Issue link: https://read.dmtmag.com/i/59336
normal curve is fitted to the data to characterize its overall "typical value" (average = 22.9) and "typical dispersion" (StDev = 18.7), without regard for the data's spatial distribution. In geographic space, the average forms a flat plane, implying that this value is assumed to be every- where within +/- 1 standard deviation about two-thirds of the time and offering no information about where values are likely more or less than typical. The fitted continuous map surface, however, details the spatial variation inherent in the field-collected samples. Nonspatial statistics identifies the "central ten- dency" of the data, whereas surface modeling maps the data's "spatial variation." Like a Rorschach ink blot, histogram and map surfaces provide two differ- ent perspectives. Clicking a histogram pillar identifies all the grid cells within that range; clicking on a grid location identifies which histogram range contains it. Murky Windows This direct link between the numerical and spatial characteristics of mapped data provides the foun- dation for the spatial-statistics operations outlined in Figure 3. The first four classes of operations are fairly self-explanatory, except the "Roving Window" summaries. This technique first identifies the grid values surrounding a location, then mathemati- cally/statistically summarizes the values, assigns the summary to that location, and then moves to the next location and repeats the process. Another specialized use of roving windows is for surface modeling. As described in Figure 2, inverse- distance weighted spatial interpolation is the weight- average of samples based on their relative distances from the focal location. For qualitative data, the total number of occurrences within a window reach can be summed for a density surface. In Figure 3, for example, a map identifying customer locations can be summed to identify the total number of customers within a roving window to generate a continuous map-surface customer density. In turn, the average and standard deviation can be used to identify "pockets" of unusually high customer density. Standard multivariate techniques using "data distance," such as maximum likelihood and clustering, can be used to classify sets of map variables. Map similarity, for example, can be used to compare each map location's pattern of values with a comparison location's pattern to create a continuous map surface of the relative degree of similarity at each map location. Statistical techniques, such as regression, can be used to develop mathematical functions among dependent and independent map variables. The dif- ference between spatial and nonspatial approaches is that the map variables are spatially consistent and Figure 3. A variety of spatial-statistics operations are illustrated. MARCH 2O12 / WWW . GEOPLA CE . C O M 11 Figure 2. Surface modeling can derive a continuous map surface from a set of discrete point data. yield a prediction map that shows where high and low estimates are to be expected. The bottom line in spatial statistics (as well as spatial analysis) is that the spatial character within and among map layers is taken into account. The grid-based representation of mapped data provides the consistent framework needed for such analyses. Author's Note: A table of URL links to further readings on the grid-based map analysis/modeling concepts, terminology, considerations and procedures described in this three-part series on spatialSTEM is posted at www.innovativegis.com/ basis/MapAnalysis/MA_Intro/sSTEM/sSTEMreading.htm.