ABSTRACT
The most fundamental statistical inference made in environmental sciences is the comparison in response between a treatment group and a concurrent, independent, control group. The comparison of a single treatment’s effects with a concurrent control group is a special case of the general two-sample or two-group setting, where the quantitative features of two independent samples or groups are compared statistically. When the independent observations are recorded as discrete counts of some environmental phenomenon, the normal distribution is no longer a valid distributional model. Besides the obvious recognition that the data are no longer continuous, it is also the case that variability of count data often changes as a function of the underlying population mean. This is a form of variance heterogeneity, and the variance heterogeneity can lead to invalid statistical inferences under standard t-tests.
