Nonparametric Tests for Equality of Distributions Based on Precedence Probabilities

• Activity Number: 468
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Rajarshi Dey*+ and Paul Nelson
• Companies: Kansas State University and Kansas State University
• Keywords: Nonparametric methods ; Precedence Probability ; ROC ; K-sample Problem

Abstract

Let X(i) be a random variable with continuous distribution function F(i) ; i=1,2,...,K. Using precedence probabilities, we propose and explore a class of nonparametric tests based on independent random samples for the null hypothesis that all distribution functions are equal. One of these tests, designed to find any type of difference among the distributions, performs well in cases where the distributions differ only in location, only in scale or both in location and scale. Another member of this class is effective in testing for the volume under the Receiver Operating Characteristic surface , which, for K = 2 , is widely used in medical studies as a summary index of diagnostic accuracy. Comparisons to the performance of standard tests for these problems will be presented to show the proposed tests as a viable alternative to the standard procedures.