A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 ร 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel-Haenszel chi-square statistic (c 2 MH ), the adjusted Mantel-Haenszel chi-square statistics of Rao and Scott using both an unpooled design effect (c 2 RSN ) and a pooled design effect (c 2 RSP ), the adjusted Mantel-Haenszel chi-square statistic of Donald and Donner (c 2 DD ), the chi-square statistic using the GEE approach (c 2 GEE ), the adjusted Mantel-Haenszel chi-square statistic of Begg (c 2 B ), the Wald (c 2 W ), the robust Wald (c 2 RW ), the score (c 2 S ), the robust score (c 2 RS ), and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (c 2 ZBP and c 2 ZBN ). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic c 2 RS and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (c 2 ZBP and c 2 ZBN ) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intracluster correlation is zero or the cluster sizes are balanced. c 2 RS performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.