Choropleth map

# Choropleth map

Overview

Discussion

Encyclopedia

A choropleth map

A choropleth map (Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

χώρος + πληθαίν:, ("area/region" + "multiply") is a thematic map
Thematic map
A thematic map is a type of map or chart especially designed to show a particular theme connected with a specific geographic area. These maps "can portray physical, social, political, cultural, economic, sociological, agricultural, or any other aspects of a city, state, region,nation , or...

in which areas are shaded or patterned in proportion to the measurement of the statistical variable being displayed on the map, such as population density
Population density
Population density is a measurement of population per unit area or unit volume. It is frequently applied to living organisms, and particularly to humans...

or per-capita income.

The choropleth map provides an easy way to visualize how a measurement varies across a geographic area or it shows the level of variability within a region.

A special type of choropleth map is a prism map, a three-dimensional map in which a given region's height on the map is proportional to the statistical variable's value for that region.

## Overview

The earliest known choropleth map was created in 1826 by Baron Pierre Charles Dupin
Charles Dupin
Pierre Charles François Dupin was a French Catholic mathematician.He studied geometry with Monge at the École Polytechnique and then became a naval engineer. In 1819 he was appointed professor at the Conservatoire des Arts et Métiers; he kept this post until 1854...

. The term "choroplethe map" was introduced 1938 by the geographer John Kirtland Wright
John Kirtland Wright
John Kirtland Wright was an American geographer, notable for his cartography, geosophy, and study of the history of geographical thought. He was the son of classical scholar John Henry Wright and novelist Mary Tappan Wright, and the brother of legal scholar and utopian novelist Austin Tappan...

in "Problems in Population Mapping".

Choropleth maps are based on statistical data aggregated over previously defined regions (e.g., counties), in contrast to area-class and isarithmic
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...

maps, in which region boundaries are defined by data patterns. Thus, where defined regions are important to a discussion, as in an election map divided by electoral regions, choropleths are preferred.

Where real-world patterns may not conform to the regions discussed, issues such as the ecological fallacy
Ecological fallacy
An ecological fallacy is a logical fallacy in the interpretation of statistical data in an ecological study, whereby inferences about the nature of specific individuals are based solely upon aggregate statistics collected for the group to which those individuals belong...

and the modifiable areal unit problem
Modifiable Areal Unit Problem
The modifiable areal unit problem is a source of statistical bias that can radically affect the results of statistical hypothesis tests. It affects results when point-based measures of spatial phenomena are aggregated into districts. The resulting summary values are influenced by the choice of...

(MAUP) can lead to major misinterpretations, and other techniques are preferable. Choropleth maps are frequently used in inappropriate applications due to the abundance of choropleth data and the ease of design using Geographic Information Systems.
The dasymetric technique
Dasymetric map
The dasymetric map is a method of thematic mapping, which uses areal symbols to spatially classify volumetric data. The method was developed and named by Benjamin Petrovich Semenov-Tyan-Shansky and popularised by J.K. Wright....

can be thought of as a compromise approach in many situations. Broadly speaking choropleths represent two types of data: Spatially Extensive or Spatially Intensive. Spatially Extensive data are things like populations. The population of the UK might be 60 million, but it would not be accurate to cut the UK into two halves of equal area and say that the population of each half of the UK is 30 million. Spatially Intensive data are things like rates, densities and proportions. These can be thought of conceptually as field data that is averaged over an area.

Another common error in choropleths is the use of raw data values to represent magnitude rather than normalized values to produce a map of densities. This is problematic because the eye naturally integrates over areas of the same color, giving undue prominence to larger polygons of moderate magnitude and minimizing the significance of smaller polygons with high magnitudes. Compare the circled features in the maps at right.

## Color progression

When mapping quantitative data, a specific color progression should be used to depict the data properly. There are several different types of color progressions used by cartographers. The following are described in detail in Robinson et al. (1995)

Single-hue progressions fade from a dark shade of the chosen color to a very light or white shade of relatively the same hue. This is a common method used to map magnitude. The darkest hue represents the greatest number in the data set and the lightest shade representing the least number.

Two-variables may be shown through the use of two overprinted single color scales. The hues typically used are from red to white for the first data set and blue to white for the second, they are then overprinted to produce varying hues. These type of maps show the magnitude of the values in relation to each other.
Bi-polar progressions are normally used with two opposite hues to show a change in value from negative to positive or on either side of some either central tendency, such as the mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

of the variable being mapped or other significant value like room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...

. For example a typical progression when mapping temperatures is from dark blue (for cold) to dark red (for hot) with white in the middle. When one extreme can be considered better than the other (like this map of life expectancy) then it is common to denote the poor alternative with shades of red, and the good alternative with green.

Complementary hue progressions are a type of bi-polar progression. This can be done with any of the complementary colors and will fade from each of the darker end point hues into a gray shade representing the middle. An example would be using blue and yellow as the two end points.
Blended hue progressions use related hues to blend together the two end point hues. This type of color progression is typically used to show elevation changes. For example from yellow through orange to brown.
Partial spectral hue progressions are used to map mixtures of two distinct sets of data. This type of hue progression will blend two adjacent opponent hues and show the magnitude of the mixing data classes. When the two colors chosen match the solar spectrum that shows the greatest magnitude.

Full spectral progression contains hues from blue through red. This is common on relief maps and modern weather maps. This type of progression is not recommended under other circumstances because certain color connotations can confuse the map user.
Value progression maps are monochromatic. Although any color may be used, the archetype is from black to white with intervening shades of gray that represent magnitude. According to Robinson et al (1995). this is the best way to portray a magnitude message to the map audience. It is clearly understood by the user and easy to produce in print.

### Usability

When using any of these methods there are two important principles: first is that darker colors are perceived as being higher in magnitude and second is that while there are millions of color variations the human eye is limited to how many colors it can easily distinguish. Generally five to seven color categories is recommended. The map user should be able to easily identify the implied magnitude of the hue and match it with the legend.