Lesson 1.4 · Unit 1 · Thinking spatially
How the answer changes when the unit changes
Scale is the most underrated idea in geography. The same data can show a strong pattern, no pattern, or the opposite pattern depending entirely on the size of the units you aggregate it into, and that is not a flaw in the data.
- Cartographic scale is the ratio between distance on the map and distance on the ground, expressed as a fraction such as one to fifty thousand.
- Large scale means a small area in great detail. One to ten thousand is large scale; one to ten million is small scale, which is the opposite of what the words suggest.
- Scale of analysis is different: the level at which a question is asked, from local through regional and national to global.
- Patterns are scale dependent. A phenomenon clustered at one scale can appear evenly spread at another, and both descriptions are correct at their own level.
- The modifiable areal unit problem is the formal name for this: results change when the boundaries or the size of the aggregation units change.
- It has two components, the zoning effect from moving boundaries and the scale effect from changing unit size, and each can reverse a finding.
- Gerrymandering is the deliberate exploitation of the zoning effect, which is examined in unit 4.
Where students lose marks: stating a pattern without stating the scale. "Population is concentrated" means nothing until you say concentrated at what level, because the answer differs at every one.
A constructed dataset. Invented figures designed so the reversal is visible. A region has eight districts, each with 100 voters, voting for two parties.
The data. Districts 1 to 4 vote 70 for Party X and 30 for Party Y. Districts 5 to 8 vote 40 for X and 60 for Y.
Step one: count the region as a whole. Party X gets four districts at 70, which is 280, plus four at 40, which is 160, giving 440. Party Y gets four at 30, which is 120, plus four at 60, which is 240, giving 360. Across the region, X leads 440 to 360.
Step two: count by district. X wins districts 1 to 4 and Y wins districts 5 to 8, so the result is four districts each. The region-wide vote favors X and the district count is tied.
Step three: now pair the districts differently. Group them as 1 with 5, 2 with 6, 3 with 7, and 4 with 8. Each pair has 110 for X and 90 for Y, so X wins all four pairs, four to nothing.
Step four: pair them the other way. Group 1 with 2, 3 with 4, 5 with 6, and 7 with 8. X wins the first two pairs 140 to 60 and loses the last two 80 to 120, so the result is two to two.
Step five: list the outcomes. From identical votes: X leads by 80 overall, ties four to four by district, wins four to nothing under one pairing, and ties two to two under another. Nobody's vote changed.
Step six: name the two effects separately. Changing from eight districts to four pairs is the scale effect. Choosing which districts to pair is the zoning effect. Both were demonstrated above and both reversed the answer.
Step seven: apply this beyond elections. The same problem affects poverty rates, disease clusters, crime statistics and segregation measures. A city can look integrated when measured by city and sharply segregated when measured by block, and both figures are correct.
Step eight: state the rule that follows. Never report a spatial finding without reporting the unit it was measured at, and where possible test whether the finding survives a change of unit. A pattern that appears at every scale is robust; one that appears at only one is a property of the units.
Questions 1 to 5 are recall. Questions 6 to 10 ask for reasoning.
- What is cartographic scale?
Show the full solution
The ratio between distance on the map and distance on the ground
- Which shows more detail, one to ten thousand or one to ten million?
Show the full solution
One to ten thousand, which is large scale and shows a small area in detail
- What is scale of analysis?
Show the full solution
The level at which a question is asked, from local through regional and national to global
- Name the two components of the modifiable areal unit problem.
Show the full solution
The zoning effect from moving boundaries, and the scale effect from changing unit size
- In the worked example, what is the region-wide vote?
Show the full solution
440 for Party X against 360 for Party Y
- Work through how identical votes produce four different results.
Show the full solution
Counted region-wide, X leads 440 to 360. Counted by the eight original districts, X wins four and Y wins four, a tie. Pairing district 1 with 5, 2 with 6, 3 with 7 and 4 with 8 gives every pair 110 for X and 90 for Y, so X wins four to nothing. Pairing 1 with 2, 3 with 4, 5 with 6 and 7 with 8 gives two to two. No voter changed their choice in any of these. X leads by 80, ties 4-4, wins 4-0, and ties 2-2, from identical votes
- Distinguish the zoning effect from the scale effect using the example.
Show the full solution
The scale effect is the change from reporting eight districts to reporting four pairs: the size of the unit changed, and the result moved from a four-four tie to something else. The zoning effect is the difference between the two ways of pairing the same eight districts into four: the unit size is identical and only the boundaries differ, yet one pairing gives four to nothing and the other gives two to two. Scale is changing unit size; zoning is moving boundaries at the same size
- Why is "population is concentrated" an incomplete statement?
Show the full solution
Because concentration is a property of the measurement as much as of the population. A country's people can be evenly spread across its provinces, heavily concentrated within each province into a few cities, and evenly spread again within each city across its neighborhoods. All three statements are true at their own scale and they appear to contradict each other. Naming the scale converts a meaningless claim into a checkable one. Concentration differs at every scale, so the claim is untestable without one
- Give an example of the problem outside elections.
Show the full solution
Residential segregation. A city measured as a whole may show a population distribution close to the national average, which looks integrated. Measured by census block, the same city may show almost every block overwhelmingly one group, which is severe segregation. Both figures are computed correctly from the same people living in the same houses, and a policy debate can be conducted entirely by each side choosing its preferred unit. A city can look integrated by city and segregated by block, both correctly
- What rule follows from the modifiable areal unit problem?
Show the full solution
Never report a spatial finding without reporting the unit it was measured at, and where possible test whether the finding survives a change of unit. A pattern that appears consistently at several scales is robust and probably reflects something real about the distribution. A pattern that appears at one scale and vanishes or reverses at others is a property of the chosen units rather than of the phenomenon, and should be reported as such. State the unit, and test whether the finding survives changing it