Abstract
<title>Abstract</title> <p>Abstract: There is broad and deep interest in ranking units in a collection of K(at least 2) units or populations. For example, estimated rankings of K populations may communicate quickly high level useful messagesregarding traits of those populations with desirable (or undesirable) ranks. We consider the question, "Should a (data) table showing sample estimates for K populations that is produced by a national statistical agency be presented explicitly as an estimated ranking table?" Assuming the answer is "yes", we discuss a method to help produce such an estimated ranking table which presents an over all estimated ranking and construct a 100(1 - alpha)% joint confidence region for the overall true ranking of the K populations. With the assumption of normality for the K independent estimators, we only need K estimates and their associated standard errors to produce this joint confidence region. We also illustrate a theory-based visual showing at once: (1) a joint confidence region revealing uncertainty in the estimated ranking; (2) possible true rankings, beyond the estimated ranking; (3) a marginal confidence set for population k true rank, where k = 1, ..., K; and (4) a marginal confidence set for each rank r_k.</p>