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What is Spatial Analysis?

Spatial analysis is a set of techniques for analyzing spatial data.  The results of spatial analysis are dependent on the locations of the objects being analyzed.  Software that implements spatial analysis techniques requires access to both the locations of objects and their attributes.

(after Goodchild)

This Wikipedia page provides a good overview of the types of spatial analysis:
http://en.wikipedia.org/wiki/Spatial_statistics

This on-line version of the book "Geospatial Anlaysis - a comprehensive guide" is a good introduction to spatial analysis:
http://www.spatialanalysisonline.com/output/

Spatial statistics extends traditional statistics to support the analysis of geographic data.  It provides techniques to describe the distribution of data in the geographic space (descriptive spatial statistics) , analyze the spatial patterns of the data (spatial pattern analysis), identify and measure spatial relationships (spatial regression), and create a surface from sampled data (spatial interpolation, usually categorized as geostatistics).  In this interview, Dr. Lauren Scott from ESRI explains the differences between traditional statistics, spatial statistics, and geostatistics:
http://www.esri.com/news/arcwatch/0410/lauren-scott.html

 
For more information about spatial analysis, go to the resrouces page for Spatial Analysis: https://apps.carleton.edu/collab/gis/Resources/SpatialAnalysis/