Irregular Sudoku-type designs for animal experiments

Abstract

In experiments involving animals, it may be a difficult task for the experimenter to get homogeneous groups of animals. Blocking is commonly practiced to eliminate variability present in experimental material due to some known sources such as age, breed, housing condition, initial body weight, litter size, etc. When there are two noninteracting sources of variation in the experimental material, experimental designs under two-way blocking structure are advised. However, these designs are not appropriate when a third source of variability is present in the experimental material as they may not be able to mark out the third features that tend to clump the animals into a third set of compact groups. Many times the clumps may be irregular, having no uniformity. In this paper, four methods of constructing designs under three way blocking structure for irregular clumps were developed in which two methods give designs with clumps having empty nodes. These designs assure more precise comparison among the treatments under study by removing three known sources of variability present in the experimental material.