19. Conclusion

The maps presented in this monograph suggest just a few of the numerous ways that demographers can use contour maps to clearly, efficiently, and simultaneously display both persistent global and prominent local patterns in population rates or levels over two dimensions. In particular, contour maps can strikingly reveal the interaction between age, period, and cohort patterns. By using small multiples, computer movies, or ratio surfaces demographers can use the maps to gain access to several dimensions.

Even in cases where some demographic data already have been carefully scrutinized by perceptive analysts who have uncovered most of the interesting patterns, contour maps may be useful in highlighting these patterns. With contour maps, what was before understood now can be seen. Furthermore, the maps, by giving demographers a new perspective on data, may focus attention on some neglected aspects and patterns in even thoroughly studied data.

Beyond efficient description, contour maps can help demographers with exploratory data analysis and with model building. Surfaces can be computed relative to some part of the surface or to another surface; and different surfaces can be placed next to each other and compared. The patterns produced by a model can be displayed for different parameter values as can the fit of the model to some empirical data. If the data are defined over two dimensions, then a contour map can be used to display the residuals, i.e., the differences between the actual values and the values predicted by the model. By scrutinizing the pattern of the residuals, an analyst may glean some clues as to how to improve the model. Tukey (1977) and Mosteller and Tukey (1977) provide clear discussions of the use of residuals in data analysis and model building and several statistical software packages enable users to conveniently plot contour maps of residents.

The resulting contour maps can be displayed not only as printed output but also on a computer monitor. The shades used in most of the maps presented in this monograph range from black to light grey, but the maps can be produced in glowing colors, on a color computer monitor or using a color printer, as illustrated by the 12 color maps included in this monograph and by the maps on the diskette included with the monograph: the effects are dramatic.

Tufte, in his lucid exposition of The Visual Display of Quantitative Information (1983), concludes that graphic designs should give "visual access to the subtle and difficult, that is, the revelation of the complex." Demographic surfaces can be particularly complex. A mortality surface, for example, might be defined over a century of age and a century of time, comprising 10,000 data points that may vary over four orders of magnitude. Contour maps are a striking, efficient, and clear means of giving demographers visual access to such surfaces.

William Playfair (1801), the pioneer of graphical methods for presenting statistical data, argued that with a good visual display "as much information may be obtained in five minutes as would require whole days to imprint on the memory, in a lasting manner, by a table of figures." The 100 Lexis maps in this monograph summarize more than half a million data points in a memorable, revealing manner.

Updated by L. Andreeva, 23-Sep-1998