Geographic Information Systems: An Introduction, 3rd Edition

14.4 General Statistical Operations

Statistical operations are performed primarily on attribute data, but may also be effected on some types of geometric data. Most GISs support a range of statistical operations, including sum, maxima, minima, average, weighted average, frequency distribution, bidirectional comparison, standard deviation, multivariate, and others. The computation of averages requires averaging two or more attribute values and stating the result as a new attribute. Frequency distributions are used to compile histograms, charts comprising rectangles whose areas are proportional to relative frequencies and whose widths are proportional to class intervals. The data used to draw a histogram may also be employed to plot a curve. Other statistical operations in common use include least-squares computations of transformation parameters from regression models, with the standard deviation as an expression of accuracy. Bidirectional comparison involves point-by-point correlation of two themes to produce a new statistical thematic layer and hence a new attribute.

In geometry, for points one can use statistical methods to look at the pattern in their spatial distribution (evenly distributed, randomly distributed, distributed in groups). To do this, nearest neighbor analysis is used. This is based on the middle value of all distances between each point and its closest neighbor. Curve shape can be expressed as the relationship between the straight distance and the real distance. ...