#### Overview of this book

Spatial statistics has the potential to provide insight that is not otherwise available through traditional GIS tools. This book is designed to introduce you to the use of spatial statistics so you can solve complex geographic analysis. The book begins by introducing you to the many spatial statistics tools available in ArcGIS. You will learn how to analyze patterns, map clusters, and model spatial relationships with these tools. Further on, you will explore how to extend the spatial statistics tools currently available in ArcGIS, and use the R programming language to create custom tools in ArcGIS through the ArcGIS Bridge using real-world examples. At the end of the book, you will be presented with two exciting case studies where you will be able to practically apply all your learning to analyze and gain insights into real estate data.
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Introduction to Spatial Statistics in ArcGIS and R
Measuring Geographic Distributions with ArcGIS Tools
Analyzing Patterns with ArcGIS Tools
Modeling Spatial Relationships with ArcGIS Tools
Working with the Utilities Toolset
Introduction to the R Programming Language
Creating Custom ArcGIS Tools with ArcGIS Bridge and R
Application of Spatial Statistics to Crime Analysis
Application of Spatial Statistics to Real Estate Analysis

## The Analyzing Patterns toolset

The `Analyzing Patterns` toolset, found in the `Spatial Statistics Tools` toolbox and shown in the following screenshot, contains a set of tools that perform pattern analysis against a dataset. Each of these tools returns statistical information about the entire dataset. The output of these tools is not a map, but rather statistical information that helps determine if a dataset is clustered, dispersed, or has a random pattern.

To help interpret the results of these tools, this section will provide information about the null hypothesis, p-values, z-scores, and standard deviations.

### Understanding the null hypothesis

All the pattern analysis tools that we examine in this chapter work on the premise that our features or the values associated with those features are randomly distributed. This is known as Complete Spatial Randomness (CSR). This is the null hypothesis used with all the ArcGIS spatial statistics tools.

The pattern analysis tools return z-scores and p-values...