Minimally selected p and other tests for a single abrupt changepoint in a binary sequence

A novel changepoint statistic based on the minimum value, over possible changepoint locations, of Fisher's Exact Test, is introduced. Specific points in the exact distribution of the minimally selected Fisher's value may be rapidly calculated as a lattice-path counting problem via known recurrence methods. The test is compared to the Kolmogorov-Smirnov two-sample test, the maximally selected chi-square, and a likelihood ratio test. The tests are applied to assessing recombination in genetic sequences of HIV.