Spatial Analysis

Getis-Ord Gi*: Finding Statistically Real Hot Spots

Concept article · Updated · by Dr. Anant Kumar Pathak

Any map has highs and lows, but which clusters are real and which are noise? The Getis-Ord Gi* statistic separates genuine spatial concentrations — hot spots and cold spots — from random chance, with a confidence level attached.

The physical basis

For each feature, Gi* compares the sum of its value and its neighbours' values against what you would expect if values were distributed randomly, returning a z-score. Large positive z-scores mark clusters of high values (hot spots); large negative z-scores mark clusters of lows (cold spots); the p-value tells you how confident to be.

The formula

Getis-Ord Gi* = Gi* z-score = (Σ wijxj − X̄ Σ wij) / (S · √[(n Σ wij² − (Σ wij)²)/(n−1)])

Reading the values

Typical range: A z-score (in standard deviations)

> +1.96 significant hot spot · < −1.96 significant cold spot · in between = not significant (95% confidence).

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What it runs on

Operates onA point or polygon layer with a numeric attribute — not tied to specific spectral bands.

In practice

It is used in epidemiology (disease clusters), crime analysis, and retail-demand and hazard mapping — anywhere you need defensible clusters rather than eyeballed ones.

Where it struggles

Results hinge on the distance band / neighbourhood definition and need enough features; multiple testing inflates false positives.

Results hinge entirely on how you define "neighbours" (distance band or contiguity), so justify that choice; and with many features, correct for multiple testing (for example a false-discovery-rate adjustment) to avoid spurious hot spots.

Compute Getis-Ord Gi* on your own study area

Skip the code. Draw or upload a boundary and Spatial Research Suite runs Getis-Ord Gi* on live data — with cloud masking, exports and citations built in.

Run this analysis in GISforus →

Frequently asked

What does the Gi* z-score mean?

It measures how strongly high (or low) values cluster around a feature: above +1.96 is a significant hot spot, below −1.96 a significant cold spot, at 95% confidence.

Why does the neighbourhood definition matter?

Gi* is computed over neighbours, so the distance band or contiguity rule you choose directly determines which clusters appear.

Primary reference: Getis, A. & Ord, J.K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis 24(3), 189–206.