Multiple Comparisons of Means Using Simultaneous Confidence Intervals

Abstract

The state of the art of multiple comparisons of means using simultaneous confidence intervals is discussed. Several industrial examples are used to illustrate the procedures. Attention is limited to those procedures that are recommended for use in practice (the Tukey-Kramer procedure, Scheffé's procedure, Šidák's studentized maximum modulus (SMM) procedure, and Dunnett's comparison with a control) and some common, but inferior, competitors (the Bonferroni procedure, the Dunn-Šidák procedure, and Hochberg's GT2 procedure). New tables of quantiles of the SMM distribution are presented, and as an example of the application of Šidák's SMM procedure it is shown that these quantiles can be used to obtain uniformly tighter (but still conservative) decision lines than were previously suggested for the analysis of means with unequal sample sizes.

• Analysis of Means
• Multiple Comparisons
• Pairwise Comparisons
• Simultaneous Inference
• Studentized Maximum Modulus Distribution

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Peter R. Nelson

Dr. Nelson is a Professor of Statistics in the Department of Mathematical Sciences. He is a Fellow of ASQC.