Moran's I

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A statistic, introduced by Moran in 1950, that measures spatial autocorrelation using information only from specified pairs of spatial observations. Suppose there are n locations, and the observed value at location j is xj and the overall mean value is . Let wjk=1 if the comparison of the value at location j to the value at location k is of interest, and let wjk=0 otherwise. By definition, wjj=0, for all j. Usually, the only comparisons of interest are those between immediate neighbours. The statistic is given by .

Subjects: Probability and Statistics.

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