Moran's I (Moran 1950) is a weighted correlation coefficient used to detect departures from spatial randomness. Departures from randomness indicate spatial patterns, such as clusters. The statistic may identify other kinds of pattern such as geographic trend.
Moran's I tests for global spatial autocorrelation in disease rates (group-level data). Positive spatial autocorrelation means that nearby areas have similar rates, indicating global spatial clustering. Nearby areas have similar rates when their populations and exposures are alike. When rates in nearby areas are similar, Moran's I will be large and positive. When rates are dissimilar, Moran's I will be negative.
Moran's I requires full enumeration of the connections among the observations, which may be a problem when the number of areas becomes large. When full enumeration isn't possible use Grimson's method, and estimate the Grimson input data from a sample of areas. Moran's I is biased by large differences in population size across areas. Use Oden's Ipop when population size data are available.
