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When a ranking of institutions such as medical centers or universities isbased on an indicator provided with a standard error, confidence intervalsshould be calculated to assess the quality of these ranks. We consider theproblem of constructing simultaneous confidence intervals (CIs) for the ranksof centers based on an observed sample. We present a novel method based onTukey's honest significant difference test (HSD) which is the first method toproduce valid simultaneous CIs for ranks. Moreover, we introduce a new variantof Tukey's HSD based on the sequential rejection principle. The new algorithmensures familywise error control, and produces simultaneous confidenceintervals for the ranks uniformly shorter than those provided by Tukey's HSDfor the same level of significance. We illustrate the method through bothsimulations 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 codefor the simulations and proofs of the propositions presented in this paper.

An improvement of Tukey's HSD with application to ranking institutions