# 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

$C = \frac{(N-1) \sum_{i} \sum_{j} w_{ij} (X_i-X_j)^2}{2 W \sum_{i}(X_i-\bar X)^2}$

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

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.