Simultaneous confidence intervals based on one-sided max t test

Simultaneous lower bounds (SLB) for the isotonic contrasts in normal means are obtained. In particular a SLB for the range is given. These SLBs are obtained from the one-sided max t test. It is then generalized to obtain simultaneous upper bounds for the responses at lower levels. Under the assumption of the convexity of the response curve at lower levels the upper bounds are further improved. The method compares very well with other available methods numerically as well as in real examples.