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.
AREBA, B (2021). Testing For Homogeneity Of Proportions Using New Mcdonald Generalized Beta-Binomial Distribution. Afribary. Retrieved from https://tracking.afribary.com/works/testing-for-homogeneity-of-proportions-using-new-mcdonald-generalized-beta-binomial-distribution
AREBA, BICHANGA "Testing For Homogeneity Of Proportions Using New Mcdonald Generalized Beta-Binomial Distribution" Afribary. Afribary, 15 May. 2021, https://tracking.afribary.com/works/testing-for-homogeneity-of-proportions-using-new-mcdonald-generalized-beta-binomial-distribution. Accessed 09 Nov. 2024.
AREBA, BICHANGA . "Testing For Homogeneity Of Proportions Using New Mcdonald Generalized Beta-Binomial Distribution". Afribary, Afribary, 15 May. 2021. Web. 09 Nov. 2024. < https://tracking.afribary.com/works/testing-for-homogeneity-of-proportions-using-new-mcdonald-generalized-beta-binomial-distribution >.
AREBA, BICHANGA . "Testing For Homogeneity Of Proportions Using New Mcdonald Generalized Beta-Binomial Distribution" Afribary (2021). Accessed November 09, 2024. https://tracking.afribary.com/works/testing-for-homogeneity-of-proportions-using-new-mcdonald-generalized-beta-binomial-distribution