On the construction of balanced repeated measurements designs with good circular properties

Figures & data

Table

	Experimental Subjects
Periods	1	2	3	4	5	6	7	8	9	10	11	12
1	0	1	2	3	4	5	6	7	8	9	10	11
2	3	4	5	6	7	8	9	10	11	0	1	2
3	7	8	9	10	11	0	1	2	3	4	5	6
4	4	5	6	7	8	9	10	11	0	1	2	3
5	9	10	11	0	1	2	3	4	5	6	7	8
6	5	6	7	8	9	10	11	0	1	2	3	4

Table

	Subjects
Periods	13	14	15	16	17	18	19	20	21	22	23	24
1	0	1	2	3	4	5	6	7	8	9	10	11
2	6	7	8	9	10	11	0	1	2	3	4	5
3	12	12	12	12	12	12	12	12	12	12	12	12

Table

Subjects
1	2	3	4	5	6	7	8	9	10
00	11	22	33	44	55	66	77	88	99
10	21	32	43	54	65	76	87	98	09
81	92	03	14	25	36	47	58	69	70
28	39	40	51	62	73	84	95	06	17
52	63	74	85	96	07	18	29	30	41
45	56	67	78	89	90	01	12	23	34
04	15	26	37	48	59	60	71	82	93

Table

Subjects
1	2	3	4	5	6	7	8	9	10
010	110	210	310	410	510	610	710	810	910
20	31	42	53	64	75	86	97	08	19
72	83	94	05	16	27	38	49	50	61
57	68	79	80	91	02	13	24	35	46
105	106	107	108	109	100	101	102	103	104

Table

Subjects
1	2	3	4	5	6	7	8	9	10	11	12
05	16	27	38	49	510	611	70	81	92	103	114
30	41	52	63	74	85	96	107	118	09	110	211
73	84	95	106	117	08	19	210	311	40	51	62
47	58	69	710	811	90	101	112	03	14	25	36
94	105	116	07	18	29	310	411	50	61	72	83
59	610	711	80	91	102	113	04	15	26	37	48

Table

Subjects
13	14	15	16	17	18	19	20	21	22	23	24
00	11	22	33	44	55	66	77	88	99	1010	1111
10	21	32	43	54	65	76	87	98	109	1110	011
31	42	53	64	75	86	97	108	119	010	111	20
23	34	45	56	67	78	89	910	1011	110	01	12
02	13	24	35	46	57	68	79	810	911	100	111

Table

Subjects
25	26	27	28	29	30	31	32	33	34	35	36
012	112	212	312	412	512	612	712	812	912	1012	1112
60	71	82	93	104	115	06	17	28	39	410	511
126	127	128	129	1210	1211	120	121	122	123	124	125

Table A1. List of sets of shifts for CNBs in two different sizes of periods and treatments smaller than 30.

