The PLAN Procedure

Example 74.5 A Generalized Cyclic Incomplete Block Design

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 $(e_1 ~ e_2 ~ \cdots ~ e_ k)$ and increment number i.

 

factors b=b p=k ;

 

treatments t=k of v cyclic ($e_1 ~ e_2 ~ \cdots ~ e_ k$ ) i ;

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 74.5.1.

Output 74.5.1: A Generalized Cyclic Incomplete Block Design

The PLAN Procedure

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