Geary's C is a measure of spatial autocorrelation or an attempt to determine if adjacent observations of the same phenomenon are correlated. Spatial autocorrelation is more complex than autocorrelation because the correlation is multi-dimensional and bi-directional.
Geary's C is defined as
where is the number of spatial units indexed by and ; is the variable of interest; is the mean of ; is a matrix of spatial weights with zeroes on the diagonal (i.e., ); and is the sum of all .
The value of Geary's C lies between 0 and some unspecified value greater than 1. Values significantly lower than 1 demonstrate increasing positive spatial autocorrelation, whilst values significantly higher than 1 illustrate increasing negative spatial autocorrelation.
Geary's C is inversely related to Moran's I, but it is not identical. Moran's I is a measure of global spatial autocorrelation, while Geary's C is more sensitive to local spatial autocorrelation.
Geary's C is also known as Geary's contiguity ratio or simply Geary's ratio.
- J. N. R. Jeffers (1973). "A Basic Subroutine for Geary's Contiguity Ratio". Journal of the Royal Statistical Society (Series D). Wiley. 22 (4).
- Geary, R. C. (1954). "The Contiguity Ratio and Statistical Mapping". The Incorporated Statistician. The Incorporated Statistician. 5 (3): 115–145. JSTOR 2986645. doi:10.2307/2986645.
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