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Graduated Symbol Maps

Introduction

Previous Lecture: Introduction to Designing Symbols for Data in Areas

• discrete versus continuous dimensions in "Phenomena Space"

• abrupt versus smooth variation in "Phenomena Space"

  
  

  

  From MacEachren

  
  
  

  match to discrete versus continuous dimensions in "Symbolization Space"

  match to abrupt versus smooth variation in "Symbolization Space"

  
  

  

  From MacEachren

  
  
  

  Example: Mapping AIDS in Pennsylvania:

  
  

  Source: MacEachren

Given the same data (data in geographic units): four appropriate techniques

• representing continuous phenomena with abrupt variation: choropleth map
  • choropleth = graduated color map (in ArcGIS)

• representing discrete phenomena with smooth variation: dot map
  • dot map = dot density map (in ArcGIS)

• representing continuous phenomena with smooth variation: isarithmic map

• representing discrete phenomena with abrupt variation:
  • graduated symbol map
    • graduated symbol map = proportional symbol map (in ArcGIS)

    • range graded graduated symbol map = graduated symbol map (in ArcGIS)

  • cartograms (variation on the graduated symbol map)

1. Graduated Symbol Maps: Characteristics and History

Source: Robinson

Graduated symbol maps

• also called proportional point symbol mapping

• variable point symbol mapping

• ArcGIS: Graduated (classed) vs Proportional (unclassed) symbol maps

When to use a graduated symbol map:

• discreet phenomena (data) with abrupt variation

• use anytime you want to show relative magnitudes of phenomena

  
  

  
  
  Source: Monmonier

Should be magnitude data

ex) whole numbers rather than derived (eg., not densities: use choropleth)

ex) total population, retail sales, total employment...

The graduated symbol map uses one symbol, of which the visual variable size varies with the quantity of the data, for each area on a map

• easy to interpret and frequently used

History of the Graduated Symbol Map

William Playfair developed the first use of graduated symbols in 1801 but not on maps

• Playfair used circles: still the most common shape

• Playfair scaled the symbol areas (rather than diameters or circumferences) to the data quantities - and this method also persists to date

First use on maps by Henry Harness, August Peterman, and Minard (1850s):

Menard Graduated Circle Map (1858) (Source: Robinson)

Slow to be adopted in the United States: first show up in academic books and articles in the early part of 1900s

2. Designing Graduated Symbol Maps

• Basic design issues with graduated symbol maps

2a. Symbol Shape and Graduated Symbol Maps

Circles are most common and have the longest history, but almost any other shape you can think of can and has been used

Graduated Bars






Graduated Bars






Graduated Coffee Cups and Bags

Problem: bars and other symbol shapes can be more difficult to compare and relate to each other than circles

Source: Dent fig. 8.3


Compact circles, squares, and triangles are the easiest to interpret
The area of such symbols are scaled to the magnitude of the data values

Circles have some advantages over other symbols

• the most compact symbol

• circle scaling is easy (vs. scaling coffee cups): use square root of the radius

• circles are more 'visually stable' than most other symbols

• circles have a more subtile, smooth feel (vs pointy edged squares, triangles)

It is also possible to have 3D symbols: cubes, prisms, triangles

Source: Dent fig. 8.4


scale the volume to the cube root of the data
drawback: difficult to judge relative volumes

Demo) ArcGIS: graduated/proportional symbols

2b. Symbol Scaling and Graduated Symbol Maps

• Two basic ways to scale graduated symbols:

Absolute scaling: pick a minimum and maximum size and scale each of the symbols to the particular data values associated with an area on the map

• this is a direct, proportional scaling of magnitudes to the symbols area

• ...thus a proportional symbol map in ArcGIS

• Example) range of values in data set from 1600 to 6400
  • set up a proportion
    • area of circle = ¼R2 (where R = radius of circle)

