Question

How to set up experimental design for 3 factors at 4 different levels. I get in total I should end up with 81 experimental runs. Can you help me to determine how to distribute these 4 levels across 3 factors?

Answer 1

How to set up experimental design for 3 factors at 4 different levels. I get in total I should end up with 81 experimental runs. Can you help me to determine how to distribute these 4 levels across 3 factors?

I understand that your design is of 4³ = 4*4*4 (3 factors each at 4 levels). In this case if you are doing a full factorial design than you’ll have 64 factor combinations. ( not 81).

Let A,B,C be the 3 factors and 1,2,3,4 be the four levels

Then the actor combinations are:

1	A1	B1	C1
2	A1	B1	C2
3	A1	B1	C3
4	A1	B1	C4
5	A1	B2	C1
6	A1	B2	C2
7	A1	B2	C3
8	A1	B2	C4
9	A1	B3	C1
10	A1	B3	C2
11	A1	B3	C3
12	A1	B3	C4
13	A1	B4	C1
14	A1	B4	C2
15	A1	B4	C3
16	A1	B4	C4
17	A2	B1	C1
18	A2	B1	C2
19	A2	B1	C3
20	A2	B1	C4
21	A2	B2	C1
22	A2	B2	C2
23	A2	B2	C3
24	A2	B2	C4
25	A2	B3	C1
26	A2	B3	C2
27	A2	B3	C3
28	A2	B3	C4
29	A2	B4	C1
30	A2	B4	C2
31	A2	B4	C3
32	A2	B4	C4
33	A3	B1	C1
34	A3	B1	C2
35	A3	B1	C3
36	A3	B1	C4
37	A3	B2	C1
38	A3	B2	C2
39	A3	B2	C3
40	A3	B2	C4
41	A3	B3	C1
42	A3	B3	C2
43	A3	B3	C3
44	A3	B3	C4
45	A3	B4	C1
46	A3	B4	C2
47	A3	B4	C3
48	A3	B4	C4
49	A4	B1	C1
50	A4	B1	C2
51	A4	B1	C3
52	A4	B1	C4
53	A4	B2	C1
54	A4	B2	C2
55	A4	B2	C3
56	A4	B2	C4
57	A4	B3	C1
58	A4	B3	C2
59	A4	B3	C3
60	A4	B3	C4
61	A4	B4	C1
62	A4	B4	C2
63	A4	B4	C3
64	A4	B4	C4