In this example, we consider the location of playgrounds in part of Seattle. The position of playgrounds can be considered a spatial justice issue if we desire all parts of the city to have a playground in close proximity. We can compare the spatial distribution of play areas to that of theaters. While clustering in space might be acceptable for theaters, we would hope that play areas would be less clustered.

The initial map is composed in Quantum GIS (QGIS) with point shapefiles for play areas and theatres and a polygons shapefile for the boundaries of the study area. For an online tutorial on GIS basics with QGIS see: Introducing GIS worksheet (external link).

Initial Map of Play Areas and Theaters


In general, the play areas appear to be less clustered and more evenly distributed than the theaters, but how can this be established more objectively?  We will next look at how nearest neighbor analysis can answer this question.


The fTools plug-in for QGIS provides several “Analysis Tools” that are helpful in analyzing spatial inequality.  We will begin with the Nearest Neighbor tool, which can be accessed from the “Tools” menu when the fTools plug in has been installed.

The nearest neighbor tool brings up a dialog in which you only need to select the relevant layer and click OK.  Below are the results of the nearest neighbor analysis for the play areas and theaters.  The results indicate that play areas are significantly dispersed and theaters are significantly clustered, as explained below.


  • Expected Mean Distance:  would be the average distance between a point and its closest neighbor if the N-number of points were distributed randomly
  • Observed Mean Distance: the actual average distance between each point and the closest neighboring point.
  • The Nearest Neighbor index equals 1 if the observed and expected mean distances area equal, greater than 1 if observed distances are greater than expected and less that 1 if  observed differences are less than expected.
  • Z-Score: compares the nearest neighbor index to a theoretical distribution of random patterns, with values between -1 and 1 being within 1 standard deviation of the average random pattern.  Positive values above 2 may be said to exhibit a statistically significant degree of dispersal while negative values below -2 exhibit significant clustering.



Mean center calculations offer a way of summarizing information about spatial location and incorporating it into the map.

The Mean Coordinates tool offers a menu to generate a new single point shapefile from a layer of your choice.  The mean center point can also be depicted as mean circle where the diameter is equal to the average nearest neighbor distance.  Mean circles therefore help to visualize the “core” area of a given set of points.Mean circles can be created as follows:

  • Add a new field called “distance” in the properties for the mean coordinate layer
  • Turn on editing mode and enter the Observed Mean Distance from the Nearest Neighbor Analysis tool.
  • Modify the symbology in the layer properties to add a scaling factor for the size of the point based on the distance field.


In many cases, neighborhood boundaries are important in analyzing locations.  We often want to consider locations relative to characteristics of the resident population, given in Census Tract data.   If we need to determine the number of parks within each neighborhood or census track then the Points in Polygon tool is very useful.
The map above shows the study area divided into Census Tracts.  A Census Tract shapefile has been added to the map, which can be used with the Points in Polygon tool.  The points in polygon tool produces a new shapefile that include counts of the points within the attribute information for the polygons.  Changing the symbology for the layer produces the map below, which uses a color scheme to indicate the number of playgrounds within each tract.


Although the nearest neighbor analysis indicated that play areas are more evenly distributed than random, the Census Tract analysis indicates that some tracts have no play areas.  The lack of play areas in some tracts may be an instance of spatial inequality, although one weakness is that some of these tracts have play areas very close to their boundary.



To address the weakness inherent in treating playgrounds as single points in space, we use buffering to add a 1,000 ft service area around each play area. The image below shows the Buffer tool (fTools plug-in) dialog alongside the resulting map. The buffer distance uses the map units, in this case feet.  The new buffer layer has been added to the map between the play area points and Census Tracts layer.


After buffering, it is apparent that some of the Census Tracts that do contain a play area are in fact very close to a play area.  On the other hand, there are still tracts that are not near any play area.  Using the Join by Attributes by Location tool, we can then count the number of play areas within 1000 ft  of each tract.

The play area buffer attributes area added to the Census Tract layer and summarized by the Sum operation.  The crucial field in the resulting shapefile is “count,” which gives the number of play areas within 1000ft.  (Null values occur in tracts with no nearby play areas.)  The resulting shapefile is mapped below using a continuous color based on the count field.

The tracts with zero nerby play areas could now be considered under-served.  We might describe this as a form of spatial inequality, given the assumptions we have used in the example.  A logical next step would be to consider some demographic differences between the under-served tracts and those with play areas.  This is covered in the next section on analyzing distributions across territories.