Dissertation Defenses

Doctoral Dissertation Announcement

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Candidate: Marwan Daoud

Degree of: Doctor of Philosophy

Department: Statistics

Title: Extensions of Two-part Tests to Compare K Independent Populations

Committee:
Dr. M. Niewiadomska Bugaj, Chair
Dr. Joshua Naranjo
Dr. J.C. Wang
Dr. Daniel Frobish


Date: Monday, June 25, 2007 2:00 p.m. – 4:00 p.m.
Everett Tower, Alavi Commons Room

Abstract:
This dissertation considers two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The models may assume a particular distribution h(x) for the continuous part, such as a log-normal or a gamma. The response variable, y, is defined as y=(x, d), where d=1 if x>0 and d=0 if x=0. The probability distribution function has the following form:

f(x,d) = [p]1-d x [(1-p) x h(x)]d

Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. This dissertation proposes a two-part Wald test and a two-part likelihood ratio test of compare 0 = (p,m) (p is the proportion of zeros and m is the mean of h(x)), hence the equality of overall means in K independent populations where h(x) is a lognormal distribution. These two test statistics have asymptotically chi-square distribution with 2(k – 1) degrees of freedom. A simulation study was conducted to compare the size and the power of the proposed tests with several other tests (ANOVA, Welch, Brown-Forsythe, and Kruskal-Wallis).