Let us consider the following Balanced Incomplete Block Design (B.I.B.

Question

Let us consider the following Balanced Incomplete Block Design (B.I.B.D.) with parameters $v=9,\quad b=7,\quad r=7,\quad k=4,\quad\lambda=2$

Block Label	Design
I	1 3 4 5
II	1 4 6 7
III	1 2 5 7
IV	3 5 6 7
V	2 3 4 7
VI	1 2 3 6
VII	2 4 5 6

Obtain a derived design from the above Balanced Incomplete Block Design (B.I.B.D.) and find the parameters of the obtained design.

29 Apr 2025

Answer :

Word Count : 281

We are given a Balanced Incomplete Block Design (BIBD) with parameters: $$ v = 9,\quad b = 7,\quad r = 7,\quad k = 4,\quad \lambda = 2 $$ From this, the given incidence matrix represents a BIBD with 9 treatments, 7 blocks, each of size 4. _______ _____ _______ _____ ___ ____ ______ ______ __________ _________ _______.
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Farm	2024	2026	Farm	2024	2026
1	12	14	11	11	14
2	22	25	12	17	19
3	38	37	13	12	12
4	15	18	14	22	23
5	18	20	15	14	16
6	31	30	16	26	28
7	15	15	17	08	09
8	20	21	18	16	15
9	10	12	19	13	15
10	25	12	20	19	20

Cluster	Y - values	Cluster	Y - values
1	2, 4, 6, 1, 3, 5	4	3, 2, 5, 1, 6, 4
2	2, 5, 3, 4, 7, 4	5	2, 4, 6, 8, 3, 5
3	4, 3, 6, 2, 1, 5	6	4, 1, 2, 7, 5, 3