Testing Homogeneity of the Multinomial Proportions

• Activity Number: 378
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 12:00 PM to 1:50 PM
• Sponsor: General Methodology
• Author(s): Cristina P. Sison*+ and Joseph Glaz
• Companies: North Shore-LIJ Research Institute and University of Connecticut
• Keywords: multinomial ; product type approximations ; parametric bootstrap ; likelihood ratio test ; inequalities

Abstract

Let X1,X2,...,Xk be a random vector of observations which follow a multinomial distribution, with parameters n and p1,p2,...,pk . We are interested in testing the null hypothesis, H0: p1=p2=...=pk0=p0=1/k0 versus the alternative H1: at least one pi, i=1 le i le k0,2 le k0 le k is different from p0. When k0=k then p0=1/k. Testing homogeneity of the multinomial proportions plays an important role in several applications and is discussed widely in the literature. Our study focuses on the Monte Carlo implementations of the likelihood ratio tests. We initially focus on the simpler problem when k0=k, where H0 is completely specified. When the null hypothesis of uniformity is violated, cell frequencies will tend to be small or large. We propose to investigate the performance of test statistics based on functions of the minimal sufficient statistic. The performance of the likelihood ratio tests (asymptotic and simulated exact distribution) will be compared to tests based on the following: X(k),X(1),(X(1),X(k)), Range= X(k)-X(1), and X(k)/X(1). We also investigate problem of testing homogeneity of a subset of the p. Simulation studies are presented to evaluate accuracy and power.