  When a ranking of institutions such as medical centers or universities is
based on an indicator provided with a standard error, confidence intervals
should be calculated to assess the quality of these ranks. We consider the
problem of constructing simultaneous confidence intervals (CIs) for the ranks
of centers based on an observed sample. We present a novel method based on
Tukey's honest significant difference test (HSD) which is the first method to
produce valid simultaneous CIs for ranks. Moreover, we introduce a new variant
of Tukey's HSD based on the sequential rejection principle. The new algorithm
ensures familywise error control, and produces simultaneous confidence
intervals for the ranks uniformly shorter than those provided by Tukey's HSD
for the same level of significance. We illustrate the method through both
simulations and real data analysis from 64 hospitals in the Netherlands.
Software for our new methods is available online in package \texttt{ICRanks}
downloadable from CRAN. Supplementary materials include supplementary R code
for the simulations and proofs of the propositions presented in this paper.
