An incomplete block design is a block design in which each block contains fewer than all 
treatments. If there are 
blocks, every block contains 
treatments, every treatment occurs in 
blocks, and every pair of distinct treatments occurs together
in 
blocks, the design is called a balanced incomplete block design with parameters 
.
Counting treatment-block incidences and ordered pairs in two ways gives
 |  |  |
(1)
|
 |  |  |
(2)
|
Incomplete blocks permit treatment comparisons when experimental units can accommodate only a subset of all treatments. Without the balance conditions, replication and pairwise concurrence can vary between treatments.
