An approximation for the rank adjacency statistic for spatial clustering with sparse data

The rank adjacency statistic D provides a simple method to assess regional clustering. It is defined as the weighted average absolute difference in ra nks of the data, taken over all possible pairs of adjacent regions. In this paper the usual normal approximation to the D statistic is found to give i naccurate results if the data are sparse and some regions have tied ranks. Adjusted formulae for the moments of D that allow for the existence of ties are derived. An example of analyses of sparse mortality data (with many re gions having no deaths, and hence tied ranks) showed satisfactory agreement between the adjusted formulae and the empirical distribution of the D stat istic. We conclude that the D statistic, when, used with adjusted moments, provides a valid approximate method to evaluate spatial clustering, even in sparse data situations.