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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