Ranking Tables and Uncertainty

Thomas M. Menino Convention & Exhibition Center 

Abstract
There is broad and deep interest in ranking units in a collection of K(≥ 2) units or populations. For
example, estimated rankings of K populations may communicate quickly high level useful messages
regarding traits of those populations with desirable (or undesirable) ranks. We consider the question,
"Should a table showing sample estimates for K populations that is produced by a national
statistical agency be presented explicitly as a ranking table?" Assuming the answer is "Yes", we
discuss a method to help produce such a ranking table which presents an overall estimated ranking
and construct a 100(1-α)% joint con�fidence region for the overall true ranking of the K populations.
Assuming normality for the K independent estimators, we only need K estimates
and their associated standard errors to produce this joint confi�dence region. We also illustrate a
theoretically based visual showing at once: (1) a joint confi�dence region revealing uncertainty in
the estimated ranking; (2) possible true rankings, beyond the estimated ranking; (3) a marginal
con�fidence set for population k true rank, for k=1,...,K; and (4) a marginal confidence set for each rank r.

Estimated Ranking

DIFF Joint Confidence Region

Statistical Agencies 

Survey Research Methods Section