Analysis of Overdispersed Count Data from Single-Factor Experiments: A Comparative Study

Abstract

Methods of analyzing overdispersed count data arising from one-way designs are compared through Monte Carlo simulation. The negative binomial distribution is used as a model for overdispersion. Tests for differences in treatment effects are based on the general linear model analysis of the raw or transformed data and on the generalized linear model specifying either the Poisson or negative binomial distribution. The estimated type I error rates are compared to the nominal 0.01, 0.05, and 0.10 significance levels. Using SAS to do the generalized linear models analyses, convergence problems increased as the mean decreased, overdispersion increased, the number of treatments increased, and the number of replications per treatment decreased. The general linear model is recommended, especially in the case of large overdispersion, large numbers of treatments, and small numbers of replications per treatment.