Geary's C

Synonyms

Geary's index; Geary ratio; Geary coefficient

Definition

Geary's C tests statistics for spatial autocorrelation by using the sum of squared differences between pairs of data of variable x as a measure of covariation

$$ C=\frac{(n-1)\sum\limits_i {\sum\limits_j {w_{ij} (x_i -x_j)^2}}} {2nS^2\sum\limits_i {\sum\limits_j {w_{ij}} } }\:. $$

Where x _i denotes the observed value at location i,

$$ S^2=\frac{1}{n}\sum\limits_i \left({x_i}-\bar x\right)^2\:, $$

$\bar x$ is the mean of the variable x over the n locations and w _ij are the elements of the spatial weights matrix, defined as 1 if location i is contiguous to location j and 0 otherwise. Other spatial weights matrices can also be used.

Main Text

Geary's C ranges from 0 to a positive value. The value of C is 1 in the absence of spatial autocorrelation. A low value of C (0 < C < 1) represents a positive spatial autocorrelation and approaches zero for strong autocorrelation. A high value (C> 1) represents negative spatial...