Incomplete Block Designs for Three or Four Replicates of Many Treatments

Abstract

Some practical situations are described where many treatments have to be compared in trials with only a small amount of replication. Appropriate designs are given for three or four replicates with most of the attention being given to designs having from 25 to 100 treatments, some of which may be duplicated. Some of the designs are partially balanced incomplete block designs with two associate classes (PBIBD(2)), most of which are already known, while others are duals of PBIBD (2) or balanced incomplete block designs. WVhen a trial has been conducted, not all treatments may be worth analyzing, and the results are best analyzed by direct matrix inversion methods.