Directional Error Rates of Closed Testing Procedures

Peter H. Westfall, Frank Bretz, Randall D. Tobias

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Closed multiple testing procedures are common in biopharmaceutical protocols. Whether their directional error rates are controlled is largely an open problem. In this article, directional error rates are investigated using analytical, numerical, and Monte Carlo methods. This article presents a Monte Carlo variance-reduction method amenable to this purpose. A factorial design is used to identify possible problem areas, and directional error rates are simulated. No cases of excess directional error are found for typical applications involving noncentral multivariate T distributions. However, directional error rates in excess of the nominal are found when using regression function tests with nearly collinear linear combinations, both for one-sided and two-sided tests.

Original languageEnglish
Pages (from-to)345-355
Number of pages11
JournalStatistics in Biopharmaceutical Research
Issue number4
StatePublished - Nov 2013


  • Closure principle
  • Familywise error rate
  • Logical constraints
  • Multiple testing
  • Type III errors


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