Title

Tests of homogeneity of several location and scale populations, and analysis of paired count data with zero-inflation and over-dispersion.

Date of Award

2004

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Paul, S. R.,

Keywords

Statistics.

Rights

CC BY-NC-ND 4.0

Abstract

This thesis consists of two parts, referred as Part I and Part II. Part I. Testing homogeneity of several location-scale populations. The widely used method for testing homogeneity of several normal populations is to test the equality of means based on the assumption that the variances among different groups are same. But in practice, we often get data which are different not only in means but also in variances. Singh (1986) tests the homogeneity of several normal populations simultaneously regarding commonality of means and variances based on a method by Fisher (1950). However, this problem arises not only in normal populations but also in other populations. In this thesis, I extend Fisher's method to location-scale models in general. The location-scale models encompass all two parameter mean-variance models, such as the normal, negative binomial and beta-binomial models. Two test statistics are developed, one of which is based on the combination of two likelihood ratio statistics and the other is based on the combination of two score test statistics. Theoretical and empirical properties of these procedures are studied and applied to real life data analysis problems. Part II. Analysis of paired count data with zero-inflation and over-dispersion. Data in the form of paired counts (pre-treatment and post-treatment counts) arise in many fields such as biomedical, toxicology, epidemiology and so on. Poisson and binomial models are the most widely used models for these data. Frequently encountered problems in these data are the presence of extra-zeros and extra-dispersion and, the possible correlation between the pre-treatment and post-treatment count. In this thesis I developed methods of analysis for two different sets of paired count data, one of the data set is obtained from an experiment on premature ventricular contractions (PVC) (Berry, 1987) and the other set is a dental epidemiology data representing decayed, missing and filled teeth (DMFT) index (Bohning, Dietz, Schlattmann, Mendonca and Kirchner, 1999). I then study properties of these methods and analyse the PVC data and the DMFT index data.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .J53. Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5219. Adviser: S. R. Paul. Thesis (Ph.D.)--University of Windsor (Canada), 2004.