Forward selection two sample binomial test.

Fisher's exact test (FET) is a conditional method that is frequently used to analyze data in a 2 × 2 table for small samples. This test is conservative and attempts have been made to modify the test to make it less conservative. For example, Crans and Shuster (2008) proposed adding more points in the rejection region to make the test more powerful. We provide another way to modify the test to make it less conservative by using two independent binomial distributions as the reference distribution for the test statistic. We compare our new test with several methods and show that our test has advantages over existing methods in terms of control of the type 1 and type 2 errors. We reanalyze results from an oncology trial using our proposed method and our software which is freely available to the reader.