Spatial Statistics

Measuring Spatial Distributions

There are many different types of spatial statistics. Some spatial statistics are descriptive in nature and are concerned with summarizing the salient characteristics of a spatial distribution. Similar to the way that an average, or a mean, can be used to summarize a set of data values, feature pattern analysis tools such as mean or median center identify the geometric center or central tendency for a spatial distribution of geographic features. Computing the mean center for counties weighted by population in the state of California every decade from 1900 to 2000, for example, would find that the center of population was initially located in the northern half of the state near San Francisco but moved south every decade as population growth in Southern California outpaced population growth in the state's northern counties.

A traditional statistical computation such as standard deviation, which quantifies the variation and range of values around a mean value, has spatial equivalents with the standard distance and standard deviational ellipse feature pattern analysis tools. These tools quantify the spatial distribution of geographic features around their geometric center and provide information about dispersion and orientation for that spatial distribution. A crime analyst, for example, may want to compare the location and orientation of a standard deviational ellipse computed for daytime crimes with one computed for nighttime crimes to determine whether the spatial pattern is different. A shift in the location of the ellipse or a change in the size of the ellipse provides information about differences in crime concentration, dispersion, and orientation (to particular transportation networks or areas of day versus nighttime activities) and may have important implications for the allocation of police patrol resources.

Measuring Shape

Shape metrics are tools used to analyze feature shape, pattern, composition, and configuration. The most commonly measured characteristic for polygon features is compactness, often represented as a ratio of the length of the polygon's perimeter to its area. For linear features, a common shape metric quantifies

sinuosity. Other shape metrics assess the spatial arrangement, connectivity, diversity, or fragmentation among a set of geographic features or over an entire region.

Applying theory that relates ecological processes to environmental patterns, landscape ecologists employ shape metrics to assess biological diversity and habitat quality (habitat loss and fragmentation, for example). Some animal species require suitable habitat patches larger than some specified minimum size and/or may be adversely affected by edges (e.g., roads or urban development). Shape metrics for assessing the core area for each habitat patch in a landscape, the connectivity of these patches, and patch insularity are used to compute probabilities for species occupation and persistence.

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