Quantitative choropleth maps

Definition

Quantitative Choropleth maps visualize the ratios of two values. The denominator of the ratio often corresponds to the reference area of the second value. The ratio can also be built by two absolute, non-areal values. The absolute values have to be related to an area because this area is coloured or hatched depending on the value of the ratio. The population per km², called population density, is an example for the first option. An example for the second option is the ratio of protestants to catholics per district (Witt 1967, p. 186).

Choropleth map according to option 1 (Institut für Kartografie 2004)

Choropleth map according to option 1 (Imhof 1972)

Choropleth maps are not meant to be used for the presentation of graded absolute values. This presentation provokes a wrong data interpretation. The map user multiplies the ratio value automatically by the district areas. Thus, large areas with lower ratios get more attention than small areas with higher ratios. For the visualization of absolute values point and area diagram maps are used (c.v. the following chapter).

Properties of Chotopleth maps

Visualization
The areas on which the relative values refer, are symbolized by area colours or patterns. Dark colours and dense patterns implicate large values or a high object density and vice versa.

Classification
Usually, relative values or densities are divided into different stepped classes. Areas, whose values belong to the same class, are represented by the same colour or pattern. The optimal number of classes varies in subject to the dataset and maps purpose. In order to get a readable map, it is important to use easily distinguishable colours.

Types of Choropleth Maps

According to the type of reference area, choropleth maps are divided into 3 main types.

• Choropleth maps with administrative structures refer to political borders like municipal, district, country borders etc..
• Dasymetric maps try to portray the real density situation, independent of political boundaries.
• Choropleth maps with regular raster fields use regular geometric forms as reference areas.

Below, each type of the mentioned choropleth maps is specified.

Choropleth Maps with Administrative Structures

Properties

This kind of map is also called "choropleth map according to the statistic method " (Imhof 1972, p. 164). The relative values represented in the map refer to political areas such as communities, districts or countries. The chosen area type depends on the purpose and the topic of the map as well as on the map scale. Occasionally, economic regions like "in the forest" or inhabited areas are used as well.

The following map is an example of a choropleth map with administrative structures. It shows the population density per district in Switzerland.

Population desity per district in Switzerland (Institut für Kartografie 2004)

The choice of the administrative reference unit, the classification and the class limits are deciding factors of the creation of this map type. Those parameters can strongly influence the map's statement by accenting or restraining certain values.

Advantages and Disadvantages of Choropleth Maps with Administrative Structures

Advantages

• The graphical visualisation of statistic data can be realised relatively easy and fast, due to the fact that the statistic data usually is related to political areas.
• Choropleth maps with administrative structures are applicable to any scale, provided that the areas do not become too small. In that case, there is the possibility to aggregate the date to the next higher administrative level: per example instead of communities districts are used. (Imhof 1972, p. 166).

Disadvantages

• The comparison of datasets from different years can be difficult, for example when the administrative areas change due to the aggregation of municipalities.
• Choropleth maps presume that the object density within a reference area is constant. In case that the real object density varies within an area the map falsifies reality. You can observe this effect for instance in mountainous regions where the populated part of the communities is much smaller than the effective community areas. The following example shows the problem: The most dense section does not appear in the map because it is compensated by the less dense part.
  
  

Dasymetric Maps

Properties

Dasymetric maps are also called "choropleth maps according to the geographic method" (Imhof 1972, p. 167) .

In comparison to the administrative area structure, the map is not divided into political areas but into areas of approximate object densities.

The following map extract shows a dasymetric map. Click on the image to see the entire map.

(Spiess 2004)

Konstruktionsmethoden

There are different methods to create a dasymetric map. Most of them use dot maps as a basis. Click here to recieve more detailed information about these methods.

Advantages and Disadvantages of Dasymetric Maps

Below, the advantages and disadvantages of dasymetric maps are listed:

Advantages

• Dasymetric maps allow the presentation of areas of approximate continuous object density.
• The possibility, that extremely dense and less dense areas compensate each other is minimal.

Disadvantages

• The map result varies depending on the cartographer.
• The construction of dasymetric maps is very time-consuming and expensive.
• The boundaries are sometimes arguable.
• Dasymetric maps are not appropriate for large scaled maps because of uncertainties and arbitrariness during the construction of the areas.
• The comparison of datasets from different years is not possible.

Coropleth Maps with Regular Pattern Structure

Properties

Choropleth maps with regular patterns structure are also called "Choropleth maps according to the geometric method" (Imhof 1972, p. 171)

The reference areas are defined by a regular grid of identical regular polygons like squares, triangles or hexagons. The polygon dimension varies depending on the map scale and the base data. Hectare, square kilometer or more coarsely meshed grids are conceivable. The closer the mesh, the more precise becomes the information in the map.
If a square pattern is used, it is reasonable to adjust the grid to the national coordinate system, especially for supra-regional presentations. Besides it simplifies the spatial extension of the database.

Triangle, square and hexagon raster

The basis data for the area formation preferably consists of coordinate based point data. The Swiss Federal Statistic Office provides several data as raster dataset (for example the population density hectare raster). Such datasets simplify the creation of choropleth maps with regular pattern structure.

Advantages and Disadvantages of the Regular Pattern Structure

Im Below the advantages and disadvantages are listed.

Advantages

• It is easy to compare the different reference areas because of the constant area.
• The comparison of different time observations is possible due to the fact that the reference areas contain their shape and size, independent from the spatial or political situation.
• It is possible to automate the mapping with the current data processing methods (e.g. GIS) (Hake et al. 2002, p. 478).
• Due to the constant reference raster areas it is possible to visualize absolute values.

Disadvantages

• Most of the statistical data does not exist in a raster or point related format. The data preparation is a time consuming and expensive process.
• Especially in wide meshed grids, the object density depends a lot on the position of the grid. On this account, small meshed rasters are recommended.
• In the map, natural boundaries, like e.g. the forest limit, can not be recognized anymore.

Generalization of Choropleth Maps

There are different methods to generalize choropleth maps. They can be used independently or in combination with each other. The main objectiv is, to preserve the minimal dimensions regarding the reference areas. The minimal dimensions depend on the following factors: the area's shape, colour and fill pattern and the colour and kind of its contour line. The following image provides an overview of minimal dimensions for areas of choropleth maps.

Minimal dimensions für Mosaikflächen (Spiess)

In case some reference areas fall bellow the minimal dimensions, it becomes necessary to generalize the areas. If political areas are required, the areas can be merged into the next higher hierarchic level (e.g municipalities are merged into districts). If this kind of generalization generates inhomogeneity within an area, its also possible to use e.g. municipality groups instead districts.

If the density values refer just to the settlement area of a municipality, it is possible to scale up too small areas or to merge them with larger areas, depending on their importance. In the second case, the value has to be newly calculated.

Grid maps can be generalized by increasing the mesh size: E.g four squares are merged into a new one and its value is newly calculated.

An other generalization method which works for all kinds of choropleth maps, is the reduction of the number of classes.

Besides the dataset and the area size, the counter lines have to be adapted to the map scale by simplifying and smoothing. This method is not relevant to grid maps because they already consist in simplified areas. The following images show an example for counter line generalisation.

Map extract befor and after the generalisation (Spiess)