Comment, by C. Frank Starmer, James E. Grizzle and P. K. Sen.

In the discussion of hypothesis testing in 2 X 2 contingency tables, Fisher's exact test is often used as the standard against which competing tests are measured. Statisticians should not be led into a semantic trap by the words "exact test." Statistician interpreted the phrase to mean that it yields the exact probability of observing a result identical to a more extreme probability under the assumption that a particular 2 X 2 table was generated by sampling from a four-variable hypergeometric distribution. The result shown by statistician K.D. Tocher shows that the exact test, supplemented by randomization to achieve the desired significance α is the most powerful test against one-sided alternatives when both, one or no margin totals are fixed in advance. Therefore, the randomized exact test should be the standard to which competing tests are compared. Even though most statisticians would not use the randomized test in practice, it could be used for judging the value of competing tests.