Ecological Inference

Data are often reported using one kind of grouping (“aggregation”), while investigators need information about a different sort of grouping. Can one disaggregate and reaggregate the data—take the results apart and put them back together—by statistical methods? That is what ecological inference tries to do.

For example, take a voting rights case where Hispanic plaintiffs seek redistricting. The question is whether the non-Hispanic majority generally votes as a bloc to defeat the candidate preferred by the Hispanics. For any precinct, the number of votes for each candidate is a matter of public record. So is the number of Hispanic voters. However, the secret ballot prevents us from knowing how the non-Hispanics voted, or which candidate the Hispanics preferred. The vote totals are aggregated by precinct, but ...