A likelihood ratio test for equality of deviations from randomness

The use of the sample variance-to-mean ratio as a measure of deviation from randomness in spatial pattern is reviewed. The likelihood ratio method of constructing a statistical test for the equality of several population variance-to-mean ratios is described, and details are provided for the special case where counts are modelled as arising from a negative binomial distribution. This test is illustrated by application to example data sets in ecology. Likelihood ratio tests represent a general methodology whereby relationships among several indices of aggregation can be systematically investigated, provided one is able to specify a suitable parametric form for the underlying distributions.