t	k1	k2	Sets of shifts	ES
9	6	4	[1,3,2,7,6] + [4,0]t	96
10	6	5	[1,3,2,8,7] + [4,5,0]t	97
11	8	4	[1,3,2,4,9,8,7] + [5,0]t	97
13	6	4	[1,3,2,11,10] + [4,5,8] + [6,0]t	98
13	8	6	[1,3,2,4,11,10,9] + [5,6,7,0]t	98
13	10	4	[1,3,2,4,5,11,10,9,8] + [6,0]t	98
14	8	7	[1,3,2,4,12,11,10] + [5,6,7,8,0]t	98
15	6	4	[1,3,2,13,12] + [4,5,6,10,9] + [7,0]t	98
15	6	5	[1,2,3,13,12] + [4,5,10,9] + [6,7,8]t	98
15	8	4	[1,3,2,4,13,12,11] + [5,6,9] + [7,0]t	98
16	6	5	[1,3,2,14,13] + [4,5,6,11,10] + [7,8,0]t	98
17	10	4	[1,3,2,4,5,15,14,13] + [6,7,10] + [8,0]t	99
17	10	8	[1,3,2,4,5,15,14,13,12] + [6,7,8,10,9,0]t	99
18	10	9	[1,3,2,4,5,16,15,14,13] + [6,7,8,9,10,11,0]t	99
19	6	4	[1,3,2,17,16] + [4,5,6,14,13] + [7,8,11] + [9,0]t	99
19	8	4	[1,3,2,4,17,16,15] + [5,6,7,8,13,12,11] + [9,0]t	99
21	6	4	[1,3,2,19,18] + [4,5,6,16,15] + [7,8,9,13,12] + [10,0]t	99
21	6	5	[1,2,3,19,18] + [4,5,6,16,15] + [7,8,13,12] + [9,10,11]t	99
21	8	6	[1,3,2,4,19,18,17] + [5,6,7,8,15,14,13] + [9,11,10,0]t	99
21	8	7	[1,2,3,4,19,18,17] + [5,6,7,15,14,13] + [8,9,10,12,11]t	99
22	6	5	[1,3,2,20,19] + [4,5,6,17,16] + [7,8,9,14,13] + [10,11,0]t	99
22	8	7	[1,3,2,4,20,19,18] + [5,6,7,8,16,15,14] + [9,10,11,12,0]t	99
23	8	4	[1,3,2,4,21,20,19] + [5,6,7,8,17,16,15] + [9,10,13] + [11,0]t	99
23	10	4	[1,3,2,4,5,21,20,19,18] + [6,7,8,9,10,16,15,14,13] + [11,0]t	99
25	6	4	[1,3,2,23,22] + [4,5,6,20,19] + [7,8,9,17,16] + [10,11,14] + [12,0]t	99
27	6	4	[1,3,2,25,24] + [4,5,6,22,21] + [7,8,9,19,18] + [10,11,12,16,15] + [13,0]t	99
27	6	5	[1,2,3,25,24] + [4,5,6,22,21] + [7,8,9,19,18] + [10,11,16,15] + [12,13,14]t	99
27	8	4	[1,3,2,4,25,24,23] + [5,6,7,8,21,20,19] + [9,10,11,12,17,16,15] + [13,0]t	99
27	10	4	[1,3,2,4,5,25,24,23,22] + [6,7,8,9,10,20,19,18,17] + [11,12,15] + [13,0]t	99
27	10	8	[1,3,2,4,5,25,24,23,22] + [6,7,8,9,10,20,19,18,17] + [11,12,13,15,14,0]t	99
27	10	9	[1,2,3,4,5,25,24,23,22] + [6,7,8,9,20,19,18,17] + [10,11,12,16,15,14,13]t	99
28	6	5	[1,3,2,26,25] + [4,5,6,23,22] + [7,8,9,20,19] + [10,11,12,17,16] + [13,14,0]t	99
28	10	9	[1,3,2,4,5,26,25,24,23] + [6,7,8,9,10,21,20,19,18] + [11,12,13,14,15,16,0]t	99
29	8	6	[1,3,2,4,27,26,25] + [5,6,7,8,23,22,21] + [9,10,11,12,19,18,17] + [13,15,14,0]t	99
29	8	7	[1,2,3,4,27,26,25] + [5,6,7,8,23,22,21] + [9,10,11,19,18,17] + [12,13,14,16,15]t	99

Table A2. List of sets of shifts for CNBs in three different sizes of periods and treatments smaller than 30.

t	k1	k2	k3	Sets of shifts	ES
14	6	5	4	[1,2,3,12,11] + [4,5,9,8] + [6,7]t	98
17	8	6	4	[1,2,3,4,15,14,13] + [5,6,7,11,10] + [8,0]t	99
19	8	7	5	[1,2,3,4,17,16,15] + [5,6,7,13,12,11] + [8,9,10]t	99
20	6	5	4	[1,2,3,18,17] + [4,5,6,15,14] + [7,8,12,11] + [9,10]t	99
20	8	7	6	[1,2,3,4,18,17,16] + [5,6,7,14,13,12] + [8,9,11,10]t	99
23	10	8	6	[1,2,3,4,5,21,20,19,18] + [6,7,8,9,16,15,14] + [10,11,12,0]t	99
25	8	6	4	[1,2,3,4,23,22,21] + [5,6,7,8,19,18,17] + [9,10,11,15,14] + [12,0]t	99
25	10	9	7	[1,2,3,4,5,23,22,21,20] + [6,7,8,9,18,17,16,15] + [10,11,12,13,14]t	99
26	6	5	4	[1,2,3,24,23] + [4,5,6,21,20,19] + [7,8,9,18,17,16] + [10,11,15,14] + [12,13]t	99
26	10	9	8	[1,2,3,4,5,24,23,22,21] + [6,7,8,9,19,18,17,16] + [10,11,12,15,14,13]t	99
27	8	7	5	[1,2,3,4,25,24,23] + [5,6,7,8,21,20,19] + [9,10,11,17,16,15] + [12,13,14]t	99
28	8	7	6	[1,2,3,4,26,25,24] + [5,6,7,8,22,21,20] + [9,10,11,18,17,16] + [12,13,15,14]t	99