For my “first take” on the Spatial Statistics Resources blog, I learned more about the mathematical statistics contained within the tools of the Spatial Statistics toolbox. I quickly realized that the tools can be grouped by common mathematical principle. For example, all hot spot identification is found using something called the Getis-Ord Gi* statistic. Looking at the Desktop 10 Help website list of sample applications, most tools are listed with an associated mathematical statistic (usually listed in parentheses). For example:
Question: Is the data spatially correlated?
Tool: Spatial Autocorrelation (Global Moran’s I)
Some of the mathematical concepts I am fairly well acquainted with, like ordinary least squares. Others I had never heard of. The Getis-Ord statistic is one I’d never encountered before. I used one of my primary research tools, the internet, and found the statistic was developed in the mid-nineties by the method’s namesake statisticians.
Link to the 1995 paper on the Getis-Ord statistic
But one need not always consult the internet at large. ESRI provides some explanation of each tool in various articles scattered around the Spatial Statistics folder from Desktop 10.0 Help. I’ve begun assembling a list with the link to each math principle/tool/statistics below. I would like to learn about these statistics, what their strengths and weaknesses are, and especially when it is not appropriate to use them (what are the assumptions?).
List of Mathematical Principles/Statistics Underlying the Suite of Available Spatial Statistics
Analyzing Patterns:
How Multi-Distance Spatial Cluster Analysis (Ripley’s K-function) works
How Spatial Autocorrelation (Global Moran’s I) works
How High/Low Clustering (Getis-Ord General G) works
Mapping Clusters:
How Hot Spot Analysis (Getis-Ord Gi*) works
How Cluster and Outlier Analysis (Anselin Local Moran’s I) works
Measuring Geographic Distributions:
How Directional Distribution (Standard Deviational Ellipse) works
Modeling Spatial Relationships:
Geographically Weighted Regression (GWR) (Spatial Statistics)
Ordinary Least Squares (OLS) (Spatial Statistics)