Discussion
Consider the following statements :
(1) If the presence of interaction inflates the error mean square, one should use factorial designs.
(2) Two contrasts with coefficient \(\{c_{i}\}\) and \(\{d_{i}\}\) are orthogonal if \(\sum_{i=1}^{a} c_{i}d_{i} = 0\).
(3) Confounding is a design technique for arranging a complete factorial experiment in blocks.
Which of the above statements are correct ?
Answer: D
All are correct.
(1): if factors interact and a one-factor-at-a-time or main-effects analysis is used, the interaction is left in the error term, inflating the error mean square and hiding real effects. A factorial design estimates the interaction separately, so it should be used.
(2): with equal replication, contrasts \(\sum c_{i}\mu_{i}\) and \(\sum d_{i}\mu_{i}\) are orthogonal when \(\sum c_{i}d_{i} = 0\); their sums of squares are then independent components of the treatment sum of squares.
(3): confounding is the technique of arranging a complete factorial in blocks smaller than a full replicate, by deliberately making some (usually high-order) interactions indistinguishable from block effects. Since all three hold, the answer is D.
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