#### Date of Award

12-2007

#### Degree Name

Doctor of Philosophy

#### Department

Statistics

#### First Advisor

Dr. M. Niewiadomska Bugaj

#### Second Advisor

Dr. Joshua Naranjo

#### Third Advisor

Dr. J. C. Wang

#### Fourth Advisor

Dr. Daniel Frobish

#### Abstract

We consider two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The model may assume a particular distribution*h*(*x*) for the continuous part such as a log-normal or a gamma. The response variable 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: fx,d=p ^{1-d}×1-p ×hx ^{d}.

Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. We proposed a two-part Wald test and a two-part likelihood ratio test to compare &thetas; = (*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).

#### Access Setting

Dissertation-Open Access

#### Recommended Citation

Daoud, Marwan, "Extensions of Two-Part Tests to Compare *K* Independent Populations" (2007). *Dissertations*. 848.

https://scholarworks.wmich.edu/dissertations/848