A K-SAMPLE RANK TEST BASED ON MODIFIED BAUMGARTNER STATISTIC AND ITS POWER COMPARISON

Abstract

The purpose of this paper is to develop a nonparametric k-sample test based on a modified Baumgartner statistic. We define a new modified Baumgartner statistic B* and give some critical values. Then we compare the power of the B* statistic with the t-test, the Wilcoxon test, the Kolmogorov-Smirnov test, the Cramer-von Mises test, the Anderson-Darling test and the original Baumgartner statistic. The B* statistic is more suitable than the Baumgartner statistic for the location parameter when the sample sizes are not equal. Also, the B* statistic has almost the same power as the Wilcoxon test for location parameter. For scale parameter, the power of the B* statistic is more efficient than the Cramer-von Mises test and the Anderson-Darling test when the sizes are equal. The power of the B* statistic is higher than the Kolmogorov-Smirnov test for location and scale parameters. Then the B* statistic is generalized from two-sample to k-sample problems. The Bk* statistic denotes a k-sample statistic based on the B* statistic. We compare the power of the Bk* statistic with the Kruskal-Wallis test, the k-sample Kolmogorov-Smirnov test, the k-sample Cramer-von Mises test, the k-sample Anderson-Darling test and the k-sample Baumgartner statistic. Finally, we investigate the behavior of power about the Bk* statistics by simulation studies. As a result, we obtain that the Bk* statistic is more suitable than the other statistics.