Discussion
8 treatments are arranged in a row-column design as given below :
| 1 | 2 | 3 | 4 |
| 5 | 6 | 7 | 8 |
| 3 | 8 | 1 | 6 |
| 7 | 4 | 5 | 2 |
Hence it is a :
Answer: C
It is a quasi-Latin square design.
The layout is \(4 \times 4\), but it holds 8 treatments, each appearing twice, and each row and each column contains only 4 of them. A Latin square would need 4 treatments, each exactly once in every row and column, so this is not one.
A quasi-Latin square (Yates) arranges the \(2^{3} = 8\) treatment combinations of a factorial in a square of side 4, with rows and columns acting as incomplete blocks that confound different interactions: here rows 1 and 2 hold {1, 2, 3, 4} and {5, 6, 7, 8}, rows 3 and 4 hold {1, 3, 6, 8} and {2, 4, 5, 7}, and the columns split the treatments a third way.
A Youden square is an incomplete Latin square whose rows are complete blocks, which these are not, and 'incomplete block design' describes one-way blocking, not a row-column layout.
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