S3U

Geography / Grid maps and scale / Undergraduate / ggd01

Aggregation, Denominators, and Ecological Inference

Interpret regional rates without attributing them to individuals.

All worksheets
5 questions0m 0s

Prerequisites

Weighted averages, rates, maps, and population versus individual comparisons.

Learn the skill

Aggregate counts and denominators before calculating a pooled rate. An unweighted average of area rates answers a different question. Associations among areas do not determine individual-level associations within them.

Worked example

An area with 1 event among 10 people and another with 9 among 90 both have 10% rates. Their totals also give 10%; unequal rates with unequal populations need population weighting.

Model and Assumptions

Fictional districts: North has 80 library members among 100 residents; South has 20 among 400 residents. The districts differ in income and age composition. Membership and income are available only as district aggregates.

1. What is the combined membership rate?
2. What is the unweighted average of district rates?
3. What does the unweighted average describe here?
4. Can these aggregates identify whether richer individuals join more often?
5. Why investigate alternate district boundaries?

Further inquiry

Construct two individual-level allocations consistent with each district's membership count but with different income-membership relationships. Explain what additional data would distinguish them without collecting unnecessary identifiers.

Review criteria

  • Keep every supplied count unchanged.
  • Exhibit different within-district associations.
  • Specify the analytical unit and a privacy-preserving data requirement.