Getis-Ord Global G

Introduction

The focus of the family of G statistics derived by Getis and Ord (1992; Ord and Getis, 1995) is on spatial autocorrelation at the local level (local Gi statistics). However, they did include a global measure of spatial autocorrelation. The Global G is defined as (Getis and Ord, 1992: 194)

\(G(d) = {{\sum\nolimits_{i=1}^n\sum\nolimits_{j=1}^n w_{ij}(d)X_{i}X_{j}}\over{\sum\nolimits_{i=1}^n\sum\nolimits_{j=1}^n X_{i}X_{j}}}\)

Following the recommendation of Bivand (2013: 57) all spatial weight matrices will be converted to binary weights (style “B”) if they are not already.

The \(G(d)\) statistic is concerned with the overall concentration or lack of concentration in all pairs that are neighbours given the definition of neighbouring areas. The variable must contain only positive values to be used.

Inputs

To compute the Getis-Ord Global G statistic, we will look at socio-economic data in Melbourne to examine the extent of spatial-autocorrelation.

To do this:

  • Select Melbourne GCCSA as your area
  • Select SA2 SEIFA 2011 – The Index of Relative Socio-Economic Advantage and Disadvantage (IRSAD)  as your dataset, selecting all variables
  • Spatialise the dataset, naming it something like SPATIALISED SEIFA IRSAD Melbourne
  • Generate a Contiguous Spatial Weights Matrix for the spatialised dataset, using 1st order Queen contiguity. Name it something like Contig SWM Melbourne SA2s

Once you have done this, open the Getis-Ord Global G tool (Tools → Spatial Statistics → Getis-Ord Global G) and enter the parameters as they appear in the image below. These are also explained underneath the image

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  • Dataset Input: the dataset that contains the variable(s) to be tested. Here we use the dataset named SPATIALISED SEIFA IRSAD Melbourne
  • Spatial Weights Matrix: the spatial weight matrix to be used (described here). In this instance we use the one name Contig SWM Melbourne SA2s 
  • Variable: the variable(s) to be tested. Here we use Score
  • Alternative Hypothesis: indicates the alternative hypothesis; can be two.sided, greater. Here we use two.side

Once you have entered the parameters, click Add and Run to execute the tool

Outputs

Once your tool has run, click the Display button on the pop up dialogue box. This will open a text editor which should look something like the image below.

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These outputs are:

  • Global G with the corresponding standard deviate and p-value.
  • Global G with its expectation and variance.
  • The alternative hypothesis.