Scale - Spatial Mathematics: Theory and Practice through Mapping - page 114

the randomizing layer only or if the scale of the view has been altered so
that clustering patterns are seen from a scale perspective broader than that
afforded by only the randomizing layer.
In addition, there are a number of other subtle, but important, points that
underlie the construction of a dot density map. Certainly we had to decide
how many people were represented by a single dot. But, in addition, we
have the option to choose whether such representation is absolute or relative.
Absolute representation is one dot represents 1000 people. Relative repre-
sentation is one dot represents 0.1% of the population of the state, county, or
other areal unit. For the sake of communicating example in the sequence of
images above, we chose an absolute representation. If instead, we had wished
to make comparisons between regions by tossing a unit square on a map and
comparing populations within selected unit squares to the random one, then
choosing a relative representation would have been appropriate.
Finally, in order to make valid comparisons from one area to the next, make
sure to choose an equal area projection (so that Greenland does not look big-
ger than Brazil, or another similar areal inaccuracy). This is another impor-
tant, yet perhaps subtle, point that means more at the global level than it does
at the local level. The base map chosen for the figure sequence above was an
Albers Equal Area conic projection (more on projections in Chapter 9). When
looking at a dot density map, consider therefore the projection on which it
is based—it should be an equal area projection. Otherwise, areal distortions
may lead to inaccurate conclusions about the density of the phenomenon
being studied, because the dots may be spread out or clustered simply to
cover the distorted areas.
To summarize the decisions:
• Select an equal area projection (such as an Albers Equal Area Conic
for the United States).
• Select a distribution that can usefully be represented, in an absolute
or relative manner, as dot scatter—such as population.
• Then, choose polygonal nets of at least two different scales—such
as state and county boundaries. To extract the most meaning, make
sure that the smaller units “nest” inside the larger units (rather than
overfitting or underfitting them).
• Let the map with the smallest spatial unit that is practical (such as
counties) be used as the randomizing layer—the dot scatter is spread
around randomly within each unit.
• View the scatter through polygons (states) that are larger than are
those of the randomizing layer (counties). Figure 5.4 shows the results
of removing the county boundaries. The clustering of dots at the state
level means something; at the county level it is merely random.
• Since the underlying projection is an equal area projection, a unit
square (or other polygon) may be placed anywhere on the map and
comparisons may be made between one location and another.