GEOG 486
Cartography and Visualization

Multivariate Symbols


There are generally two motivations that cartographers might have for creating a multivariate symbol: either we want to display multiple attributes at the same time to facilitate comparison between distributions, or we want to use multiple visual channels to redundantly represent one attribute for special emphasis. Different combinations of visual variables may better support different map reading tasks (e.g., determining if there is a geographical correlation between two variables or presenting two related variables intended to be read separately). We can turn to psychological research on visual attention to help guide our creation of multivariate symbol sets.

The term visual attention refers to the map user's focusing of his or her gaze and concentration on some particular area of the map. Psychologists have identified two main types of attention that lie on opposite ends of the attention spectrum: selective attention and divided attention. In selective attention, a map user can focus on one visual variable while ignoring another. Visual variable combinations that enable map users to easily read separate data variables are known as separable, whereas visual variable combinations that use divided attention, and are harder to read independently, are known as integral (see Figure, below). A third, intermediate type of symbol, known as a configural symbol, shows characteristics of being both separable and integral, i.e. it is possible to separate the dimensions of the multivariate symbol, while at the same time it is possible to extract relational information from the symbol (Nelson 2000).

A display of multivariate symbols. See text for more details
Figure This figure shows variable combinations that are separable, integral and configural. Notice how your eye can easily focus on either the light or dark, or big or small circles (or orange or blue, or squares or circles) in the separable symbol sets. Now if you concentrate on the integral symbol set, using saturation and value, are the differences as immediately apparent to your eye? This particular configural combination may work well because the size differences that are paired also produce shape differences (in the overall symbol) when one variable has a greater magnitude than another (and size/shape is a separable variable combination, see text below).

Separable visual variable combinations allow map users to easily compare two places on one or another attribute, but will be more difficult for the map user to determine whether there is some overall relationship between the two variables. In her study, Nelson (2000) found the following visual variable combinations to be separable: hue/shape, hue/size, hue/orientation, value/shape, and value/size. See Figure for an example of a map using separable bivariate symbols.

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Figure This map uses the separable visual variable combination of hue and size to communicate two attributes about immigration during the 1970s for each county in the U.S. Hue, a qualitative visual variable, is used to communicate the largest foreign-born group for each county, and size, a quantitative visual variable, is used to communicate the county's foreign-born population. Note that it is fairly easy to inspect the map for the two different variables independently, i.e. only where the majority of immigrants in each county are from, or only the relative amounts of immigrant population across counties. Go to the full interactive version of the New York Times Immigration Explorer, from which this map comes, to explore this data and symbolization further.
Credit: The New York Times

Integral visual variable combinations prevent a map reader from attending to one symbol dimension while ignoring another. Nelson (2000) identified height/width (of rectangular symbols), and color saturation/value as integral. Many other visual variable combinations in Nelson's study (2000) exhibited asymmetrical effects, meaning that one of the visual variables tends to give a stronger visual cue to the reader than the other. For example, the bivariate choropleth map shown in Figure uses a hue and value combination to communicate county attributes about population density. Hue is used to communicate three classes of population density in 1990, and value is used to communicate the percent change in population from 1990 to 2000. Between hue and value, hue is the dominant visual variable providing the stronger visual cue, and therefore the reader is better able to separate the differences of hue (and classes of population density) than value (and the change in population density). Other asymmetrical visual variable combinations Nelson (2000) found include hue/pattern and shape/size, with the dominant variable listed first.

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Figure This map illustrates the use of hue and value in a bivariate choropleth symbol to communicate two county attributes. Hue represents three classes of 1990 population density, and value represents three classes of percent change in population from 1990 to 2000.
Credit: United States Census Bureau

Nelson also found that using the same visual variable to represent two variables (e.g., in a segmented point symbol) can produce a configural variable combination that supports cross-variable comparisons. Finally, she found that the combination of value/chroma (or value/saturation) was an integral combination. This finding perhaps provides support for some cartographers' contention that map readers find it difficult to read maps that represent data using color chroma.

Want more examples of maps with multivariate symbols?

Discuss these maps, or other examples you know of, in the Lesson 5 discussion forum in ANGEL.

Recommended Readings

If you are interested in investigating this subject further, I recommend the following:

  • Nelson, E.S. 2000. "Designing effective bivariate symbols: the influence of perceptual grouping processes." Cartography and Geographic Information Science. 27(4): 261-78.