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# Standard Getis-Ord G*¶

The standard definition of Getis-Ord $G^*_i$ statistic1 assumes a study area with $n$ points with measurements $X = [x_1, \ldots, x_n]$. Moreover, it assumes weights $w_{i,j}$ to be defined between all pairs of points $i$ and $j$ (for all $i,j \in \{ 1, \ldots, n\}$). The formula to compute $G^*_i$ at a given point $i$ is then:

G^*_i = \frac{ \sum_{j=1}^{n}w_{i,j}x_j - \bar{X}\sum_{j=1}^{n}w_{i,j} }{ S \sqrt{ \frac{ n \sum_{j=1}^{n}w_{i,j}^2 - (\sum_{j=1}^{n}w_{i,j})^2 }{n-1} } }

where:

• $\bar{X}$ is the mean of all measurements,
• $S$ is the standard deviation of all measurements.

As it is known, this statistic creates a z-score, which denotes the significance of an area in relation to its surrounding areas.

Note

For $x \in X$, the $zscore(x) = \frac{x - mean(X)}{stdev(X)}$

1. Ord, J. K. and A. Getis (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis 27.