Blocking is a key statistical method introduced almost a century ago by Ronald Fisher. Blocking controls the effect of “nuisance” variables that are not of direct interest but introduce unwanted variation into the experimental response. Block factors, such as cage, litter, or time, are used to group experimental units into homogeneous subsets. There are two types of block designs: complete and incomplete. In complete block designs every treatment appears in every block. Examples include the Randomized Complete Block Design (RCBD) with a single block factor, and variants such as Latin square and Graeco-Latin square designs with multiple block factors. RCBDs are simple, flexible, and the most widely used. Replicated and nested Latin square designs allow more rigorous control of complex nuisance structures with minimal sample size. Incomplete block designs are extremely useful when practical constraints (e.g., caging density or varying litter sizes) restrict complete treatment replication across all blocks. Because not all treatments appear in every block, these designs require computer-generated allocation plans to obtain optimum balance and efficiency. Each of the seven blocking designs described in this paper includes a practical example from the research literature, the corresponding skeleton analysis of variance and R code for random allocation plans. By increasing precision and power to detect treatment effects, blocking promotes ethical research by maximizing the amount of information for a minimum number of animals, supporting the 3Rs principle of Reduction.
P. S. Reynolds (Sun,) studied this question.