What search distance should I use when I create a hotspot map?

When using some of the Spatial Statistics tools (such as the Getis-Ord Gi*) or when undertaking a Point Density Analysis it is sometimes hard to know what search distance to set. There are different strategies for defining the optimal distance:

  1. You could guess
  2. If you understand your data you could make an educated guess based on needing approximately 8 other features within the search distance
  3. You could let your data tell you.

Clearly 3. is the preferred option!

There has been a really useful tool in the Spatial Statistics toolbox*, the Spatial Autocorrelation (Global Moran’s I), for some time which helps you measure spatial autocorrelation based on features locations and their attribute values (the data must have attribute values for this method to work). This will provide you with a Z score which indicated statistical significance. To determine the optimal search distance however you need to take this tool and run it multiple times (say 20) over different distances and noting each Z Score you plot them in Excel (or the Charting tools in ArcGIS Desktop) and based on where the z score peaks this will provide you with an idea of where you should set the search distance.

This method works really well although running the tool multiple times can take a while, especially if your dataset is quite big. You could of course be clever and build this into a Geoprocessing Model to iterate the Global Moran’s I tool. However, Esri have just released a “Supplementary Spatial Statistics” Toolbox which contains a Incremental Spatial Autocorrelation tool which does exactly what is described above except it iterates over multiple distances, thus meaning you don’t have to run the Global Moran’s I tool multiple times. It also provides you with an outputted table and a nice little graph showing you the plotted Z Scores.

You can download the Toolbox for ArcGIS 10 here.

In addition to the Incremental Spatial Autocorrelation tool there is also a tool for Exploratory Regression.


Whilst I’m writing this post, it provides me with a good opportunity to provide a link to one of the most useful spatial statistics resources on the ArcGIS Resource Centre. It contains many useful “How to” videos, presentations and case studies. If you’re new to Spatial Statistics in ArcGIS then this is definitely worth a visit. These resources can be found here.

* the Spatial Statistics Toolbox is available at ALL ArcGIS Desktop Licence levels.