Geary's C


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 ; 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.
This statistic was developed by Roy C. Geary.