Testing For Homogeneity Of Proportions Using New Mcdonald Generalized Beta-Binomial Distribution

ABSTRACT

Testing for homogeneity of proportions in handling over-dispersion is employed in toxicology,

teratology, consumers purchasing behavior, alcohol drinking behavior, in studies of dental caries

in children and other similar fields. An important inference problem of interest is to compare

proportions of certain characteristic in several groups. However, these proportions often exhibit

variation greater than predicted by a simple binomial model. In real world applications, the

binomial outcome data are widely encountered and the binomial distribution often fails to test

homogeneity of proportions due to over-dispersion. The binomial proportion is assigned a

continuous distribution defined on the standard unit interval as one way of handling overdispersion

in the test for homogeneity of proportions. The new McDonald Generalized Beta-

Binomial distribution (McGBB) with three shape parameters has been shown to give better fit to

binomial outcome data than the Kumaraswamy-Binomial (KB) distribution and Beta-Binomial

(BB) distribution based on both simulated data and real data sets and hence considered in this

work. This thesis considered derivation of the C (a ) tests based on Quasi-likelihood (QL) and

Extended Quasi-likelihood (EQL) estimating functions using the new McGBB distribution which

have not been done in testing homogeneity of the proportions. Simulation was done by using R

package and also real data was used to calculate p-values for both C (a ) tests and LR test. The

size and power of a test was compared for the simulated data and showed that C (a ) tests

maintained nominal level well and had higher power than LR test. The comparison of p-values

for real data showed that C (a ) tests had smaller p-values than LR test hence C (a ) tests were

preffered since they require estimates only under the null hypothesis. Thus, this thesis has

provided a better tests ( C (a ) tests) based on Quasi-likelihood and Extended Quasi-likelihood

estimating functions for testing homogeneity of proportions in presence of overdispersion using the new McGBB distribution.