On a New Distribution-Free Two-Sample Test

• Activity Number: 90
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jamye Curry*+ and Xin Dang and Hailin Sang
• Companies: The University of Mississippi and University of Mississippi and The University of Mississippi
• Keywords: distribution-free ; univariate ; rank-based

Abstract

We propose a new distribution-free test based on standardized ranks for the univariate two-sample problem. The test statistic is the difference between the average of between-group distances of ranks and the average within-group distances. It is closely related to the two-sample Cramer-von Mises criterion. They have the same population counterpart and have the same limiting distribution. They are the same when the sizes of two samples are equal. However, the proposed test has advantages over the Cramer-von Mises test for unequal sizes. The accuracy of approximation of the limit distribution to the exact distribution is much better than in the case of Cramer-von Mises test statistic for moderate but unequal sample sizes. A numerical comparison with other popular tests demonstrates the competitive power performance of the proposed test.