahata & Takuya Yoshimoto, 2015. "Marginal asymmetry model for square contingency tables with ordered categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 371-379, February.

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