Geary's C

Geary's C is a measure of spatial or an attempt to determine if adjacent observations of the same phenomenon are correlated. Spatial autocorrelation is more complex than because the correlation is multi-dimensional and bi-directional.

Geary's C is defined as

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 with zeroes on the diagonal (i.e., ${\displaystyle w_{ii}=0}$); and ${\displaystyle W}$ is the sum of all ${\displaystyle w_{ij}}$.

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