Suppose that y 1, …, yk are normal random variables with ordered means u 1 ≤ u 2 ≤ … ≤ uk . A confidence bound is found for each ui that takes advantage of the ordering. The upper and lower bounds are the maximum and minimum values of x such that the hypotheses that x < ui and ui < x are accepted by their respective likelihood ratio tests. These bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low-dose extrapolation. Simultaneous intervals for u 1, …, uk are also derived.
No takes yet. Share an insight, caveat, or question.
David Schoenfeld (1986) studied this question.