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
  • Partition features into similar groups
  • Identify features with similar characteristics
  • Model spatial relationships

Summarize Key Characteristics


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 sightings, 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


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)

or Optimized Hot Spot Analysis

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*)

or Optimized Hot Spot Analysis

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*)

or Optimized Hot Spot Analysis

Where should evacuation sites be located?

Which features are most alike? What does the spatial fabric of the data look like?

Spatially Constrained Multivariate Clustering

Multivariate Clustering

Which crimes in the database are most similar to the one just committed?

Are there distinct spatial regimes of test scores? Which regions are associated with high test scores and which with low test scores?

Which disease incidents are likely part of the same outbreak based on space, time, and symptoms?

Which features are most similar or most dissimilar?

Similarity Search

Which locations have similar characteristics to those with my best performing stores?

How do salaries for my employees compare to salaries for equivalent jobs in other cities most like mine?

Which crimes in the database most closely match a particular crime of interest?

Assess Overall Spatial Patterns


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 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?

At which distances is spatial clustering most pronounced?

Incremental Spatial Autocorrelation

Which distance best reflects an appropriate scale for my analysis?

Model Relationships


Is there a correlation? How strong is the relationship? Which variables are the most consistent predictors? Are the relationships consistent across the study area?

Ordinary Least Squares (OLS) , Exploratory Regression, 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?

Which combinations of the candidate explanatory variables will yield properly specified regression models?

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) , Exploratory Regression, Geographically Weighted Regression (GWR) and Forest-based Classification and Regression

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) Geographically Weighted Regression (GWR) and Forest-based Classification and Regression

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)

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 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 analytic 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.

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