Distribution-free multiple comparisons between successive treatments

Distribution-free methods are proposed for one- and two-sided comparison of adjacent pairs of r≧3 ordered treatments in the one-way layout. A table of exact probability points isgiven for use with Mann Whitney statistics in the equal sample size case for one-sided inference with r = 3 or 4 and for two-sided inference with r = 3. Approximations are investigated for use with larger r. Asymptotic probability points are found for use with all Chernoff-Savage statistics. Asymptotically optimal designs for these methods use approximately equal numbers of observations for even r and approximately ((r+l)/(r-1))1/2 times as many observations from each even numbered treatment as from each odd numbered treatment when r is odd. The asymptotic relative efficiency oftwo proceduresis identical to that of their two-sample counterparts