A class of permutational and multinomial tests arising in epidemiological research.

Suppose that, in a population of size N, for subgroup a of size Na (a = 1, ... , c), R. individuals develop disease. Let Xa0n be a measure, perhaps one related to the geographical separation between the subgroups, designed to help detect a specified form of departure from randomness in the occurrence of the disease. If the XaEs measure is summed over all pairs of cases of the disease, summary measures Z and W are