  Many statistical experiments involve comparing multiple population groups.
For example, a public opinion poll may ask which of several political
candidates commands the most support; a social scientific survey may report the
most common of several responses to a question; or, a clinical trial may
compare binary patient outcomes under several treatment conditions to determine
the most effective treatment. Having observed the "winner" (largest observed
response) in a noisy experiment, it is natural to ask whether that candidate,
survey response, or treatment is actually the "best" (stochastically largest
response). This article concerns the problem of rank verification --- post hoc
significance tests of whether the orderings discovered in the data reflect the
population ranks. For exponential family models, we show under mild conditions
that an unadjusted two-tailed pairwise test comparing the top two observations
(i.e., comparing the "winner" to the "runner-up") is a valid test of whether
the winner is truly the best. We extend our analysis to provide equally simple
procedures to obtain lower confidence bounds on the gap between the winning
population and the others, and to verify ranks beyond the first.
