The PLAN Procedure

Example 74.3 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 74.3.1 and Output 74.3.2:

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 74.3.1: 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 74.3.2: 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

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

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

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

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

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

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