Unconditional exact tests are a more powerful alternative to Fisher’s exact test for analyzing 2x2 tables. However, there is still no consensus between the best unconditional exact test. Suissa and Shuster (1985) recommend using the Z-pooled statistic, Berger (1994) suggests Boschloo’s test, and Mato and Andres (1997) recommend using the CSM test. A modified version of the CSM test is proposed which is substantially faster than the original. I compared several unconditional exact tests considering over 10,000 scenarios with various allocation ratios and proportions.
While there is no unconditional exact test uniformly more powerful than the others, the modified CSM test is typically the most powerful under various scenarios. For example, when the proportions are 0.99 and 0.60, the Z-pooled, Boschloo’s, and modified CSM each have a specific sample size that yields greater power than the others. However, the modified CSM attains the greatest power most often as the sample size increases. The Z-pooled statistic can have problems with unbalanced designs, while Boschloo’s test can have lower power when the proportions are near the extremes. The modified CSM test is recommended.