John Spurrier
Department of Statistics
University of South Carolina
Exact Multiple Comparisons of Three or More Regression Lines:
Pairwise Comparisons and Comparisons with a Control
Abstract: The problem of finding exact simultaneous confidence bounds for
differences in regression models for k groups via the union-intersection
method is considered. The error terms are taken to be iid normal random
variables. Under an assumption slightly more general than having identical
design matrices for each of the k groups, it is shown that an existing
probability point for the multivariate studentized range can be used to find
the necessary probability point for pairwise comparisons of regression
models. The resulting methods can be used with simple or multiple
regression. Under a weaker assumption on the k design matrices that allows
more observations to be taken from the control group than from the k-1
treatment groups, a method is developed for computing exact probability
points for comparing the simple linear regression models of the k-1 groups
to that of the control. Within a class of designs, the optimal design for
comparisons with a control takes the square root of (k-1) times as many
observations from the control than from each treatment group. The
simultaneous confidence bounds for all pairwise differences and for
comparisons with a control are much narrower than Spurrier's intervals for
all contrasts of k regression lines.
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