We specify several count data models, parameterizing the probability densities in terms of their means for easier comparison between models. In addition, we derived a correction of these probability densities for differences in sample sizes, which is a contribution to the count data literature as far as we are aware. We then empirically implement these models using data from a mail survey of firms using prescribed fire to estimate the expected number of escapes from prescribed burns. We find that the not correcting for sample size differences can lead to erroneous conclusions concerning the statistical significance of variables.