Pairwise Comparisons and Homogeneity of Odds Ratios in Stratified 2 X 2 Contingency Tables

Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Magdalena Niewiadomska-Bugaj

Second Advisor

Dr. Joshua D. Naranjo

Third Advisor

Dr. Joseph W. McKean

Fourth Advisor

Dr. Jezaniah-Kira S. Tena


Pairwise comparisons, homogeneity of odd' s ratios, stratified contingency, Bonferroni procedure, Holm-Bonferroni procedure, Holland-Copenhaver procedure


Categorical data are used in almost every field. When confounding variables are encountered, data are stratified. This study is about testing homogeneity in stratified 2 x 2 contingency tables. We propose the Range test and perform a series of pairwise comparison methods. Test statistics are obtained by using the variance of the log odds ratio estimator based on the second order Taylor expansion. For testing homogeneity of odds ratios across strata, the Breslow-Daytest (Breslow and Day, 1980) is widely used. We propose the Range test for testing equal odds ratios across strata for large sample sizes relative to the number of strata. The Range test can be used as an equivalent for the Breslow-Day test. Among the pairwise comparison methods proposed, the Holland-Copenhaver procedure and the Holm-Bonferroni procedure can be used regardless of the sample sizes. The Bonferroni and the Dunn-Šidák procedures outperform the Holland-Copenhaver and the Holm-Bonferroni procedures for large sample sizes.

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