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Getis-Ord Gi* is used to find hotspots and coldspots of a feature in space. A hotspot is a cluster of high values in space, and a coldspot is a cluster of low values in space. Getis-Ord Gi* is essentially the z-score of the spatially lagged value of the feature at each location \(i\) ($j w{ij}x_j $), where \(w_{ij}\) is the spatial weight. In the original publication for Getis-Ord Gi* from 1992 (Getis and Ord 1992), the spatial weight is a distance-based binary weight indicating whether another location is within a certain distance from each location \(i\). Getis-Ord Gi excludes the location \(i\) itself in the computation of mean and variance of the lagged value, while Gi* includes the location \(i\) itself. Usually Gi and Gi* yield similar results. The mean and variance used in the z-score differ in Gi and Gi* and is described in this paper from 1995 (Ord and Getis 1995) and derived in (Getis and Ord 1992). Binary weights in the spatial neighborhood graph are recommended for Getis-Ord Gi*.

Below is a list of vignettes that use Getis-Ord Gi*. The links point to the sections that use Getis-Ord Gi*. The corresponding Google Colab notebooks are also linked to. The list is sorted by technology.

Vignette Colab Notebook Description
Spatial Visium exploratory data analysis Colab Notebook Getis-Ord Gi* of gene Myh2 (myosin heavy chain 2) in mouse skeletal muscle dataset


Getis, Arthur, and J Keith Ord. 1992. “The Analysis of Spatial Association by Use of Distance Statistics.” In Perspectives on Spatial Data Analysis, edited by Luc Anselin and Sergio J Rey, 127–45. Berlin, Heidelberg: Springer Berlin Heidelberg.
Ord, J K, and Arthur Getis. 1995. “Local Spatial Autocorrelation Statistics: Distributional Issues and an Application.” Geogr. Anal. 27 (4): 286–306.