Cartograms, or "value-by-area maps," are a traditional teaching and display device, for example to compare the relative populations or GNPs of different countries. Such cartograms include hand-drawn cartograms, rectangular cartograms, and non-contiguous area cartograms, which do not involve sophisticated programming techniques.
A cartogram by itself is useful for displaying data. Or, a cartogram can be used as a base map for choropleth (shaded) mapping of almost any variable, for example to enhance the relative visibility of small but populous areas.
Much of the published literature goes no further than this in considering the possible applications of cartograms, or density equalized maps.
A more sophisticated use of cartograms is for dot maps which display the geographic distribution of discrete events, such as cases of disease. Such maps, which have been called "population maps," require a "contiguous area cartogram," also known as an "anamorphosis" or Density Equalized Map Projection (DEMP). On a dot map where population has been density-equalized, cases should be randomly distributed if disease risk is everywhere equal.
For use in such applications, an appropriate density-equalizing variable is any denominator quantity that is customarily used to calculate rates; for example, any of the following:
Given a digital map file and its density-equalized counterpart(s), one can easily transform any given point from the original map to the transformed map, or vice versa. Thus the transformed map can be made recognizable via inclusion of internal boundaries, roads, landmarks, latitutde/longitude grids, etc. The same holds true for case locations if the exact address of residence is known.
If the exact address of residence is NOT known, all the cases in a given polygon should be plotted at random locations within the tract. The cases can be plotted on the original map and then transformed, or simply plotted at random locations within the transformed tract boundaries.
Visual analysis of density equalized maps is useful for quickly identifying areas of elevated risk. However, the inexperienced observer is rather prone to overestimate the significance of small clusters, which will always occur through random variation. This is especially true if the observer holds an a priori belief which happens to coincide with a small fluctuation in the data.
Statistical analysis is required to properly assess the significance of geographic disease distributions. Many techniques are available to calculate the probability (p-value) that an observed anomaly could have occurred through chance alone. Spatial analysis is greatly simplified on the density equalized map, where cases have a random distribution under the null hypothesis of equal risk. It is up to the individual analyst to provide the numerator case data that will be analyzed, and to develop the statistical technique(s) that will be used. We discuss some common pitfalls which can cause the unwary analyst to obtain biased results.
DEMP processing of user map files
Density Equalizing Map Projections (DEMP)