An Incomplete Block Design
Example 72.3 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 72.3.1 and Output 72.3.2:
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 72.3.1: A Generalized Cyclic Block Design
8 |
52 |
Cyclic |
(1 2 3 4 32 43 46 49) / 4 |
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 72.3.2: A Generalized Cyclic Block Design
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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