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Copyright © John Lindsay, 2015

Error Propagation

• When there is error in a spatial data layer and we combine it with other layers as part of a GIS analysis workflow, the result will reflect the inaccuracies of the lowest-quality input.
• Error propagates in a workflow in very complex ways that can be difficult to model analytically.
• The Monte-Carlo method (stochastic simulation) is commonly used to study error.

Stochastic Simulation

Error Propagation

Spatially Aggregated Data

• Many geographic data are aggregates of data at a more detailed level:
  • National census: collected at the household level but reported for practical and privacy reasons at various levels of aggregation (block, neighbourhood, postcode, county, province, etc.)
  • Traffic Analysis Zone (TAZ)
  • School district
  • Watersheds
  • Pixels

Ecological Fallacy

• The Ecological Fallacy is a situation that can occur when a researcher or analyst makes an inference about an individual based on aggregate data for a group.
• The conclusions we draw from a GIS analysis of spatially aggregated data only apply at the scale of the aggregation

Ecological Fallacy

• Example: we might observe a strong relationship between income and crime at the county level, with lower-income areas being associated with higher crime rate.
• Conclusion
• Lower-income persons are more likely to commit crime
• Lower-income areas are associated with higher crime rates
• Lower-income counties tend to experience higher crime rates

Ecological Fallacy

The Modifiable Areal Unit Problem (MAUP)

• "A problem arising from the imposition of artificial units of spatial reporting on continuous geographic phenomena resulting in the generation of artificial spatial patterns."
• That is, it involves data that are spatially aggregated using arbitrary boundaries and affects our ability to quantify apparent relations, statistical or otherwise.

The Modifiable Areal Unit Problem (MAUP)

• In a series of publications in the 1970s Stan Openshaw demonstrated that by changing the aggregation characteristics of spatial data, it is possible to measure correlations between -1.0 and 1.0!
• The MAUP has two manifestations:
  1. the aggregation effect
  2. the scale effect

The Modifiable Areal Unit Problem (MAUP)

MAUP Example: Electoral Districts & Voting

• It's not just who you vote for but also where you vote that counts.
• In the 2000 U.S. presidential election, Al Gore, won more of the popular vote than George Bush, but failed to become president.
• A different aggregation of U.S. counties into states could have produced a different outcome (switching just one northern Florida county to Georgia or Alabama would have produced a different outcome).

Gerrymandering

• The practice of setting electoral district boundaries to favour a particular outcome.
• We have to be very careful whenever we modify the geographic boundaries of voting aggregation areas.
• Gerrymandering is commonplace in many countries, sometimes even legal!