  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 for the ranks of
means based on an observed sample. For this aim, the only available method from
the literature uses Monte-Carlo simulations and is highly anticonservative
especially when the means are close to each other or have ties. We present a
novel method based on Tukey's honest significant difference test (HSD). Our new
method is on the contrary conservative when there are no ties. By properly
rescaling these two methods to the nominal confidence level, they surprisingly
perform very similarly. The Monte-Carlo method is however unscalable when the
number of institutions is large than 30 to 50 and stays thus anticonservative.
We provide extensive simulations to support our claims and the two methods are
compared in terms of their simultaneous coverage and their efficiency. We
provide a data analysis for 64 hospitals in the Netherlands and compare both
methods. Software for our new methods is available online in package ICRanks
downloadable from CRAN. Supplementary materials include supplementary R code
for the simulations and proofs of the propositions presented in this paper.