  • ¼R12 / ¼R22 = data value 1 / data value 2

  • reduce to R12 / R22 = data value 1 / data value 2

  • take square root of both sides: R1 / R2 = sqr root of data value 1 / sqr root of data value 2

  • and for our example we have R1 / R2 = sqr root of 6400 / sqr root of 1600

  • and R1 / R2 = 80 / 40 = 2 / 1

  • so the radius of value 1 is twice the radius of value 2

Important to have a sense of what is happening here; but few people calculate graduated symbols by hand anymore: automated

Perceptual scaling: scaling adapted to take into account human perceptual abilities; also called apparent magnitude scaling

ArcGIS Proportional Symbol window: Appearance Compensation (Flannery)
Source: Dent fig. 8.5

• Studies by cartographers and others have shown that people tend to correctly estimate lengths, but tend to underestimate areas and volumes
  • in other words, when asked to pick a circle that is two times the size of another in a range of different circle sizes, most people would pick a circle that was about 1.8 times the size.

• This tendency gets worse with larger areas, and is worse in general for estimations of volumes

• The implication was that absolute scaling on graduated symbol maps led to inaccurate perception of actual values
  • While the circles were scaled accurately, the perception of the areas were wrong.

• The solution was to devise a method of "perceptual scaling" of graduated symbols

• Through lots of perceptual tests on thousands of humans, cartographers figured out a means of scaling circles which took into account this perceptual problem

  
  

  

  Source: Dent fig. 8.6

  
  

• The result: a means of scaling the circles so that most people perceive correct areas and thus correct values

  
  Demo) ArcGIS: proportional symbols appearance compensation

  
  
  

• But is there a problem here?
  • what if someone tries to get a value from the map by measuring the circle?

  • need to warn the user if this type of scaling is used

  • further: most computer mapping programs don't incorporate perceptual scaling (but ArcGIS now does!)

  • further: opinions about perceptual scaling have grown increasingly negative

  • so absolute scaling is the norm

Other problems with graduated circles: visual illusions

Source: Dent fig. 8.7

When a circle is seen among smaller circles, it is perceived as about 13% larger than if the same circle is seen among larger circles

Graduated squares are somewhat easier to calculate but are not quite as easy to interpret as circles because they are not as compact

Source: Dent fig. 8.9


squares do not have the perceptual problems of circles
people do not underestimate the area of squares as they do with circles

Range grading

In ArcGIS: Graduated Symbol Map

Another option when scaling graduated symbols is to classify the data and come up with 4 to 6 different graduated symbol sizes (or more, or less)

Source: Dent fig. 8.12


the benefits of classification: easy to pick out what class a symbol falls into
although you lose some of the detail in the map: all the fine gradiations in data are not visible

Demo) ArcGIS: Graduated Symbol Map (classified)

2c. Graphic Design Guidelines for Graduated Symbol Maps

Multivariate Graduated Symbol Maps: there are benefits to displaying more information on one map than the same amount of information on a series of maps (comparison problems).

• ex) size of symbol represents one variable, value represents 2nd variable:

• ArcGIS???

  
  

  

  Source: Robinson fig. 25.10

  
  
  

  ArcGIS: graduated symbol map over choropleth map (and problems)

  But: potential problem with symbol overload

  
  

  

  Multi-variate Graduated Triangles (Japan Economic Data) and Circles (Dent 8.14)

Chernoff Faces: variation on the graduated symbol theme: many variables for each symbol:

Source: Eugene Turner

• Manual graduated symbol map production: tedious

  
  

• much easier with computer aided graduated symbol maps
  • can set the smallest and largest circles you want and the rest are calculated

  • can have different abstract shapes (but often not realistic shapes)

  • can have transparent vs opaque (value, hue) symbols

  • and can classify (range grade) if you want to

  
  

• ArcGIS and Graduated and Proportional Symbol Maps
  • process

Summary

1. Graduated Symbol Maps: Characteristics and History

• when to use a graduated symbol map:
  • discreet phenomena (data) with abrupt variation

