Bootstrap Precedence Tests for K-Samples

• Activity Number: 229
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Rajarshi Dey*+ and Paul Nelson
• Companies: and Kansas State University
• Keywords: Precedence probability ; K-sample Test ; Bootstrap ; Effect Size ; Location, Scale and Shape problem

Abstract

Let X_{i} be a random variable with continuous distribution function F_{i}; i=1,2,.,K. Also, let Q be the set of all permutations of the numbers (1,2,.,K). Then, P(X_{i1}< X_{i2} < .< X_{ik}) is a precedence probability if (i1, i2, ., ik) belongs to Q. A new approximate nonparametric test for the equality of K> 2 continuous distributions based on independent random samples is developed and explored. The test uses a one sided confidence interval for the maximum of all K! precedence probabilities to construct the critical region. For K = 2 the test is comparable in structure to a two sided Mann-Whitney test. Simulations indicate that the new test effectively holds its nominal type I error rate and has competitive power compared to standard tests in a wide variety of settings, including differences in location, scale and shape.