Incomplete Block Design

Incomplete block designs (IBD) are block designs in which some or all blocks are incomplete in the sense that these blocks do not have all treatments. These designs were introduced to eliminate heterogeneity to a greater extent when testing a larger number of treatments in blocks. Since the precision of estimating the difference between two treatment depends on the number of replications, the treatments are allocated to the experimental units in different blocks of equal sizes such that each treatment occurs at most once in a block and it has an equal number of replications, and each pair of treatments has the same or nearly equal number of replications. If all pair of treatments occur equal number of times, then we have an important class of designs called balance incomplete block design (BIB); otherwise, we have a partially balance incomplete block design (PBIB).