1\name{gearyc} 2 3\alias{gearyc} 4 5\title{Geary's C Autocorrelation Statistic} 6 7 8\description{ 9Geary's c statistic is used to measure autocorrelation between areas within 10a region, as follows: 11 12\deqn{ 13c=\frac{(n-1)\sum_i \sum_j W_{ij}(Z_i-Z_j)^2}{2(\sum_i\sum_jW_{ij})\sum_k (Z_k-\overline{Z})^2} 14}{ 15c = (n-1) [sum_i sum_j W_ij (Z_i-Z_j)^2]/[2(sum_i sum_j W_ij) sum_k (Z_k-mean({Z))^2} 16} 17 18\eqn{W}{W} is a squared matrix which represents the relationship between each 19pair of regions. An usual approach is set \eqn{w_{ij}}{w_ij} to 1 if regions 20\eqn{i}{i} and \eqn{j}{j} have a common boundary and 0 otherwise, or it may 21represent the inverse distance between the centroids of that two regions. 22 23Small values of this statistic may indicate the presence of highly 24correlated areas, which may be a cluster. 25} 26 27 28\seealso{ 29DCluster, gearyc.stat, gearyc.boot, gearyc.pboot 30} 31 32\references{ 33Geary, R. C. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician 5, 115-145. 34} 35 36\keyword{spatial} 37