Discussion
Under a \(2^{3}\) factorial design with factors A, B, C arranged in a single replicate of two blocks, the containts of block-I (in Yate's notation) are {1, a, ab, b}. Which of the following effects is confounded with blocks ?
Answer: D
The effect confounded with blocks is C.
Block I contains 1, a, b, ab, exactly the treatment combinations in which factor C is at its low level, and block II therefore contains c, ac, bc, abc. The main effect of C is the contrast (c + ac + bc + abc) - (1 + a + b + ab), which is the same as the block difference, so C cannot be separated from blocks.
For AB the block would have to be {1, ab, c, abc}, for AC {1, ac, b, abc}, and for ABC {1, ab, ac, bc}. Confounding a main effect is unusual in practice, but it is what this allocation does.
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