Abstract

Relative efficiency is a measure used to assess the effectiveness of blocking in experimental designs. This paper develops and evaluates the asymptotic relative efficiency of randomized complete block designs compared to completely randomized designs, based on multiple comparison procedures. The asymptotic relative efficiency is expressed as the ratio of the expected squared half-lengths of multiple comparison procedures (Tukey, Bonferroni, and Scheffé simultaneous confidence limits). A simulation study demonstrates the applicability of the developed methods. The results show that randomized complete block designs are more efficient than completely randomized designs across almost all the different values of treatments and blocks considered in this study.