A class of statistical models to weaken independence in two-way contingency tables

Bootstrap tests for independence in two-way ordinal contingency tables

For the analysis of an r by c contingency table having ordered row categories and ordered column categories, a bootstrap method is applied for the model-based likelihood ratio test for independence. A model-based likelihood ratio chi-square statistic and the statistic of the maximum eigenvalue of a Wishart matrix are also discussed. A simulation study is performed to compare the proposed method...

Nonparametric tests for conditional independence in two-way contingency tables

Consider a two-way contingency table, built on two categorical variables R and S. A fundamental question in this context is whether R and S are independent or not. This over-studied testing problem mostly relies on the chi-square or the likelihood ratio test statistics. The principal drawback of the classical way of doing is that probabilities for an individual to fall in a cell of the table ar...

Analysis of Two-way Contingency Tables

Pearson’s test and likelihood ratio test are two of the classical tests frequently used for testing the equality of r distributions using the data in the contingency tables. Presently we suggest an alternative test for testing the equality of distributions. It is found that the alternative test has, in general, more satisfactory levels of the acceptance probabilities under the null hypothesis, ...

The Geometry of Statistical Models for Two-way Contingency Tables with Fixed Odds Ratios

We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers to the general case of two-way contingency tables are also given and an application to case-control studies is presented.

A Flexible Method for Testing Independence in Two-Way Contingency Tables