## Quick Reference

A measure of the extent to which a set of observed frequencies (for example the numbers of plants in randomly distributed quadrats) follow a Poisson distribution. For a sample of *n* observations, let *x̄* and *s*^{2} denote, respectively, the sample mean and the sample variance (using the (*n*−1) divisor). Under the null hypothesis of a Poisson distribution the quantity *I* (the index of dispersion), given by , has an approximate chi-squared distribution with (*n*−1) degrees of freedom. According to the null hypothesis the value of *I* should be near (*n*−1). This test is called the dispersion test.

If *I* is unusually large then the data are described as being over dispersed, and, in the case of plants (or stars, or other point objects), the data are described as clustered. If *I* is unusually small then the data are described as displaying regularity. See extra-binomial variation.

*Subjects:*
Probability and Statistics.