# The PLAN Procedure

### Example 86.3 An Incomplete Block Design

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 Output 86.3.1 and Output 86.3.2:

```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;
```

Output 86.3.1: 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 86.3.2: 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