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The asymptotic Pearson's chi-squared test and Fisher's exact test have long been the most used for testing association in 2x2 tables. Unconditional tests preserve the significance level and generally are more powerful than Fisher's exact test for moderate to small samples, but previously were disadvantaged by being computationally demanding. This disadvantage is now moot, as software to facilitate unconditional tests has been available for years. Moreover, Fisher's exact test with mid-p adjustment gives about the same results as an unconditional test. Consequently, several better tests are available, and the choice of a test should depend only on its merits for the application involved. Unconditional tests and the mid-p approach ought to be used more than they now are. The traditional Fisher's exact test should practically never be used.
Lydersen et al. (Fri,) studied this question.
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