Global Getis-Ord Gi* Statistic
Also known as: Global G statistic, Getis-Ord General G, General G*, Global spatial clustering statistic
The Global Getis-Ord Gi* statistic measures the overall degree of spatial clustering of high or low values across an entire study region. It answers whether the study area, taken as a whole, exhibits significant concentration of high values (hot clustering) or low values (cold clustering), returning a single summary Z-score for the entire dataset.
Key highlights
- Provides a directional test — distinguishes between clustering of high values versus clustering of low values, unlike Moran's I.
- Produces a single interpretable Z-score with a straightforward p-value for the entire study area.
- Computationally simple and well-supported in major GIS and spatial statistics packages (ArcGIS, GeoDa, spdep in R).
- Backed by a well-established asymptotic distributional theory, enabling standard normal inference in large samples.
- Useful as a preliminary global diagnostic before running computationally intensive local statistics.
Intuition
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How it works
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When to use it
Use Global Gi* when you need a single, study-wide test for whether high or low attribute values cluster spatially — for example, checking whether disease incidence, property prices, or pollution concentrations exhibit overall hot or cold clustering before conducting local analyses. It is appropriate when you have a continuous non-negative attribute, a defined study area, and a theoretically motivated distance threshold. Do not use it when values can be negative (the statistic assumes non-negative data), when you need to locate specific hot or cold spots (use Local Gi* instead), or when spatial association rather than clustering direction is the primary question (prefer Moran's I in that case).
Strengths & limitations
- Provides a directional test — distinguishes between clustering of high values versus clustering of low values, unlike Moran's I.
- Produces a single interpretable Z-score with a straightforward p-value for the entire study area.
- Computationally simple and well-supported in major GIS and spatial statistics packages (ArcGIS, GeoDa, spdep in R).
- Backed by a well-established asymptotic distributional theory, enabling standard normal inference in large samples.
- Useful as a preliminary global diagnostic before running computationally intensive local statistics.
- Requires non-negative attribute values; negative data violate the statistic's theoretical basis.
- The result is highly sensitive to the choice of distance threshold d — different thresholds can yield different significance conclusions.
- As a global statistic it masks local variation: a non-significant global G does not rule out local hot or cold spots that cancel each other out.
- Assumes stationarity — the clustering process is assumed to operate uniformly across the study region, which may not hold in heterogeneous landscapes.
- The asymptotic normal approximation can be unreliable for small datasets or irregular spatial configurations; permutation-based inference is safer.
Common pitfalls
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Applications
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Frequently asked
What is the difference between Global Gi* and Moran's I?
Moran's I tests for general spatial autocorrelation (any pattern of similar values clustering together) and can detect both positive and negative associations. Global Gi* is directional: a positive Z-score specifically indicates clustering of high values and a negative Z-score indicates clustering of low values. Gi* also requires non-negative data, while Moran's I does not.
How do I choose the distance threshold d?
The threshold should reflect the spatial scale of the process you hypothesise is driving clustering. A practical approach is to plot G(d) against a range of distances and look for the distance at which clustering is strongest, or to use a distance that ensures each location has at least one neighbour on average. Substantive domain knowledge should guide the final choice.
Why does my Global Gi* show no significance when I can see obvious clusters on the map?
A global statistic can yield a non-significant result when high-value clusters and low-value clusters co-exist and statistically cancel each other. In that case, run the Local Gi* (hot spot analysis) to identify the individual cluster locations.
Can I use permutation inference instead of the normal approximation?
Yes, and it is often preferable for small or irregular datasets. Permutation testing randomly reassigns attribute values across locations many times to build an empirical null distribution, avoiding reliance on the asymptotic normal approximation.
Does the Global Gi* control for multiple comparisons?
No — the Global G produces a single test for the whole study area, so multiple-comparison correction is not directly relevant. However, if you test multiple distance thresholds, you should adjust for multiple testing (e.g., Bonferroni correction) to avoid spurious significance.
Sources
- 1.Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189-206.
- 2.Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286-306.
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Cite this page
ScholarGate. (2026, June 3). Global Getis-Ord Gi*. ScholarGate. https://scholargate.app/spatial-analysis/global-getis-ord-gi-star