A Semiparametric Method to Compare the Means of Several Populations

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Suohong Wang* and Biao Zhang and Wencan He
• Companies: Meredith College and University of Toledo and University of Toledo
• Keywords: density ratio model ; ANOVA ; semi-parametric

Abstract

We consider the classical statistical problem of comparing the means of several populations. Although the parametric ANOVA method has been widely used, the normal and equal variance assumptions are frequently ignored and often violated when used in real world application. The power of ANOVA suffers a significant decrease for non-symmetric distributions. We propose a semi-parametric method to compare the means of several populations under a multiple-sample density ratio model. The method is built upon semi-parametric estimation of the differences between the population means. We show that the semi-parametric test statistic converges to a chi-square distribution. A simulation study and an analysis of three real data sets are provided. The simulation results show that our semi-parametric method is comparable to the parametric ANOVA when data are normal, and is significantly better than the parametric ANOVA and non-parametric Kruskal-Wallis test when data are far from normal.