The PLAN Procedure
Example 92.3 An Incomplete Block Design
(View the complete code for this example.)
Jarrett and Hall (1978) give an example of a generalized cyclic design with good efficiency characteristics. The design consists of two replicates of 52 treatments in 13 blocks of size 8. The following statements use the PLAN procedure to generate this design in an appropriately randomized form and store it in a SAS data set GCBD. Then the design is sorted and transposed to display in randomized order. The following statements produce Figure 10 and Output 92.3.1:
title 'Generalized Cyclic Block Design';
proc plan seed=33373;
factors Block=13 Plot=8;
treatments Treatment=8 of 52 cyclic (1 2 3 4 32 43 46 49) 4;
output out=GCBD;
quit;
proc sort data=GCBD out=GCBD;
by Block Plot;
run;
proc transpose data= GCBD(rename=(Plot=_NAME_))
out =tGCBD(drop=_NAME_);
by Block;
var Treatment;
run;
proc print data=tGCBD noobs;
run;
Figure 10: A Generalized Cyclic Block Design
| Generalized Cyclic Block Design |
The PLAN Procedure
| Plot Factors | |||
|---|---|---|---|
| Factor | Select | Levels | Order |
| Block | 13 | 13 | Random |
| Plot | 8 | 8 | Random |
| Treatment Factors | ||||
|---|---|---|---|---|
| Factor | Select | Levels | Order | Initial Block / Increment |
| Treatment | 8 | 52 | Cyclic | (1 2 3 4 32 43 46 49) / 4 |
| Block | Plot | Treatment | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 7 | 4 | 8 | 1 | 2 | 3 | 5 | 6 | 1 | 2 | 3 | 4 | 32 | 43 | 46 | 49 |
| 8 | 1 | 2 | 4 | 3 | 8 | 6 | 5 | 7 | 5 | 6 | 7 | 8 | 36 | 47 | 50 | 1 |
| 9 | 2 | 5 | 4 | 7 | 3 | 1 | 8 | 6 | 9 | 10 | 11 | 12 | 40 | 51 | 2 | 5 |
| 6 | 4 | 2 | 6 | 8 | 3 | 7 | 1 | 5 | 13 | 14 | 15 | 16 | 44 | 3 | 6 | 9 |
| 7 | 4 | 7 | 6 | 3 | 1 | 2 | 8 | 5 | 17 | 18 | 19 | 20 | 48 | 7 | 10 | 13 |
| 4 | 4 | 8 | 1 | 5 | 3 | 6 | 7 | 2 | 21 | 22 | 23 | 24 | 52 | 11 | 14 | 17 |
| 2 | 6 | 2 | 3 | 8 | 7 | 5 | 1 | 4 | 25 | 26 | 27 | 28 | 4 | 15 | 18 | 21 |
| 3 | 6 | 2 | 3 | 1 | 7 | 4 | 5 | 8 | 29 | 30 | 31 | 32 | 8 | 19 | 22 | 25 |
| 1 | 1 | 2 | 7 | 8 | 5 | 6 | 3 | 4 | 33 | 34 | 35 | 36 | 12 | 23 | 26 | 29 |
| 5 | 5 | 7 | 6 | 8 | 4 | 3 | 1 | 2 | 37 | 38 | 39 | 40 | 16 | 27 | 30 | 33 |
| 12 | 5 | 8 | 1 | 4 | 7 | 3 | 6 | 2 | 41 | 42 | 43 | 44 | 20 | 31 | 34 | 37 |
| 13 | 3 | 5 | 1 | 8 | 4 | 2 | 6 | 7 | 45 | 46 | 47 | 48 | 24 | 35 | 38 | 41 |
| 11 | 4 | 1 | 5 | 2 | 3 | 8 | 6 | 7 | 49 | 50 | 51 | 52 | 28 | 39 | 42 | 45 |
Output 92.3.1: A Generalized Cyclic Block Design
| Generalized Cyclic Block Design |
| Block | _1 | _2 | _3 | _4 | _5 | _6 | _7 | _8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 33 | 34 | 26 | 29 | 12 | 23 | 35 | 36 |
| 2 | 18 | 26 | 27 | 21 | 15 | 25 | 4 | 28 |
| 3 | 32 | 30 | 31 | 19 | 22 | 29 | 8 | 25 |
| 4 | 23 | 17 | 52 | 21 | 24 | 11 | 14 | 22 |
| 5 | 30 | 33 | 27 | 16 | 37 | 39 | 38 | 40 |
| 6 | 6 | 14 | 44 | 13 | 9 | 15 | 3 | 16 |
| 7 | 48 | 7 | 20 | 17 | 13 | 19 | 18 | 10 |
| 8 | 5 | 6 | 8 | 7 | 50 | 47 | 1 | 36 |
| 9 | 51 | 9 | 40 | 11 | 10 | 5 | 12 | 2 |
| 10 | 4 | 32 | 43 | 2 | 46 | 49 | 1 | 3 |
| 11 | 50 | 52 | 28 | 49 | 51 | 42 | 45 | 39 |
| 12 | 43 | 37 | 31 | 44 | 41 | 34 | 20 | 42 |
| 13 | 47 | 35 | 45 | 24 | 46 | 38 | 41 | 48 |
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Last updated: October 28, 2020