Optimal designs for successive comparisons between ordered treatments
Abstract
Lee and Spurrier [1] proposed a method for one-and two-sided comparison of means of adjacent ordered treatments in the one-way layout and typical normality assumptions while maintaining a designated overall Type I error rate. Optimal experimental design for these methods is investigated for three criteria. A-optimality minimizes the sum of the variances of the successive pairwise contrasts. MV-optimality minimizes the maximum variance of the successive pairwise contrasts. Simultaneous interval optimality minimizes the length of simultaneous confidence intervals for the successive pairwise contrasts. Tables of A-optimal designs with exact critical values are presented for r = 3(1)6 treatments. For even r, the MV-optimal design is equal sample sizes. For r = 3 the MV-optimal designs are very similar to A-optimal designs. A table of MV-optimal designs with exact critical values is presented for r = 5. Simultaneous interval optimal designs appear to be very similar to A-optimal designs.
