# Standards Getis-Ord G*¶

The standard definition of Getis-Ord $$G^*_i$$ statistic 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 $$zscore(x) = \frac{x - mean(X)}{stdev(X)}$$

Todo

Julian Bruns: Add references to papers