Exercise 9.6.4 State whether each design given below is a balanced incomplete block design, and if so, give the values of

b, t, k, r, and λ .

(a) The experiment involves 5 treatments: A, B, C, D, and E. The experiment is laid out as follows.

Block Treatments Block Treatments 1 A,B,C 6 A,B,D 2 A,B,E 7 A,C,D 3 A,D,E 8 A,C,E 4 B,C,D 9 B,C,E 5 C,D,E 10 B,D,E

(b) The following design has 9 treatments: A, B, C, D, E, F, G, H, and I.

Block Treatments Block Treatments 1 B,C,D,G 6 C,D,E, I 2 A,C,E,H 7 A,D,H, I 3 A,B,F, I 8 B,E,G, I 4 A,E,F,G 9 C,F,G,H 5 B,D,F,H

(c) The following design has 7 treatments: A, B, C, D, E, F, G.

Block Treatments Block Treatments 1 C,E,F,G 5 B,C,D,G 2 A,D,F,G 6 A,C,D,E 3 A,B,E,G 7 B,D,E,F 4 A,B,C,F