  • use anytime you want to show relative magnitudes of phenomena

2. Designing Graduated Symbol Maps

2a. Symbol Shape and Graduated Symbol Maps

• abstract (circles, squares, triangles) vs. realistic symbols

• volumetric symbols

2b. Symbol Scaling and Graduated Symbol Maps

• absolute scaling

• perceptual scaling

• range grading

2c. Graphic Design Guidelines for Graduated Symbol Maps

• symbol overload, symbol redundancy

2d. Manual vs Computer Production of Graduated Symbol Maps

Introduction: Cartograms

• Symbolization Space: use with same data appropriate for graduated symbol maps

  
  

  

  From MacEachren

Cartograms are a broad and curious bunch of mapping techniques

Source: Dent

Cartograms, while geographically 'inacurate' are ideal for representing some kinds of data in areas:

States Scaled to Number of Electoral Votes (Source: New York Times)




Cool: Dr. Sara Fabricant Election 2000 Cartograms




other names: anamorphaed images, spatial transformation maps

Most common: the "value by area" cartogram

• There are many other kinds of cartograms, and they have a long history

1. Cartograms: Characteristics and History

• The fundamental characteristic of cartograms is that the visual variable "location" is not linked to actual geographical coordinates

• Any kind of map that purposefully uncouples location (of points, lines, areas) on a map from actual geographical location is a cartogram

Linear Cartograms

Examples) Transportation cartograms

• transportation maps - and particularly subway and road maps - often rearrange linear information to stress and simplify the relations between different routes

• the idea is that such a linear cartogram is easier to use than a map of the transportation routes which is based on the actual location of the lines

  
  

  

  Road Linear Cartogram

  
  

  

  Subway Linear Cartogram

Example) World rivers and mountains cartogram:

• longest rivers get straightened out and arrayed next to each other

• tallest mountains get put together in their own virtual mountain range

  
  

  

  Subway Linear Cartogram

Area Cartograms

Raisz Area/Volumetric Cartogram

Area cartograms are the most common

• early area cartograms (the direct precursor to the value by area cartogram) first show up in French textbooks in the 1860s - very diagrammetric

• Erwin Raisz (cartographer at Harvard 1930s) promoted them in his textbooks

• later cartograms were less abstract: value by area cartograms

• the narrow sense of the term "cartogram:" a map where the size of the enumeration unit is scaled to some measure other than geographical area

• greatly distorts geographic area, orientation, and contiguity, but preserves enough of these for the are to be recognizable

When to use a cartogram of this type: usually an alternative to graduated circle map (abrupt and discreet; magnitude values); sometimes an alternative to the choropleth map.

Source: Tyner






Source: Pictorial Maps

Typically unclassified: each enumeration unit scaled to value

Why use: strong visual impact: they draw attention to themselves and if created carefully are easy for people to understand

Equinational Projection (Source: Globehead!)






Suicide rate, USA (Source: Dent)

Watch out for inappropriate data

• the data varies as the size of the enumeration units
  ex) big states have big values; small states small values

Cartograms are an important and under-appreciated mapping technique

Erwin Raitz (1930s): "Value by area cartograms are important. Our socioeconomic overview of the world will be more realistic if we think of the relative importance of its parts in the proportions of a population cartogram rather than in the proportions of a map."

Source: Dorling

Daniel Dorling (discussing population area cartograms, 1990s): "The majority of the population of most countries live in small, densely populated areas which need numerous insets on a map to give any semblance of justice." "Regular" maps are "equal land maps" and they "draw our attention to the patterns in places where the fewest people live." Cartograms are more appropriate for "seeing how something is distributed spatially across groups of people"

2. Cartogram Forms

• two basic cartogram forms: contiguous and noncontiguous

  
  

  

  Contiguous vs Noncontiguous Cartograms (Source: Dent fig. 10.3)

Contiguous cartograms: the enumeration units on the map are adjacent to each other, even though contiguity may be distorted. They attempt to preserve topology.

