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Biometrika 1976 63(3):631-638; doi:10.1093/biomet/63.3.631
© 1976 by Biometrika Trust
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An extension of Tukey's method of multiple comparisons to experimental designs with random concomitant variables

J. L. BRYANT and A. S. PAULSON

Department of Operations Research and Statistics, Rensselaer Polytechnic Institute Troy, New York

A procedure is provided for the construction of simultaneous confidence intervals on all contrasts of a set of parametric functions, or tests of hypotheses concerning them, in an analysis of covariance wherein the dependent and concomitant variates have a joint (p +1)-dimensional normal distribution. This new procedure is analogous to Tukey's method of multiple comparisons in the analysis of variance, both in application and in the conditions whioh are necessary for its use. The probability distribution of the range of adjusted parametric functions, suitably studentized, is derived and its critical values tabulated. The procedure is demonstrated using a two-way cross classification model.

Key Words: Analysis of covariance • Generalized inverse • Linear model • Randomly distributed covariates • Studentized range • Tukey's method


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