Stratified data analysis is an important research topic in many biomedical studies and clinical trials. In this article, we develop five test statistics for testing the homogeneity of proportion ratios for stratified correlated bilateral binary data based on an equal correlation model assumption. Bootstrap procedures based on these test statistics are also considered. To evaluate the performance of these statistics and procedures, we conduct Monte Carlo simulations to study their empirical sizes and powers under various scenarios. Our results suggest that the procedure based on score statistic performs well generally and is highly recommended. When the sample size is large, procedures based on the commonly used weighted least square estimate and logarithmic transformation with Mantel–Haenszel estimate are recommended as they do not involve any computation of maximum likelihood estimates requiring iterative algorithms. We also derive approximate sample size formulas based on the recommended test procedures. Finally, we apply the proposed methods to analyze a multi‐center randomized clinical trial for scleroderma patients. Copyright © 2014 John Wiley & Sons, Ltd.