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Practical applicability of exact and approximate forms of the randomization test for two independent samples.

Abstract : The practical applicability of randomization tests is discussed. The randomization test for two independent samples is the specific test examined in both hypothesis and significance testing contexts. This test has optimum theoretical properties as a nonparametric procedure for comparing the means of two populations. However, the calculations that are required to actually use the test in practice can be extremely time consuming. Using the randomization test for two independent samples to conduct a significance test is shown to be a P-complete enumeration problem. This implies that a computationally efficent way to perform an exact version of the procedure is not likely to exist. Two approximate ways to perform the randomization test are studied with the aid of a simulation. One method uses a normal distribution to approximate the actual randomization distribution and the other method is the usual two sample t-test. The t test is found to yield results very close to those that are obtained from the exact randomization test under the conditions studied.