5: Simplification

5.1.1 Dot Map

On a dot map, each dot represents a fixed quantity. For one-to-one dot maps each dot represents one object or person. For example, John Snow’s famous map had one dot for each reported death from cholera around the Broad Street pump.

One to one cholera map. John Snow’s famous one-to-one map of cholera deaths centered around the Broad Street pump.^[3]

Alternatively, one dot can stand in for multiple objects or people. The figure below shows an example of a many-to-one map in which one dot represents 10,000 people.

Many-to-one dot map. This map portrays the total population of the Northeastern United States. Each dot represents 10,000 people. ^[4]

Dot maps are useful for quickly visualizing patterns of clustering and density. They do not require color to communicate, which avoids issues arising from differences in how people perceive color such as color blindness. Though they are versatile and intuitive, it can be hard to determine precise numbers based on a dot map. One area may have more dots than another, but to know how many more would require you to painstakingly count hundreds or thousands of dots.

Privacy can also be an issue for one-to-one maps. For example, you might not want exact locations known when mapping sensitive subjects such as where patients with sexually transmitted diseases live. To get around this, dots are often displaced from their actual location. By simplifying the number of dots on the map, many-to-one maps avoid privacy problems, but instead face the challenge of where to place the dots. Dots are generally positioned at an average location of the multiple objects represent ed .

Dot map simplification. The placement of dots in the middle of roads and unevenly distribution around the block are evidence that the dots in the one-to-one dot map have been displaced. The many-to-one map of the same blocks simplifies the amount of data shown and places dots at an average location. ^[5]

Note that it is crucial that dot maps be drawn using an equal area projection, or the density of the dots will be distorted.

5.1.2 Proportional Symbol Map

This type of map adjusts the size of simple symbols proportionally to the data value found at that location. The larger the symbol, the “more” of something exists. Proportional symbols can be used to represent data at precise locations (points) or data averaged over a geographic area. A key advantage of this type of map is that perception of data value is not affected by the size of the area that the symbol represents. In choropleth maps, states with small geographic areas (such as Rhode Island) may be overlooked even if they have a large data value. By contrast, the sizes of symbols in a proportional symbol map are not tied to the land area.

The downside to this is the greater likelihood of visual clutter. Symbols may overlap if locations with large values are close together. As in the figure below, the relative sizes of symbols can matter. If you choose symbols that are overall too small, it will be more difficult for the map reader to see patterns in the data (top left) but if they are too large, many symbols will overlap and make it difficult to see patterns in the data (top right). Ideally, the symbols have a slight overlap between symbols in the most crowded area of the map (bottom) without there being so much overlap that symbols are hidden.

Symbol size. Proportional symbol map of motor vehicle deaths in California, United States. Note how the relative sizes of symbols must be chosen with care. ^[6]

This problem of overlap in proportional symbol maps can get to the point where people have trouble accurately comparing symbol sizes, in the figure below. Many people underestimate differences in symbol size, especially when the difference is large. The proportional symbol map maker must strike a balance between having a range of symbol sizes and limiting their overlap.

Proportional symbol map. With this map of population by county it is difficult to make out which county each symbol represents in areas with many small populated counties. ^[7]

5.1.3 Choropleth Map

On choropleth maps, areas are shaded using hue or value to represent different quantities. Usually darker hues or values signify larger quantities. Choropleth maps are easy to make and to interpret, which has made them very popular among map makers. They can, however, be very misleading if incorrectly standardized or if the geographic phenomena being mapped are not intrinsically tied to the areas being shaded. For example, rainfall totals, soil type, and length of commute do not vary according to county or zip code boundaries. Phenomena being mapped rarely change abruptly at human-defined boundaries as they appear to do on a choropleth map, and there may be a lot of variation within an area symbolized with a single color. When working with choropleth maps, a mapmaker must try to maintain important patterns while simplifying unnecessary complexity.

Choropleth map of population density. This map of population density by county from the 2010 Census relies on users correctly interpreting the way the data are divided into groups. ^[8].

5.3.1 Equal Interval

Using the equal interval method, data is split into classes that have an equal range of values (e.g., 0-100, 100-200, 200-300, and so on). Equal interval is easy to interpret and to compare with other maps in a series. However, it does not work well for all data distributions. If there are gaps in the data values, some classes may be empty. If the data are strongly skewed or has outliers, you may end up with a map where almost all areas are in a single class. Equal interval works best when data are relatively evenly distributed between the minimum and maximum value, and there are no outliers.

Equal-interval classification. Population density by county in Minnesota, United States using equal-interval classification. ^[10]

5.3.2 Quantile

With the quantile method, data are split so that there are an equal number of observations in each class. For example, if you have 100 cities and 5 classes, there would be 20 cities in each class. This method yields attractive, visually balanced maps and can be useful if you are working with ordinal data, or those that are ranked (in this case from largest to smallest). Because it puts the same number of observations in each class without reference to the value of those observations, quantile sometimes groups very different values in the same class (e.g. 0-11,12-21,22-33,34-70,71-2961). This effect is especially notable with outliers, or especially low or high values that are out on their own. If one were to create a quantile classification that is technically exacting, it could put observations with the same value into different classes; however, mapmakers will often manually change the classification so that that observations of equal value are not separated, which makes it more like a natural breaks classification (below).

Quantile classification. Population density by county in Minnesota, United States using quantile classification. ^[11]

5.3.3 Natural Breaks

The natural breaks method attempts to maximize differences between classes and minimize differences within classes. There are multiple algorithms for how to do this, usually by putting break points where there are the largest gaps between observation values. This method works especially well for data with clusters or outliers. One drawback to natural breaks is that it establishes unique break points for each dataset and thus is difficult to use if you need to make a comparison across multiple maps (e.g. population change in a city between 1970 and 2010).

Natural breaks classification. Population density by county in Minnesota, using natural breaks classification. The smaller graphs above are scatter plots of the actual data points, and show the population density of the counties range from lowest on the left to highest on the right. You can see how the graph of all counties has many low values and just a few higher values on the right-hand side, which are the populous Twin Cities counties such as Hennepin and Ramsey. ^[12]

5.3.4 Number of Classes

In addition to selecting a classification method, map makers need to decide how many classes or categories to divide the data into. Having only a few classes can hide important details and draw attention to geographical patterns that are not actually there. Having too many classes, however, can make a map confusing.

With more classes, it can be hard to distinguish between different colors, increasing the likelihood that values in the legend will be misread. There is no ideal number of classes that will work for every choropleth map. It depends on what you are trying to convey and how your data are distributed.

Different classifications. These three maps use the same classification scheme (quantile) and data (ACS 2010 5-yr estimate), but show different patterns and locations of where older housing stock exists. ^[13]

In summary, depending on choices made about standardization, classification scheme, and number of classes, the same data can be visualized very differently. These differences can have a huge influence on the social and political conclusions drawn from a map. When making maps or looking at a map someone else has made, be very thoughtful about how your data has been divided into categories.

Resources

For more information about Thematic Map Types:

• Indie Mapper
• Map Types at University of Muenster

For information on classification:

• Choropleth Mapping with Exploratory Data Analysis at Directions Magazine