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Maps of the Census: a rough guide
Visual methods of displaying enumerated data, such as those collected in the UK Census of Population, have long been attractive to those engaged in geographic enquiry. Symbols positioned to represent sample locations can be visually configured in order to display recorded attributes in a map containing both the Gestalt to allow geographic patterns to be interpreted at a regional scale, and the detail for local variations to be detected and data values perceived. In this Case Study we address some of the issues involved in mapping such data and describe the development and use of a tool that uses maps in a highly interactive environment for exploratory data analysis, and resources which promote the approach. In cartography such displays are referred to by the word choropleth, in which choro means area and pleth indicates value.
Choropleth maps are used to visualise data that have been enumerated, or summed, over some defined areas of the Earth's surface Typically in UK these are derived from the ten yearly Census of Population, and the scientific interest lies in the spatial pattern they exhibit. The role of visualisation in this application is to allow such patterns to be detected and explored in an essentially exploratory approach to analysis.
Figure 1: A choropleth map of population density for the 187 Census wards of Leicestershire in 1991.
Figure 1 shows a choropleth map of the overall density of population in census wards drawn from 1991 census data for Leicestershire (UK). The stippled areas are zones for which the data are suppressed for confidentiality reasons.
The main elements making up this map are
In effect, what has been created is a two dimensional histogram in which the individual areas have the same role as the bins (classes) and the mapped density values are the same as the heights of the histogram bars. This type of map is described in virtually every cartography textbook (our favourite is that by Borden Dent, 1985) and has become the standard way of representing area-value data on paper. Many computer cartography programs in particular have been developed to produce such maps on screen and paper. Almost all geographical information systems (GIS) have a choropleth mapping capability. Note that in our figures we have not included any of the standard base detail, such as a scale bar, frame and north point, that is usually added to maps for publication. Our intention here is to use the maps that we produce to demonstrate variations in map design, thus they do not follow many of these usual cartographic conventions which would in this context be superfluous. Figure 1 shows that there is a concentration of population in the central city (Leicester) and the other main towns of Loughborough, Hinckley and Melton Mowbray. Although this type of map is a faithful reflection of the data (head counts and zone boundaries) used, it can often be a very poor representation of the underlying patterns it represents
Thinking of it as a two-dimensional histogram helps us see why. In statistics histograms are used to summarise sample data and provide a graphical estimate of some unknown, underlying probability density function (for example, the normal distribution). This function is often added using appropriate parameter estimates, such as when we fit a normal curve to a histogram using the estimated mean and standard deviation. When drawing a histogram the analyst has total control on the size of the classes into which the data are grouped and in most cases these bins are of equal width. Not only this but, since there are just two sources of variation, the value range shown along the x-axis and the frequencies of occurrence shown on the y-axis, the two-dimensions given by a sheet of paper or computer screen are sufficient for the required visualisation.
On a choropleth map the zone boundaries create spatial bins over which we have no control and that usually have unequal sizes and shapes. Secondly, we have three sources of variation, the (x, y) co-ordinates that make up the pattern of zones and the value assigned for each zone. The need is to represent three dimensions of variation in two, and this is accomplished by use of a classification of the zone values into categories, each of which is given a grey scale shading. Clearly, the choice of both the categories and the shades used to represent them is arbitrary, but plays an enormous role in determining the look of the finished map. The result is that our map may be as much a result of the zones used and the choice of categories and symbols as it is of the underlying geography. Although we develop these ideas for this specific type of map in his book How to Lie with Maps, Mark Monmonier (1991) provides similar examples for virtually any type of map that might be drawn. Early in the days of computer cartography attention was drawn to many of these problems by Baxter (1976) and an excellent recent summary is provided by Kennedy (1994).
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