Spatial Statistics toolbox sample applications

Epidemiologists, crime analysts, demographers, emergency response planners, transportation analysts, archaeologists, wildlife biologists, retail analysts, and many other GIS practitioners increasingly need advanced spatial analysis tools. Spatial statistics help fill this need.

Spatial statistics allow you to

• Summarize the key characteristics of a distribution.
• Identify statistically significant spatial clusters (hot spots/cold spots) and spatial outliers.
• Assess overall patterns of clustering or dispersion.
• Model spatial relationships.

Summarize Key Characteristics

Questions	Tools	Examples
Where is the center?	Mean Center or Median Center	Where is the population center and how is it changing over time?
Which feature is most accessible?	Central Feature	Where should the new support center be located?
What is the dominant direction or orientation?	Linear Directional Mean	What is the primary wind direction in the winter? How are fault lines oriented in this region?
How dispersed, compact, or integrated are features?	Standard Distance or Directional Distribution (Standard Deviational Ellipse)	Which gang operates over the broadest territory? Which disease strain has the widest distribution? Based on animal sitings, to what extent are species integrated?
Are there directional trends?	Directional Distribution (Standard Deviational Ellipse)	What is the orientation of the debris field? Where is the debris concentrated?

Identify Statistically Significant Clusters

Questions	Tools	Examples
Where are the hot spots? Where are the cold spots? How intense is the clustering?	Hot Spot Analysis (Getis-Ord Gi*) or Cluster and Outlier Analysis (Anselin Local Moran's I)	Where are the sharpest boundaries between affluence and poverty? Where are biological diversity and habitat quality highest?
Where are the outliers?	Cluster and Outlier Analysis (Anselin Local Moran's I)	Where do we find anomalous spending patterns in Los Angeles?
How can resources be most effectively deployed?	Hot Spot Analysis (Getis-Ord Gi*)	Where do we see unexpectedly high rates of diabetes? Where are kitchen fires a higher-than-expected proportion of residential fires? Do crimes committed during the daytime have the same spatial pattern as those committed at night?
Which locations are farthest from the problem?	Hot Spot Analysis (Getis-Ord Gi*)	Where should evacuation sites be located?

Assess Overall Spatial Patterns

Questions	Tools	Examples
Do spatial characteristics differ?	Spatial Autocorrelation (Global Moran's I) or Average Nearest Neighbor	Which types of crime are most spatially concentrated? Which plant species is most dispersed across the study area?
Is the spatial pattern changing over time?	Spatial Autocorrelation (Global Moran's I) or High/Low Clustering (Getis-Ord General G)	Are rich and poor becoming more or less spatially segregated? Is there an unexpected spike in pharmaceutical purchases? Is the disease remaining geographically fixed over time, or is it spreading out to neighboring places? Are containment efforts effective?
Are the spatial processes similar?	Multi-Distance Spatial Cluster Analysis (Ripley's K Function)	Does the spatial pattern of the disease mirror the spatial pattern of the population at risk? Does the spatial pattern for commercial burglary deviate from the spatial pattern for commercial establishments?
Is the data spatially correlated?	Spatial Autocorrelation (Global Moran's I)	Do regression residuals exhibit statistically significant spatial autocorrelation?

Model Relationships

Questions	Tools	Examples
Is there a correlation? How strong is the relationship? Is the relationship consistent across the study area?	Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR)	What is the relationship between educational attainment and income? Is the relationship consistent across the study area? Is there a positive relationship between vandalism and residential burglary? Does illness increase with proximity to water features?
What factors might contribute to particular outcomes? Where else might there be a similar response?	Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR)	What are the key variables that explain high forest fire frequency? What demographic characteristics contribute to high rates of public transportation usage? Which environments should be protected to encourage reintroduction of an endangered species?
Where will mitigation measures be most effective?	Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR)	Where do kids consistently turn in high test scores? What characteristics seem to be associated? Where is each characteristic most important? What factors are associated with a higher-than-expected proportion of traffic accidents? Which factors are the strongest predictors in each high accident location?
How might the pattern change? What can be done to prepare?	Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR)	Where are the 911 call hot spots? Which variables effectively predict call volumes? Given future projections, what is the expected demand for emergency response resources?
Why is this location a hot spot? Why is this location a cold spot?	Hot Spot Analysis (Getis-Ord Gi*), Ordinary Least Squares (OLS), and Geographically Weighted Regression (GWR)	Why are cancer rates so high in particular areas? Why are literacy rates low in some regions? Are there places in the United States where people are persistently dying young? Why?

GIS offers many different approaches for analyzing spatial data. Sometimes visual analysis is sufficient: a map is created and it reveals all the information needed to make a decision. Other times, however, it is difficult to draw conclusions from a map alone. Cartographers make choices when a map is constructed: which features are included or excluded, how features are symbolized, the classification thresholds selected determining whether a feature appears bright red or a less-intense pink, how titles are worded, and so on. All these cartographic elements help to communicate the context and scope of the problem being analyzed, but they can also change the characteristics of what we see and, consequently, can change our interpretation. Spatial statistics help cut through some of the subjectivity to get more directly at spatial patterns, trends, processes, and relationships. When your analytical questions are especially difficult or the decisions made as a result of your analysis are exceptionally critical, it is important to examine your data and the context of your problem from a variety of perspectives. Spatial statistics offer powerful tools that can effectively supplement and enhance visual, cartographic, and traditional (nonspatial) statistical approaches to spatial data analysis.

Additional resources:

• Mitchell, Andy. The ESRI Guide to GIS Analysis, Volume 2 . ESRI Press, 2005.
• Understanding Spatial Statistics. Free ESRI Virtual Campus Web seminar.
• Regression Analysis Basics. Free ESRI Virtual Campus Web seminar.
• ArcUser Online articles: crime, health, real estate, regression analysis.
• Tutorials: GIS Tutorial II, Hot Spot Analysis, Regression Analysis.