Geary's C Spatial Autocorrelation
Geary's C Spatial Autocorrelation Statistic · Also known as: Geary contiguity ratio, Geary's contiguity ratio, global spatial autocorrelation, Geary C mekânsal otokorelasyon
Geary's C is a global measure of spatial autocorrelation — whether nearby locations tend to have similar values — introduced by Roy Geary in 1954. Unlike Moran's I, which is built on the covariation of values around the mean, Geary's C is built on the squared differences between neighbouring values, making it more sensitive to local, short-range variation. Values below 1 indicate positive spatial autocorrelation (similar neighbours), near 1 indicate randomness, and above 1 indicate negative autocorrelation.
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When to use it
Use Geary's C to test for and quantify global spatial autocorrelation in an area-based variable — disease rates, income, pollution, vote shares — particularly when you care about local, short-range similarity between adjacent units, where it can be more sensitive than Moran's I. It is a standard companion to Moran's I in exploratory spatial data analysis and a diagnostic before fitting spatial regression models. It requires a sensible spatial weights matrix (the result depends on how neighbours are defined) and, like all global indices, reports a single summary for the whole map; to locate where clustering occurs, pair it with local indicators (LISA, Getis-Ord Gi*). A permutation test is preferred when normality of the variable is doubtful.
Strengths & limitations
- Directly captures local differences between neighbours, sensitive to short-range structure.
- Well-established global spatial-autocorrelation index, complementary to Moran's I.
- Supports both analytical and permutation-based significance testing.
- Simple to interpret on its 0–2 scale anchored at 1 for randomness.
- A single global value; it cannot show where clustering occurs.
- Sensitive to the choice of spatial weights matrix.
- Inverse, less-intuitive scale compared with Moran's I (low = clustered).
- The analytical test relies on distributional assumptions; permutation is safer.
Frequently asked
How is Geary's C different from Moran's I?
Both measure global spatial autocorrelation, but Moran's I uses cross-products of deviations from the mean while Geary's C uses squared differences between neighbouring values. Geary's C is therefore more sensitive to local, short-range differences, and its scale is inverted: values below 1 indicate clustering, whereas for Moran's I high positive values indicate clustering.
What does a Geary's C of exactly 1 mean?
It is the expected value under spatial randomness — no spatial autocorrelation. Values meaningfully below 1 indicate positive autocorrelation (similar neighbours cluster), and values above 1 indicate negative autocorrelation (dissimilar neighbours alternate). Significance must still be tested against the null.
Why does the spatial weights matrix matter?
The statistic only compares locations defined as neighbours by the weights matrix, so how you define neighbours (contiguity, k-nearest, distance band) directly shapes the result. Reporting and justifying the weights specification is essential, and sensitivity to alternative definitions is good practice.
Sources
- Geary, R. C. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician, 5(3), 115–146. DOI: 10.2307/2986645 ↗
- Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion. ISBN: 978-0-85086-081-8
How to cite this page
ScholarGate. (2026, June 2). Geary's C Spatial Autocorrelation Statistic. ScholarGate. https://scholargate.app/en/spatial-analysis/geary-c
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Getis-Ord Gi*Spatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare