Generalized randomized block design

In statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model.

Like a randomized complete block design (RCBD), a GRBD has randomization: Within each block, treatments are randomly assigned to experimental units and this randomization is independent between blocks. In a (classic) RCBD, there is no replication of treatments within blocks and so no interaction term may be estimated and tested.

Many authors do not distinguish between RCBDs and GRBDs. GRBD has the advantage that replication allows block-treatment interaction to be studied. However, if block-treatment interaction known to be negligible, the experimental protocol may specify that the interaction terms be assumed to be zero and that their degrees of freedom be used for the error term.