# 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

${\displaystyle C={\frac {(N-1)\sum _{i}\sum _{j}w_{ij}(X_{i}-X_{j})^{2}}{2W\sum _{i}(X_{i}-{\bar {X}})^{2}}}}$

where ${\displaystyle N}$ is the number of spatial units indexed by ${\displaystyle i}$ and ${\displaystyle j}$; ${\displaystyle X}$ is the variable of interest; ${\displaystyle {\bar {X}}}$ is the mean of ${\displaystyle X}$; ${\displaystyle w_{ij}}$ is a matrix of spatial weights; and ${\displaystyle W}$ is the sum of all ${\displaystyle w_{ij}}$.

The value of Geary's C lies between 0 and 2. 1 means no spatial autocorrelation. Values lower than 1 demonstrate increasing positive spatial autocorrelation, whilst values 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.[1]

This statistic was developed by Roy C. Geary.[2]

## Sources

1. ^ J. N. R. Jeffers (1973). "A Basic Subroutine for Geary's Contiguity Ratio". Journal of the Royal Statistical Society (Series D). Wiley. 22 (4).
2. ^ Geary, R. C. (1954). "The Contiguity Ratio and Statistical Mapping". The Incorporated Statistician. The Incorporated Statistician. 5 (3): 115–145. doi:10.2307/2986645. JSTOR 2986645.