Discussion
Under a Latin-Square design with V treatments, which of the following statements is not correct ?
Answer: B
The incorrect statement is it requires exactly \(V^{3}\) experimental units.
A Latin square for V treatments is a \(V \times V\) arrangement, one plot per cell, so it uses \(V^{2}\) units, each treatment once in every row and every column.
The other statements are the usual properties. The design classifies the variation three ways, by rows, columns and treatments; row, column and treatment contrasts are all estimated with the same variance \(2\sigma^{2}/V\) because the design is balanced; and the error degrees of freedom are \((V^{2} - 1) - 3(V - 1) = (V - 1)(V - 2)\).
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