Power of the rank adjacency statistic to detect spatial clustering in a small number of regions

The rank adjacency statistic D is a statistical method for assessing spatia l autocorrelation or clustering of geographical data. It was originally pro posed for summarizing the geographical patterns of cancer data in Scotland (IARC 1985). In this paper; we investigate the power of the rank adjacency statistic to detect spatial clustering when a small number of regions is in volved. The investigations were carried out using Monte Carlo simulations, which involved generating patterned/clustered values and computing the powe r with which the D statistic would detect it. To investigate the effects of region shapes, structure of the regions, and definition of weights, simula tions were carried out using two different region shapes, binary and nonbin ary weights, and three different lattice structures. The results indicate t hat in the typical example of considering Canadian total mortality at the e lectoral district level, the D statistic had adequate power to detect gener al spatial autocorrelation in twenty-five or more regions. There was an inv erse relationship between power and the level of connectedness of the regio ns, which depends on the weighting function, shape, and arrangement of the regions. The power of the D statistic was also found to compare favorably w ith that of Moran's I statistic.