Discussion
A row-column design with 7 treatments arranged in 3 rows and 7 columns is given below :
1 2 3 4 5 6 7
2 3 4 5 6 7 1
4 5 6 7 1 2 3
Hence the design is :
Answer: B
The design is a Youden square design.
Each row contains all seven treatments once, so rows are complete blocks. Each column contains three distinct treatments, and the columns form the blocks {1, 2, 4}, {2, 3, 5}, ..., the Fano plane, a BIBD with \(v = 7\), \(b = 7\), \(k = 3\), \(\lambda = 1\). A rectangle that is complete in one direction and a symmetric BIBD in the other is a Youden square, an 'incomplete Latin square'.
It is not a Latin square, which would need 7 rows. A quasi-Latin square is a confounded factorial layout, and a split-plot design has main plots and sub-plots, neither of which fits.
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