Example 50.5: A Generalized Cyclic Incomplete Block Design

The PLAN Procedure

Example 50.5: 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 (e₁ e₂ ... e_k) and increment number i.

factors b=b p=k ;

treatments t=k of v cyclic (e₁ e₂ ... 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 50.5.1.

Output 50.5.1: 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

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	`factors b=`b `p=`k `;`
	`treatments t=`k `of` v `cyclic (`e₁ e₂ ... e_k `)` i `;`