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The rank adjacency statistic D has been used to summarize the spatial autocorrelation in regional health data. It is defined as the average absolute difference in ranks of the data, taken over all possible pairs of adjacent regions. In this paper, the mean and approximate variance are derived for D, including provision for general weighting of regional pairs. Special results are given for the case of binary weights representing regional adjacencies. Empirical analysis with cancer maps from three countries shows excellent properties of a normal approximation to test the significance of D, eliminating the previous need for simulation. The calculations are further illustrated with data on the spatial pattern of urban/rural residence.
Stephen D. Walter (Mon,) studied this question.