5
Consider a greenhouse experiment on Tobacco Mosaic Virus (TMV). Each experimental unit was a single leaf on a plant and the data consisted of the number of lesions produced on the leaf by rubbing the leaf with a solution which contained the TMV. Each row of the design was a single plant. The columns were the ‘position’ from top to bottom, of the four leaves, which were used in each plant. Accordingly, the following Youden square design was constructed rep he Ee ohh er he Prhee ke re hee be Consider the following statements:
(A) . For the Youden Square Design, the rows form an RBD i.e. Randomized Block Design with v=7 treatments and r=4
replications
(B) . For the Youden Square Design, the columns form a symmetric BIBD i.e. Balanced Incomplete Block Design with
v=b=7 and r=k=4 and A=1
(C) . The given Youden Square Design is an incomplete Latin square and rather every Youden Square Design is an
incomplete Latin Square Design.
(D) . For the Youden Square Design, the ‘position’ effect is orthogonal to the treatment effect.
Choose the correct statements from the options given below:
EXPLANATION
Linear Estimation, Gauss-Markov Theorem & Bas
- Properties of Youden Square Design:
- Youden Square is an incomplete Latin square design that eliminates two sources of positional variation (rows and columns).
- For the given TMV greenhouse experiment with 7 treatments and 4 leaf positions across 7 plants:
- Plants (rows) form blocks of size $k = 4 \lt v = 7$, thus forming a Balanced Incomplete Block Design (BIBD), not a complete RBD. (False, inverted in statement)
- The columns (positions) represent complete blocks containing all treatments, while rows form a symmetric BIBD with $v = b = 7, r = k = 4, \lambda = 2$. (False as worded)
- Every Youden square design is formed by selecting $k$ rows from a full $v \times v$ Latin square, making it an incomplete Latin square. (True)
- The leaf position effect (columns) is completely orthogonal to the treatment effect. (True)
- Conclusion: Statements (A), (C) and (D) only (Option 3).
Correct option: (3) (A), (C) and (D) only.
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