Two Sample Comparisons for Non-Normal Data

• Activity Number: 182
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Luna Sun*+ and Alix I. Gitelman
• Companies: Oregon State University and Department of Statistics, Oregon State University
• Keywords: Simultaneous comparison ; Fisher's method ; Likelihood ratio test ; Score test ; Permutation test

Abstract

Motivated by an example in marine science, we use Fisher's method to combine independent likelihood ratio tests and asymptotic independent score tests to assess the equivalence of two zero-inflated Beta populations (mixtures distributions with three parameters). For each test, test statistics for the three individual parameters are combined into a single statistic to address the overall difference between the two populations. We also develop permutation-based tests for simultaneously comparing two or three features of unknown populations. Simulations show that the likelihood-based tests perform well for large sample sizes and that the statistics based on combining likelihood ratio test statistics outperforms the one based on combining score test statistics. When sample sizes are small, performance of the asymptotic tests is poor, and our permutation-based tests have overall better performance in terms of both power and Type I error rate. Our methods are easy to implement and can be expanded to more than two populations and to other multiple parameter families.