Discussion
In a \(2^{5}\) factorial design in block of 8 plots each, total number of interaction confounded with blocks is :
Answer: C
3 interactions are confounded with blocks.
A \(2^{5}\) factorial has 32 treatment combinations. In blocks of 8 plots each, one replicate needs \(32/8 = 4\) blocks, and 4 blocks carry \(4 - 1 = 3\) degrees of freedom between them. Each confounded effect in a \(2^{n}\) design uses one degree of freedom, so 3 effects are confounded.
In practice two independent interactions are chosen and their generalised interaction is confounded automatically; for example ABC and CDE force \(ABC \times CDE = ABDE\). That is why 2 is too few: the third comes for free. 7 would correspond to 8 blocks of 4 plots, and 4 is not of the form \(2^{p} - 1\), so it is never the number confounded.
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