Analysis of overdispersed count data from single-factor experiments: a comparative study

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