(a) Discuss the meaning of the term Balanced Incomplete Block. Show that it is possible to...

 

Transcribed Image Text:

(a) Discuss the meaning of the term Balanced Incomplete Block. Show that it is possible to arrange a BIB design for 5 treatments in 10 blocks of size 3, and suggest how the treatments would be arranged between the blocks and describe how the blocks should be applied in practice. [4 marks] (b) With the usual notation, show that for BIB designs: = r(k-1) t-1 Verify that the value of A is consistent for the above design. (c) (i) Explain what is meant by a cyclic design. (ii) Consider the two cyclic designs with 7 blocks for 7 treatments: 1. with initial block (1,2,3,6): 2. with initial block (1,2,3,4). Which one is the better design? Justify your answer. [2 marks] [1 mark] [4 marks] (d) Consider the following design with 8 treatments and 8 blocks, corresponding to the rows. 138 24 1 I II III 352 IV 463 V 5 7 4 VI 685 VII 7 16 VIII 8 27 Show that it is group-divisible. Specify the associate groups and the two concurrences A1 and A2. [3 marks] (a) Discuss the meaning of the term Balanced Incomplete Block. Show that it is possible to arrange a BIB design for 5 treatments in 10 blocks of size 3, and suggest how the treatments would be arranged between the blocks and describe how the blocks should be applied in practice. [4 marks] (b) With the usual notation, show that for BIB designs: = r(k-1) t-1 Verify that the value of A is consistent for the above design. (c) (i) Explain what is meant by a cyclic design. (ii) Consider the two cyclic designs with 7 blocks for 7 treatments: 1. with initial block (1,2,3,6): 2. with initial block (1,2,3,4). Which one is the better design? Justify your answer. [2 marks] [1 mark] [4 marks] (d) Consider the following design with 8 treatments and 8 blocks, corresponding to the rows. 138 24 1 I II III 352 IV 463 V 5 7 4 VI 685 VII 7 16 VIII 8 27 Show that it is group-divisible. Specify the associate groups and the two concurrences A1 and A2. [3 marks]