Multiple comparisons in the general linear model

Jason C. Hsu*, Barry L Nelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Whereas multiple comparisons computations in a one-way model are well understood, multiple comparisons computations in a general linear model (GLM) are not. For models with the so-called “one-way structure,” no new technique is needed beyond proper substitution of terms. Examples of designs that guarantee a one-way structure include variance balanced designs and orthogonal designs. For models without a one-way structure, more sophisticated computational techniques are needed. Approximations based on the probabilistic inequalities of Bonferroni, Šidák, and Slepian are too conservative. Even the second-order Hunter—Worsley inequality is rather conservative. The so-called factor analytic approximation is quite accurate for multiple comparison with a control (MCC) and multiple comparison with the best (MCB), but conditions for it to be conservative are not known. This article describes a highly accurate, deterministic, conservative approximation that is applicable to a popular class of general linear models, and a fast, stochastic, conservative approximation that is generally applicable.

Original languageEnglish (US)
Pages (from-to)23-41
Number of pages19
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - Jan 1 1998


  • Linear programming
  • Quantile estimation
  • Variance reduction

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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