Statistical analysis of spatial relationships is important in GIS.

A good understanding of spatial relationships can help predict future changes and allow for better planning. For instance, if economic growth in different areas is independent of each other, interesting issues include how urban centers and rural areas interact, and how local amenities can affect economic development of local regions. People are also interested in the spatial relationship between an individual observation and its surroundings: (1) Is the observed value at this location surrounded by a cluster of high or low values? (2) Is the observed value at this location associated positively with the surrounding observations (similarity) or negatively with the surrounding observations (dissimilarity)? The only way to answer these questions is to perform statistical analyses.

Statistical analysis of spatial data requires special techniques.

It is usually assumed in standard statistical analysis that each observation is independently and randomly distributed with a consistent structure.Those standard statistics cannot be directly applied to spatial dataif the observed values are not independent to each other, if they don't follow the same distribution, or if there is a trend along different directions. Since spatial data often violates one or more of these assumptions, analyzing the data requires specialized statistical techniques appropriate to spatial data.

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Specialized statistical package makes analysis of spatial data possible, and we show you how.

In this study, we employ the S-PLUS extension for ArcView (Bao and Martin 1997), a product of MathSoft, to compute the spatial statistics and visualize the analytical results. S-PLUS (MathSoft 1997) is a modern object-oriented language and system for multi-purpose data analysis with over 2,000 functions. It provides powerful capabilities for graphical data analysis and statistical modeling. The added module SpatialStats (MathSoft 1996) provides additional analytical functionality of spatial statistics and models such as Kriging, Moran I statistics, and spatial regression models.

This case study requires a basic understanding of geographic information systems and ArcView 3.x.If you are unfamiliar with either of these,we recommend you read our Training Manual and complete the accompanying exercises before proceeding with this case study.

• Document (SpatialData.PDF - 4.16Mb) of this case study in Adobe Acrobat Reader format.

• Data used in  this case study (SpatialData.zip - 651 Kb)

• Xtools (xtools.zip - 39 Kb),  an extension for ArcView that contains useful spatial operation tools. It is developed, collected, or modified by Mike DeLaune, Oregon Department of Forestry.

Please read the Frequently Asked Questions for the Case Studies.

This case study developed by W/SA with contributions by the following;

• Dr.Yichun Xie, Director, IGRE at Eastern Michigan University.
• Beverly Hunter, Consultant to W/SA
• Dr.Shuming Bao,China Data Center,University of Michigan.
• IGRE Staff.