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SUMMARY 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 which 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. 1. ITTRODUCTION In many practical design and analysis of experiments situations, especially in psychometric settings, it is possible to obtain cheaply concomitant information in addition to the main response variable. Frequently, this information represents the realization of random variables. It is this situation which we shall address in the sequel. More precisely, we consider the model
Bryant et al. (Thu,) studied this question.