ABSTRACT
In a completely randomized design (CRD), the treatments are assigned to the experimental units at random. This is appropriate when the units are homogeneous, as has been assumed in the designs leading to the one- and two-way analyses of variances. The normal-based inference is approximately equivalent to the permutation-based test. Since normal-based inference is much quicker, the readers usually prefer to use that. In a randomized block design, the treatment levels are assigned randomly within block. This means the randomization is restricted relative to the full randomization used in the CRD. In a complete block design, the block size is equal to the number of treatments. When the block size is less than the number of treatments, an incomplete block design must be used. In balanced incomplete block design, all the pairwise differences are identifiable and have the same standard error. Pairwise differences are more likely to be interesting than other contrasts, so the design is constructed to facilitate this.
