Geary's C
Encyclopedia
Geary's C is a measure of spatial autocorrelation. Like autocorrelation
, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, autocorrelation
is about proximity in time. Spatial autocorrelation is about proximity in (two-dimensional) space. Spatial autocorrelation is more complex than autocorrelation
because the correlation is two-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; and 
is the sum of all 
.
The value of Geary's C lies between 0 and 2. 1 means no spatial autocorrelation. Smaller (larger) than 1 means positive (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.
This statistic was developed by Roy C. Geary
.
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
is about proximity in time. Spatial autocorrelation is about proximity in (two-dimensional) space. Spatial autocorrelation is more complex than autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
because the correlation is two-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; and is the sum of all .The value of Geary's C lies between 0 and 2. 1 means no spatial autocorrelation. Smaller (larger) than 1 means positive (negative) spatial autocorrelation.
Geary's C is inversely related to Moran's I
Moran's I
In statistics, Moran's I is a measure of spatial autocorrelation developed by Patrick A.P. Moran. Spatial autocorrelation is characterized by a correlation in a signal among nearby locations in space. Spatial autocorrelation is more complex than one-dimensional autocorrelation because spatial...
, 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.
This statistic was developed by Roy C. Geary
Roy C. Geary
Dr. Robert Charles Geary was an Irish statistician and founder of both the Central Statistics Office and the Economic and Social Research Institute. He held degrees from University College Dublin and the Sorbonne. He lectured in mathematics at University College Southampton and in applied...
.