• use a contiguous cartogram if you have phenomena that is abrupt and continuous

• replacement for a choropleth map

Advantages

• boundary and orientation relationships maintained which strengthens the relationship of the cartogram to actual geographic space

• less work for the map reader (does not have to mentally pull the map together)

• shape of the mapped area closer to actual geographic space

Disadvantages

• actual boundary relationships may be distorted and give map reader erroneous impressions (eg., certain states may be adjacent on a cartogram when they are not adjacent in actual geographic space)

• in attempting to keep contiguity, the shapes of the units may have to be greatly distorted with a resultant loss or recognizability

• difficult to construct

• hard to automate

  
  

• avoid using a contiguous cartogram if you have to wildly distort the enumeration units

  
  

  

  Contiguous cartogram: Miliary Spending

Noncontiguous cartograms: does not preserve boundary relations among the enumeration units on the map; units located in approximate actual locations (in relation to other units) with gaps inbetween

• sort of an "exploded" view

  
  

  

  Non-contiguous cartogram: Wisconsin Election

  
  

  problem: familiarity with the geographic relations of the areas mapped

  
  

  use a noncontiguous cartogram if you have phenomena that is abrupt and discreet

  replacement for a graduated circle map

Advantages

• easier to scale and construct (than contiguous cartograms): can automate

• actual shapes of enumeration units can be preserved (WI looks like WI)

• somewhat easier to compare varying sizes and judge differences

Disadvantages

• does not convey the contiguity of actual geographic space (abstract)

• not compact and hard to maintain the shape of the entire area mapped

3. Multi-variate Cartograms

As with other area data mapping techniques, we show two data variables by combining a cartogram with a graduated symbol or choropleth map.

• use the size of the enumeration unit to represent one distribution of phenomena, and the value of each unit to represent another (slide)

  
  

  

  Bi-variate cartogram: Population (value) and Authorship (cartogram)

  
  
  
  

  

  Bi-variate cartogram: Dominant Land Use (shading) and Proportion of land use (cartogram)

4. Cartogram Production

Manual Methods: olde time cartogram construction

• somewhat akin to the absolute scaling of graduated symbol maps

• easy to do with noncontiguous cartograms

• just scale each enumeration unit to the appropriate size and arrange

• harder to do with contiguous cartograms

• have to figure out the size of each unit based on the data being mapped

• complicated process of preserving the shape of each unit while scaling to the appropriate size and keeping contiguity intact

• frustrating and difficult to do well (and thus not done very often)

Computer Methods

Easy to create noncontiguous cartograms: simple scaling like with graduated symbol maps then location decisions are made (try to get as close to the actual location without overlap)

Non-contiguous cartogram (Source: Tyner)

More difficult to create contiguous cartograms: but some software exists which creates such cartograms (Daniel Dorling)

Contiguous cartogram (Source: Dorling)

Hybrid Cartogram with Chernoff faces: Dorling:

Cartogram w/Chernoff Faces (Source: Dorling)






ArcGIS: Cannot really do Cartograms

Summary: Cartograms

• overview of advantages and disadvantages of cartograms

  
  

  

  States Scaled to Number of Electoral Votes (Source: New York Times)

Advantages

• can be used to good effect to "shock" a viewer; since most people seem to quickly grasp the nature of the technique, it is effective for making the user pay attention to the map

• may be a more effective way of representing data that varies inversely with enumeration unit sizes

• effective in showing distributions of phenomena that would be otherwise obscured; particularly important when there is a wide variation in enumeration unit sizes (US with Texas vs Rhode Island)

• allows the data that is the focus of the map to drive the representation, rather than the geographic area of the enumeration units

Disadvantages

• some people may feel the data is "inaccurate" because the map base seems to be inaccurate

• some people may be confused by the method; need to explain what you have done if you think the audience may be confused

• difficult to identify specific locations or enumeration units on cartograms

• hard to design very effective cartograms

E-mail: jbkrygie@owu.edu

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