The following statements depict how to create an appropriately randomized generalized cyclic incomplete block design for v treatments (given by the value of t) in b blocks (given by the value of b) of size k (with values of p indexing the cells within a block) with initial block
and increment number i.
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For example, the specification
proc plan seed=37430; factors b=10 p=4; treatments t=4 of 30 cyclic (1 3 4 26) 2; run;
generates the generalized cyclic incomplete block design given in Example 1 of Jarrett and Hall (1978), which is given by the rows and columns of the plan associated with the treatment factor t in Output 72.5.1.
Output 72.5.1: A Generalized Cyclic Incomplete Block Design
| Plot Factors | |||
|---|---|---|---|
| Factor | Select | Levels | Order |
| b | 10 | 10 | Random |
| p | 4 | 4 | Random |
| Treatment Factors | ||||
|---|---|---|---|---|
| Factor | Select | Levels | Order | Initial Block / Increment |
| t | 4 | 30 | Cyclic | (1 3 4 26) / 2 |
| b | p | t | ||||||
|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 3 | 1 | 4 | 1 | 3 | 4 | 26 |
| 1 | 3 | 2 | 4 | 1 | 3 | 5 | 6 | 28 |
| 3 | 2 | 3 | 4 | 1 | 5 | 7 | 8 | 30 |
| 10 | 4 | 2 | 3 | 1 | 7 | 9 | 10 | 2 |
| 9 | 4 | 1 | 2 | 3 | 9 | 11 | 12 | 4 |
| 4 | 1 | 3 | 2 | 4 | 11 | 13 | 14 | 6 |
| 5 | 1 | 2 | 4 | 3 | 13 | 15 | 16 | 8 |
| 8 | 3 | 2 | 4 | 1 | 15 | 17 | 18 | 10 |
| 7 | 2 | 4 | 1 | 3 | 17 | 19 | 20 | 12 |
| 6 | 2 | 1 | 4 | 3 | 19 | 21 | 22 | 14 |