Tests for Independence in Two-Way Contingency Tables with Small Samples

Tests for Independence in Two-Way Contingency Tables with Small Samples

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...

Exact tests for two-way contingency tables with structural zeros

Fisher’s exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher’s exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test ...

Intrinsic Tests of Independence in Contingency Tables

For Bayesian testing of independence in contingency tables, the priors play an important role regardless of the sample size. The simplest default prior, the uniform prior on the simplex, may sometimes not give sensible answers. However, we show that intrinsic priors derived from the uniform greatly improve the performance of Bayesian tests. The intrinsic priors give more mass to alternative par...