• Dose–response study;
  • Lim–Wolfe test;
  • Monte Carlo study;
  • Randomized block design;
  • Step-down closed test;
  • Umbrella-pattern treatment effects

Summary. Lim and Wolfe (1997, Biometrics53, 410–418) proposed rank-based multiple test procedures for identifying the dose levels that are more effective than the zero-dose control in randomized complete block designs when it can be assumed that the efficacy of the increasing dose levels is monotonically increasing up to a point, followed by a monotonic decrease. Modifications of the Lim–Wolfe tests are suggested that provide more practical and powerful alternatives. Two numerical examples are illustrated and the results of a Monte Carlo power study are presented.