Lesson 1.2 · Unit 1 · Thinking spatially
What a map includes, what it leaves out, and why that is a choice
A map is not a picture of the world. It is a selection from the world, made by someone, for a purpose. Learning to see the selection is the first skill in the subject, because every later lesson rests on data presented in maps.
- Every map is a reduction. The world contains more information than any map can show, so a mapmaker must decide what to include and what to omit.
- Reference maps show location; thematic maps show the distribution of one variable, and most maps in this course are thematic.
- The main thematic types: choropleth, shading areas by value; dot maps, one dot per quantity; isoline maps, joining points of equal value; graduated symbol maps; and cartograms, which distort area to represent the variable.
- Choropleth maps carry a specific danger. Shading a whole unit one color implies the value is uniform inside it, which it almost never is.
- The class breaks change the picture. Where the boundaries between shading categories are drawn can make the same data look evenly spread or sharply divided.
- What is measured constrains what can be shown. Data usually exists by administrative unit, so maps show counties and countries because that is what was counted.
- Geographic information systems store data in layers that can be combined and queried, which makes it easy to produce many different maps from one dataset and therefore easy to mislead.
Where students lose marks: reading a map as a fact. Ask who made it, what variable is shown, what units it is divided into and where the class breaks fall, before saying what it shows.
A constructed dataset. The figures are invented so the arithmetic can be checked. A country has five provinces and we map average household income in thousands.
The data. Province A: 22. Province B: 24. Province C: 26. Province D: 48. Province E: 50.
Step one: map it with equal intervals. The range runs from 22 to 50, so three equal classes are 22 to 31.3, 31.3 to 40.7, and 40.7 to 50. A, B and C fall in the lowest class and D and E in the highest, with nothing in the middle. The map shows a country split in two.
Step two: map the same data with quantiles. Three classes with roughly equal numbers of provinces gives A and B lowest, C middle, D and E highest. Province C has moved from the poorest category to the middle one without its income changing.
Step three: state what just happened. Two honest maps of identical data tell different stories. The first says there are poor provinces and rich ones; the second says there is a gradient. Neither is false, and the choice was the mapmaker's.
Step four: introduce the underlying problem. Suppose Province D contains one city with an average of 90 and a rural remainder with an average of 20. The province's average of 48 describes nobody. The choropleth shades the whole province as prosperous, including the rural area that is poorer than Province A.
Step five: name the error. This is the ecological fallacy: inferring something about individuals from the average of the group they belong to. A rural household in Province D is not prosperous merely because its province is.
Step six: consider changing the unit. Mapping the same country by district rather than province would reveal the city and the poor rural area separately. The pattern changes with the unit, which is the modifiable areal unit problem and is the subject of lesson 1.4.
Step seven: explain why the map was drawn by province anyway. Because income is collected by province. Data exists in the units administrators use, so maps show those units whether or not they correspond to anything real about the distribution being studied.
Step eight: state the checking routine. Before interpreting any map, ask four questions: what exactly is the variable, what unit is it aggregated to, where do the class breaks fall, and who made it and why. A map that survives all four can be used.
Questions 1 to 5 are recall. Questions 6 to 10 ask for reasoning.
- Distinguish reference maps from thematic maps.
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Reference maps show location; thematic maps show the distribution of one variable
- Name four types of thematic map.
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Choropleth, dot, isoline, graduated symbol, and cartogram
- What does a choropleth map imply that is usually false?
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That the value is uniform across the whole shaded unit
- What is the ecological fallacy?
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Inferring something about individuals from the average of the group they belong to
- What does a cartogram distort, and why?
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Area, so that the size of each unit represents the variable being mapped
- Explain how class breaks change what a map appears to show.
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In the worked example, equal intervals put provinces A, B and C in the lowest class and D and E in the highest with nothing between, so the map shows a country divided in two. Quantiles with the same data put C in the middle class, so the map shows a gradient. Province C's income did not change; only the classification did. Both maps are honest and they support different conclusions. The same data looks like a split or a gradient depending on where breaks fall
- Why is a provincial average sometimes a number describing nobody?
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Because an average conceals the distribution that produced it. If Province D contains one city averaging 90 and a rural remainder averaging 20, the provincial figure of 48 describes neither group and no household in the province is likely to be near it. The choropleth then shades the entire province as prosperous, including a rural population poorer than any household in the province with the lowest average. An average of two very different groups describes neither of them
- Why are maps usually drawn by administrative unit?
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Because that is how the data was collected. Income, population and almost everything else is gathered by governments through units they administer, so those are the units in which figures exist. Maps therefore show counties, provinces and countries whether or not those boundaries correspond to anything real about the distribution being studied. The map's shape is determined by administration rather than by the phenomenon. Data is collected by administrative unit, so maps show those units
- Why does the ability to make many maps from one dataset create a risk?
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Because a geographic information system lets anyone try different units, different class breaks and different variables until a map supports the conclusion they already wanted, and every one of those maps is technically accurate. Nothing has been falsified; a presentation has been selected. That makes the reader's checking routine more important than the mapmaker's honesty, since an honest mapmaker can still choose badly. Many truthful maps exist, so one can be selected to support any conclusion
- State the four questions to ask before interpreting any map.
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What exactly is the variable being shown, including how it was defined and measured. What unit is it aggregated to, and does that unit correspond to anything real. Where do the class breaks fall, and would other breaks change the picture. And who made the map and for what purpose. A map that survives all four questions can be used as evidence; one that fails any of them should be treated as a claim rather than a fact. Variable, unit, class breaks, and maker's purpose