A Bi-Aspect Nonparametric Test for the Two-Sample Location Problem

Permutation methods are prized for their lack of assumptions concerning distributions of variables. A bi-aspect permutation test based on the Nonparametric Combination of Dependent Tests theory is developed for testing hypotheses of location shifts of two independent populations. The test is obtained by combining the traditional permutation test with a test that takes into account whethera sample observation is less than orequal to, orgr eaterthan the pooled sample median. The procedure to compute the proposed test is presented. The type-one error rate and power of the test are investigated for many distributions and sample-size settings via Monte Carlo simulations. These simulations show that the proposed test is remarkably more powerful than the traditional permutation test under heavy-tailed distributions like the Cauchy, the half-Cauchy, a 10% and a 30% outlier distribution. When sampling from the double exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under normal, uniform, a chi-squared and a bimodal distribution, the bi-aspect test is practically as powerful as the traditional permutation test. Moreover, in these simulations the proposed test maintained its type-one error rate close to the nominal signi8cance level