# Geary's C

Geary's C is a measure of spatial autocorrelation. Like temporal autocorrelation, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, temporal autocorrelation is about proximity in time, while spatial autocorrelation is about proximity in (multi-dimensional) space. 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, Geary's ratio, or the Geary index.[citation needed]

This statistic was developed by Roy C. Geary.[1]

## Sources

1. ^ 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.