Simple Spatial Statistics

Description of the Problem

Spatial Statistics can be used to identify areas of interest for more intensive investigation. There are a variety of tools that can be used in investigation; each with their own benefits and draw-backs. The scenario presented here is an investigation of incidents and calls within EMS Battalion 2’s area of Fort Worth, Texas. The Battalion wants to investigate calls during the months of January and February 2007 to see if there are specific areas of interest so that they can better situate their response vehicles.

Strategies of Solving the Problem

In order to see where clustering has occurred a variety of spatial statistics tools (e.g. Average Nearest Neighbor, Getis-Ord General G, Multidistance Clustering, and Spatial Autocorrelation) were run on a data from calls taking place in either January or February 2007. If the spatial analysis with the highest z-score came back with a high confidence level (as close to 99.99% as possible), then then we can say the null hypothesis (i.e. random or dispersed distribution) is rejected thereby suggesting clustering around areas of interest.


This section will describe each tool used on the data opposed to a lump summarization of all tools.

  1. The Average Nearest Neighbor tool was run on the incidents from February 2007. This tool was run to see if the physical actual distributions of incidents differed from a hypothetical random distribution. A definition query was built to limit the data that was included. The results of running this tool showed a Nearest Neighbor Index of 0.715, Observed Mean Distance of 995.29, and Expected Mean Distance of 1,392.38 thus giving us a Confidence Level of 99% to reject the null hypothesis and accept there is clustering.
  2. The Getis-Ord General G tool was run on calls for January 2007 to see if calls within a given area shared any similar attribute thereby suggesting a clustering of that type of call. Distances ranging from 200 feet to 1,200 feet in 200 feet increments were tested. The results of this tool showed that the greatest Z-score, 9.861, could be found at 200 feet with a G-Index of 0.02. This resultant gives us a confidence level of 99%.
  3. The Multidistance Cluster (Ripley’s K Function) tool was run on calls for January 2007. This tool is more sensitive than the Average Nearest Neighbor tool since it can take into account multiple distances rather than what is just near. A 99 permutation envelope was run on the data starting at 200 feet and increasing by 100 feet increments to 1,100 feet. From the graph, it can be seen that the highest difference between expected and observed values is at 800 feet.
  4. The Spatial autocorrelation (Global Moran’s I) tool was run on the calls for February 2007 allowing for us to see if there is an underlying geographic clustering of the data based on both location and attribute value. After spatially joining the 200-foot square grid with the calls, the tool was run using distances starting at 250 feet to 600 feet and increasing by 50 feet increments. The highest Z-score, 3.703, was found at 550 feet with a 99% confidence to reject the null hypothesis and accept clustering at this distance.
Map 1: Average Nearest Neighbor
Map 1: Average Nearest Neighbor
Map 2: Getis-Ord General G
Map 2: Getis-Ord General G
Map 3: Multidistance Cluster (Ripley's K Function)
Map 3: Multidistance Cluster (Ripley’s K Function)
Map 4: Spatial autocorrelation (Global Moran's I)
Map 4: Spatial autocorrelation (Global Moran’s I)

Discussion of Methods

The only major issue that was encountered as attempting to import the table into Moran’s I map.

Data Evaluation Procedure

Output consistency was checked by verifying the confidence level across all tests for clustering. In some cases this meant running the tool multiple times in order to check results.

Reflection and Ideas of Other Applications

Spatial statistics have been applied in archaeological research for several decades now. However, it has been acknowledged that their use needs to be explicitly understood. As seen with this scenario, spatial statistics can take a very broad research area and suggest areas for us to focus our more intensive research. This work to narrow down research areas yet gain as much information as possible from a given research area is the goal of archaeological survey projects.