I have seen several variants of exact tests for differences and ratios of binomial parameters. How do they differ?
A. An early variant was based on inverting a test based on a very inefficient statistic due to Santner and Snell (1980). More recently, StatXact has introduced (1) Exact confidence intervals for differences and ratios of binomial parameters based on inverting the exact 1-sided score-test (Due to Chan and Zhang, 1999), and (2) Exact confidence intervals for differences and ratios of binomial parameters based on inverting the exact 2-sided score-test (due to Agresti and Min, 2001). This test is more efficient than the Chan and Zhang test because it reduces discreteness by being 2-sided.