Analysis of frequency count data using the negative binomial distribution

The statistical distributions of the counts of organisms are generally skewed, and hence not normally distributed, nor are variances constant across treatments. We present a likelihood-ratio testing framework based on the negative binomial distribution that tests for the goodness of fit of this distribution to the observed counts, and then tests for differences in the mean and/or aggregation of the counts among treatments. Inferences about differences in means among treatments as well as the dispersion of the counts are possible. Simulations demonstrated that the statistical power of ANOVA is about the same as the likelihood-ratio testing procedure for testing equality of means, but our proposed testing procedure also provides information on dispersion. Type I error rates of Poisson regression exceeded the expected 5%, even when corrected for overdispersion. Count data on Orange-crowned Warblers (Vermivora celata) are used to demonstrate the procedure.