A.1 Spatial Statistics in ArcGIS

With over a million software users worldwide, and installations at over 5,000 universities, Environmental Systems Research Institute, Inc. (ESRI), established in 1969, is a world leader for the design and development of Geographic Information Systems (GIS) software. GIS technology allows the organization, manipulation, analysis, and visualization of spatial data, often uncovering relationships, patterns, and trends. It is an important tool for urban planning (Maantay and Ziegler 2006), public health (Cromley and McLafferty 2002), law enforcement (Chainey and Ratcliffe 2005), ecology (Johnston 1998), transportation (Thill 2000), demographics (Peters and MacDonald 2004), resource management (Pettit et al. 2008), and many other industries (see http://www.esri.com/industries.html). Traditional GIS analysis techniques include spatial queries, map overlay, buffer analysis, interpolation, and proximity calculations (Mitchell 1999). Along with basic cartographic and data management tools, these analytical techniques have long been a foundation for geographic information software. Tools to perform spatial analysis have been extended over the years to include geostatistical techniques (Smith et al. 2006), raster analysis (Tomlin 1990), analytical methods for business (Pick 2008), 3D analysis (Abdul-Rahman et al. 2006), network analytics (Okabe et al. 2006), space-time dynamics (Peuquet 2002), and techniques specific to a variety of industries (e.g., Miller and Shaw 2001). In 2004, a new set of spatial statistics tools designed to describe feature patterns was added to ArcGIS 9. This chapter focuses on the methods and models found in the Spatial Statistics toolbox. Spatial statistics comprises a set of techniques for describing and modeling spatial data. In many ways they extend what the mind and eyes do, intuitively, to assess spatial patterns, distributions, trends, processes and relationships. Unlike traditional (non-spatial) statistical techniques, spatial statistical techniques actually use space – area, length, proximity, orientation, or spatial relationships – directly in their mathematics (Scott and Getis 2008).