Spatial statistics and interpolation form a specialized branch of statistics focused on analyzing, modeling, and predicting phenomena distributed across geographic space. Unlike traditional statistical methods that assume independence between observations, spatial methods explicitly account for Tobler's First Law of Geography—that nearby locations tend to be more similar than distant ones, a pattern known as spatial autocorrelation. These techniques are fundamental to fields ranging from epidemiology and environmental science to urban planning and geology, enabling practitioners to detect disease clusters, predict pollutant concentrations, map crime hotspots, and estimate resource distributions. A critical insight: spatial data violates the independence assumption of classical statistics, making specialized tools essential—yet this very dependence structure also carries valuable information about underlying processes that standard methods would miss entirely.
What This Cheat Sheet Covers
This topic spans 25 focused tables and 143 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
Table 1: Global Spatial Autocorrelation Measures
Global measures summarize spatial dependence across the entire study area as a single index, making them useful for hypothesis testing and comparing datasets but masking local variation. The expected value under spatial randomness, not zero, is the correct baseline for interpretation.
| Statistic | Example | Description |
|---|---|---|
I = \frac{n \sum_i \sum_j w_{ij}(x_i - \bar{x})(x_j - \bar{x})}{\sum_i \sum_j w_{ij} \sum_i (x_i - \bar{x})^2} | • Measures overall spatial autocorrelation across the entire study area • ranges from -1 to +1 where values above E[I] = -1/(n-1) indicate positive clustering, below indicate dispersion, and near the expected value suggest random spatial patterns. | |
C = \frac{(n-1) \sum_i \sum_j w_{ij}(x_i - x_j)^2}{2 \sum_i \sum_j w_{ij} \sum_i (x_i - \bar{x})^2} | • Global measure based on squared differences between neighboring values • C < 1 indicates positive autocorrelation, C > 1 negative autocorrelation, C \approx 1 randomness• more sensitive to local variation than Moran's I. |