Getis-Ord Gi* Hot Spot Analysis
Also known as: hot spot analysis, cold spot analysis, Gi* statistic, local Gi statistic, Getis-Ord Gi* (Sıcak/Soğuk Nokta Analizi)
Getis-Ord Gi* is a local spatial statistic, introduced by Getis and Ord in 1992 and refined in 1995, that compares the value at each location and its neighbours against the global mean to identify statistically significant clusters of high values (hot spots) and low values (cold spots).
Key highlights
- Pinpoints statistically significant local clusters and maps them directly as hot spots and cold spots.
- Produces an interpretable per-location z-score that is tested against the standard normal distribution.
- Includes the focal location itself (the starred Gi* form), so a location can belong to its own cluster.
Intuition
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How it works
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When to use it
Use Gi* when you have a continuous variable measured at georeferenced locations and want to map statistically significant hot and cold spots across cross-sectional data with a reasonable sample (at least about 30 locations). It requires a defined spatial weight matrix, based on distance or k-nearest neighbours, and a multiple-testing (FDR) correction. Results are sensitive to the chosen distance threshold, so the neighbourhood definition must be justified. Unlike a LISA decomposition, Gi* only captures high-high and low-low clustering.
Strengths & limitations
- Pinpoints statistically significant local clusters and maps them directly as hot spots and cold spots.
- Produces an interpretable per-location z-score that is tested against the standard normal distribution.
- Includes the focal location itself (the starred Gi* form), so a location can belong to its own cluster.
- Cannot be applied without coordinate data; with no spatial reference a standard (non-spatial) clustering approach is needed instead.
- Results depend on the distance threshold or neighbour count chosen for the spatial weight matrix and can shift with that choice.
- Only detects high-high and low-low clustering; unlike LISA it does not flag spatial outliers (high surrounded by low, or vice versa).
Common pitfalls
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Applications
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Frequently asked
How does Gi* differ from Local Moran's I (LISA)?
Gi* identifies only clusters of similar values — high-high (hot spots) and low-low (cold spots). Local Moran's I additionally distinguishes spatial outliers, such as a high value surrounded by low values, so LISA gives a fuller local typology while Gi* focuses on concentration.
What does the Gi* z-score mean?
It is a standardised score comparing the local weighted sum of a location and its neighbours against the global mean. A large positive z-score signals a statistically significant hot spot; a large negative one signals a cold spot; values near zero indicate no significant local clustering.
Why is a multiple-testing correction needed?
Gi* runs one significance test per location, so on a map of many locations some will appear significant by chance. A false discovery rate (FDR) correction adjusts for these simultaneous comparisons and keeps the flagged hot and cold spots trustworthy.
Why do my hot spots change when I change the distance threshold?
Gi* depends on the spatial weight matrix that defines each location's neighbours, set by a distance threshold or a number of nearest neighbours. Because results are sensitive to this choice, the neighbourhood definition should be justified and its influence checked.
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. Geographical Analysis, 27(4), 286–306.
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Cite this page
ScholarGate. (2026, June 1). Getis-Ord Gi*. ScholarGate. https://scholargate.app/spatial-analysis/getis-ord-gi