Poisson distributions are special sampling distributions generated when discrete individuals are counted from a series of sample units. Sample units should be independent and selected by random sampling. Poisson distributions are similar to the binomial distribution, except there are more than two alternative outcomes associated with the attribute.
In rangeland sampling, counting individual plants in quadrats to determine density produces a Poisson distribution. In these cases, distributions assume a skewed form, because most values are zeros or very low, and higher counts are infrequently recorded.
Sample data following a Poisson distribution cannot be analyzed using conventional inferential statistical procedures, which assume that data fits a normal distribution. Sometimes Poisson-type populations will give data which tend toward a normal distribution if sample unit size is increased, sample units are defined as a group of quadrats, or square-root transformations are applied. Procedures specific to the Poisson model can be found in most statistics textbooks.
References and Further Reading
Bonham, C.D. 1989. Measurements for terrestrial vegetation. John Wiley Sons, New York, NY. pp 79-80.
Dowdy, S. and S. Weardon. 1991. Statistics for research. John Wiley Sons, New York, NY. 2nd ed. pp 87-103, 183.