Example 50.3: An Incomplete Block Design

The PLAN Procedure

Example 50.3: 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. Then, the TABULATE procedure is used to display the randomized plan. The following statements produce Output 50.3.1 and Output 50.3.2:

   title 'Generalized Cyclic Block Design';
   proc plan seed=33373;
      treatments trtmts=8 of 52 cyclic (1 2 3 4 32 43 46 49) 4;
      factors blocks=13 plots=8;
      output out=c;
   quit;

   proc tabulate;
      class blocks plots;
      var trtmts;
      table blocks, plots*(trtmts*f=8.) / rts=8;
   run;

Output 50.3.1: A Generalized Cyclic Block Design

Generalized Cyclic Block Design

The PLAN Procedure

Plot Factors
Factor	Select	Levels	Order
blocks	13	13	Random
plots	8	8	Random

Treatment Factors
Factor	Select	Levels	Order	Initial Block / Increment
trtmts	8	52	Cyclic	(1 2 3 4 32 43 46 49) / 4

blocks	plots								trtmts
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 50.3.2: A Generalized Cyclic Block Design

Generalized Cyclic Block Design

	plots
	1	2	3	4	5	6	7	8
	trtmts	trtmts	trtmts	trtmts	trtmts	trtmts	trtmts	trtmts
	Sum	Sum	Sum	Sum	Sum	Sum	Sum	Sum
blocks	33	34	26	29	12	23	35	36
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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