Local Getis-Ord Gi* (Hot Spot Analysis)
Local Getis-Ord G-Star Statistic · Also known as: Gi* statistic, Getis-Ord Gi*, local G-star, hot spot statistic
The Local Getis-Ord Gi* statistic identifies statistically significant spatial clusters of high values (hot spots) and low values (cold spots) within a study area. Unlike global measures, it produces a z-score for every location, revealing where concentrated clustering occurs and with what statistical confidence.
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When to use it
Use Local Getis-Ord Gi* when you need to identify specific geographic locations of high-value or low-value clusters, not just confirm that global clustering exists. It is ideal for crime mapping, disease surveillance, retail site selection, environmental hazard assessment, and any application where the spatial extent and location of concentration matters. Prefer Gi* over Local Moran's I when you want to distinguish hot spots from cold spots cleanly without the spatial outlier categories. Do not use Gi* when your data lack a meaningful spatial reference, when sample sizes are very small (fewer than about 30 units), when the variable of interest is nominal or binary without meaningful magnitude, or when the research question is about global — not local — clustering. Ensure the spatial weights specification is theoretically justified and not data-driven, as ad hoc weight choices can inflate apparent significance.
Strengths & limitations
- Produces a z-score for every spatial unit, enabling direct mapping of statistically significant hot and cold spots.
- Includes the focal unit itself in the local sum, giving a more complete picture of local concentration than the Gi variant.
- Interpretable output: z-scores and p-values translate directly into confidence levels (90%, 95%, 99%) for hot spot maps.
- Computationally efficient and available in leading GIS platforms (ArcGIS, GeoDa, R spdep, Python PySAL).
- Robust to non-normality of the attribute variable when sample sizes are moderate to large, due to the asymptotic normal approximation.
- Sensitive to the choice of spatial weights matrix: different neighbourhood definitions can produce substantially different hot spot maps.
- Does not detect spatial outliers (high values surrounded by low neighbours or vice versa); Local Moran's I is better suited for that.
- Multiple testing inflation: testing significance at every location simultaneously increases the family-wise error rate unless corrected.
- Assumes the spatial process is second-order stationary (constant mean and variance across the study area); violations can generate spurious clusters.
- Edge effects can reduce reliability of Gi* values at the boundary of the study area where neighbourhood sums are incomplete.
Frequently asked
What is the difference between Gi and Gi*?
Gi excludes the focal unit i from its neighbourhood sum, whereas Gi* includes it. In practice Gi* is almost always preferred because including the focal unit gives a more complete measure of local concentration and avoids the ambiguity of how to handle self-weights. Most GIS software defaults to Gi*.
How do I choose the right distance band or neighbourhood definition?
The neighbourhood should reflect the spatial scale at which the process of interest operates — for example, walking distance for pedestrian crime, commuting distance for labour market analysis. Inspect variograms or use minimum distance ensuring every unit has at least one neighbour. Avoid choosing the bandwidth that maximises the number of significant clusters.
Should I correct for multiple testing?
Yes, when mapping Gi* across many locations simultaneously. The Benjamini-Hochberg false discovery rate (FDR) correction is commonly applied in spatial settings because it is less conservative than Bonferroni while still controlling the expected proportion of false positives.
Can Gi* detect both hot spots and spatial outliers?
Gi* detects hot spots (positive z-scores) and cold spots (negative z-scores) but cannot identify spatial outliers — locations where a high-value unit is surrounded by low-value neighbours. For spatial outliers use Local Moran's I, which produces a LISA cluster map distinguishing High-High, Low-Low, High-Low, and Low-High patterns.
What sample size is needed for reliable Gi* results?
The asymptotic normal approximation underlying Gi* z-scores becomes accurate with at least 30 spatial units and preferably more than 50, provided each unit has several neighbours. Very small study areas with fewer than 30 units should rely on permutation-based inference rather than the asymptotic z-score.
Sources
- Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189–206. DOI: 10.1111/j.1538-4632.1992.tb00261.x ↗
- Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286–306. DOI: 10.1111/j.1538-4632.1995.tb00912.x ↗
How to cite this page
ScholarGate. (2026, June 3). Local Getis-Ord G-Star Statistic. ScholarGate. https://scholargate.app/en/spatial-analysis/local-getis-ord-gi-star
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.
- Geary's CSpatial analysis↔ compare
- Hot Spot AnalysisSpatial analysis↔ compare
- Local Indicators of Spatial AssociationSpatial analysis↔ compare
- Local Moran's ISpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare