Testing for a treatment effect in the presence of nonresponders

Good (1979, Biometrics 35, 483-489) introduced a new randomization test for the two-sample problem where a proportion 1 - p of the treatment group does not respond to the treatment, and suggested that the Wilcoxon test is not effective for this situation. We show to the contrary that the Wilcoxon test is quite useful when p greater than or equal to .6 and point out an error in his definition of a one-tailed randomization test.