Example 67.5 A Generalized Cyclic Incomplete Block Design

The following statements depict how to create an appropriately randomized generalized cyclic incomplete block design for treatments (given by the value of t) in blocks (given by the value of b) of size (with values of p indexing the cells within a block) with initial block and increment number .

 

factors b=p=;

 

treatments t=of cyclic () ;

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 67.5.1.

Output 67.5.1 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