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

A bi-aspect nonparametric test for testing hypotheses of location shifts of two populations was proposed in literature. The test is based on the nonparametric combination of dependent tests theory and is obtained by combining the traditional permutation test for the two-sample location problem with a test that takes into account whether a sample observation is or is not greater than the pooled sample median. A natural multi-sample extension of the test is proposed. The extension is shown by simulation to behave very similarly to the bi-aspect test for the two-sample problem. In fact, it is shown that the proposed test is remarkably more powerful than the traditional permutation test for the multi-sample location problem under heavy-tailed distributions like the Cauchy, the half-Cauchy, the 10% and the 30% outlier distributions. 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 the considered t2 distributions, the bi-aspect test is practically as powerful as the traditional permutation test. Whereas under normal, uniform and bimodal distributions it is slightly less powerful. Moreover, the proposed test maintained the type-one error rate close to the nominal significance level and was generally slightly conservative.