SIMPLE AND COMPLEX RANDOM ASSIGNMENT IN EXPERIMENTAL DESIGNS

Valentim Rodrigues Alferes, University of Coimbra (Portugal), 2009

RECOMMENDATIONS FOR DETERMINING THE NUMBER OF EXPERIMENTAL
UNITS IN REPEATED MEASURES DESIGNS

1	Determine the minimum number of units based on power analysis.
2	Loop this number to the next integer that allows a complete counterbalancing of treatments [CC programs], or, if not practical, a carryover design [CO programs].
3	If you can’t get the number of units required for a complete counterbalancing or a carryover design, try a partial counterbalancing (Latin squares) [LS programs].
	(See Table 1 and Table 2)
4	If a partial counterbalancing is not feasible, choose truncated counterbalancing [CC, CO, or LS design with the additional “N of cases ?” line].
	Note. You can download ChooseRMD.sps, an SPSS syntax file for choosing a suitable Repeated Measures Design on the basis of the present recommendations.

Table 1 Minimum number of experimental units (N) in repeated measures designs.
Number of Treatments [T]	Complete Counterbalancing	Carryover Designs		Partial Counterbalancing
		Single	Double
	N = PT = T!	N = T	N = 2T	N = T
2	2	2	—	2
3	6	—	6	3
4	24	4	—	4
5	120	—	10	5
6	720	6	—	6
7	5040	—	14	7
8	40320	8	—	8
9	362880	—	18	9
10	3628800	10	—	10
11	39916800	—	22	11
12	479001600	12	—	12

Table 2 Suitable repeated measures designs for CC, CO, and LS programs.
Number of Units	Number of Treatments
	2	3	4	5	6	7	8	9	10	11	12
2	CC2
3		LS3
4	CC2		CO4
5				LS5
6	CC2	CC3			CO6
7						LS7
8	CC2		CO4				CO8
9		LS3						LS9
10	CC2			CO5					CO10
11										LS11
12	CC2	CC3	CO4		CO6						CO12
13
14	CC2					CO7
15		LS3		LS5
16	CC2		CO4				CO8
17
18	CC2	CC3			CO6			CO9
19
20	CC2		CO4	CO5					CO10
21		LS3				LS7
22	CC2									CO11
23
24	CC2	CC3	CC4		CO6		CO8				CO12
25				LS5
26	CC2
27		LS3						LS9
28	CC2		CO4			CO7
29
30	CC2	CC3		CO5	CO6				CO10
31
32	CC2		CO4				CO8
33		LS3								LS11
34	CC2
35				LS5		LS7
36	CC2	CC3	CO4		CO6			CO9			CO12
37
38	CC2
39		LS3
40	CC2		CO4	CO5			CO8		CO10
41
42	CC2	CC3			CO6	CO7
43
44	CC2		CO4							CO11
45		LS3		LS5				LS9
46	CC2
47
48	CC2	CC3	CC4		CO6		CO8				CO12
49						LS7
50	CC2			CO5					CO10
51		LS3
52	CC2		CO4
53
54	CC2	CC3			CO6			CO9
55				LS5						LS11
56	CC2		CO4			CO7	CO8
57		LS3
58	CC2
59
60	CC2	CC3	CO4	CO5	CO6				CO10		CO12
61
62	CC2
63		LS3				LS7		LS9
64	CC2		CO4				CO8
65				LS5
66	CC2	CC3			CO6					CO11
67
68	CC2		CO4
69		LS3
70	CC2			CO5		CO7			CO10
71
72	CC2	CC3	CC4		CO6		CO8	CO9			CO12
73
74	CC2
75		LS3		LS5
76	CC2		CO4
77						LS7				LS11
78	CC2	CC3			CO6
79
80	CC2		CO4	CO5			CO8		CO10
81		LS3						LS9
82	CC2
83
84	CC2	CC3	CO4		CO6	CO7					CO12
85				LS5
86	CC2
87		LS3
88	CC2		CO4				CO8			CO11
89
90	CC2	CC3		CO5	CO6			CO9	CO10
91						LS7
92	CC2		CO4
93		LS3
94	CC2
95				LS5
96	CC2	CC3	CC4		CO6		CO8				CO12
97
98	CC2					CO7
99		LS3						LS9		LS11
100	CC2		CO4	CO5					CO10
101
102	CC2	CC3			CO6
103
104	CC2		CO4				CO8
105		LS3		LS5		LS7
106	CC2
107
108	CC2	CC3	CO4		CO6			CO9			CO12
109
110	CC2			CO5					CO10	CO11
111		LS3
112	CC2		CO4			CO7	CO8
113
114	CC2	CC3			CO6
115				LS5
116	CC2		CO4
117		LS3						LS9
118	CC2
119						LS7
120	CC2	CC3	CC4	CC5	CO6		CO8		CO10		CO12
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