Perception of Spatial Dispersion in Point Distributions
Sadahiro, Yukio, Cartography and Geographic Information Science
Dot maps are fundamental tools for visualizing the spatial pattern of point phenomena. They convey various spatial concepts to map readers (such as clusters, regions, homogeneity, and regularity), and these concepts help the readers to detect the underlying phenomena of point distributions. Thus researchers who study spatial point patterns--cartographers, geographers, and epidemiologists--use dot maps to analyze point distributions visually.
Spatial concepts, however, cannot always be successfully communicated if map authors do not understand the perception of spatial concepts by map readers. Spatial clusters, for instance, are difficult to perceive if the points are displayed by a too small symbol. If the symbol is too large, points overlap and clustering is excessive. Map authors should choose an appropriate map symbol to communicate the concept of spatial clusters.
To improve the communication of spatial concepts, the perception of spatial concepts on dot maps was studied by a number of researchers. Sadahiro (1997) analyzed the perception of spatial clusters. He discussed the principles causing cluster perception and proposed a statistical method for predicting spatial clusters perceived on dot maps. Experiments were performed to test the validity of the model; the model were found to predict successfully perceptual clusters. The concept of spatial region was studied by McCleary (1975). He asked subjects to delineate regions on dot maps and found two distinct patterns of generalization which he called "atomists" or "generalists."
These two concepts are local rather than global; clusters and regions represent local characteristics of point distributions. In contrast to local concepts, global concepts have not yet been studied in their perceptual aspect. The concept of spatial dispersion, i.e., the overall degree of dispersion of points, is one of the most important global concepts in geography (King 1969), GIS (Fotheringham and Rogerson 1994), spatial statistics (Cressie 1991), and other related fields (Pielou 1977; de Lepper et al. 1995). The pattern of point distributions is often described by the degree of their spatial dispersion as "tightly clustered," "clustered," "dispersed," and "uniformly distributed." In spite of its importance and wide use, the perception of global dispersion has not yet been studied.
To fill this gap in knowledge, we have studied the perception of spatial dispersion on point distributions and built mathematical models representing the relationship between the perception and map characteristics. The resulting models will enable map authors to predict the degree of perceived spatial dispersion and display point objects appropriately when communicating spatial dispersion.
In the following sections, we first discuss map characteristics that affect the perception of spatial dispersion. We then conduct two experiments to investigate how the characteristics affect the perceived spatial dispersion in point distributions, and build mathematical models to represent the perception on the basis of the results of the experiments. The models enable us to predict the degree of spatial dispersion perceived by map readers and provide design guidelines for map authors to communicate the concept of spatial dispersion. Finally, we perform computer-assisted Monte-Carlo simulations to illustrate the relationship between map characteristics and the perception of spatial dispersion.
Map Characteristics Affecting Perception of Spatial Dispersion
A variety of variables affect the perception of spatial dispersion on dot maps. We classify them into two types: visual variables and spatial variables. Visual variables determine the appearance of point symbols, for instance, symbol color, symbol size, and background color. Spatial variables are related to the spatial distribution of points, including the spatial arrangement of points, the number of points, map orientation, and map scale. …