9 Blocking and confounding in the \(2^k\) design

A \(2^k\) design often has to be run in blocks. If whole replicates fit in blocks, the design is a randomised complete block design with the \(2^k\) combinations as treatments (Section 7). Often, however, a single replicate is too large for one block: a batch of raw material is enough for only four runs, or only eight runs can be made in a day. Then each block can hold only part of a replicate, and the price is that some effect becomes indistinguishable from the difference between blocks. The art is to choose that effect, so that only an unimportant one is lost.

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