Likelihood Ratio Test Against Stochastic Order in Three Way Contingency Tables

Abstract

Trend tests in dose-response have been central problems in medicine. The likelihood ratio test is often used to test hypotheses involving a stochastic order. Stratified contingency tables are common in practice. The distribution theory of likelihood ratio test has not been full developed for stratified tables and more than two stochastically ordered distributions. Under c strata of m × r tables, for testing the conditional independence against simple stochastic order alternative, this article introduces a model-free test method and gives the asymptotic distribution of the test statistic, which is a chi-bar-squared distribution. A real data set concerning an ordered stratified table will be used to show the validity of this test method.

Keywords:

• Asymptotic distribution
• Chi-bar-squared distribution
• Contingency tables
• Likelihood ratio test
• Stochastic order

Mathematics Subject Classification:

• Primary 62G10
• Secondary 62F05

Acknowledgments

The authors wish to thank the associate editor and the referees for their helpful recommendations and criticism in reviewing the manuscript. This research is supported by NSFC (Grant No. 10671089) and SRFDP of China (Grant No. 20060254006).

Notes

Source: 1991 General Social Survey, National Opinion Research Center, University of Chicago.