Consider a 2 4 design. We must estimate the four main effects and the six two-factor interactions,

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Consider a 24 design. We must estimate the four main effects and the six two-factor interactions, but the full 24 factorial cannot be run. The largest possible block size contains 12 runs. These 12 runs can be obtained from the four one-quarter replicates defined by I = ±AB = ±ACD = ±BCD by omitting the principal fraction. Show how the remaining three 24- 2 fractions can be combined to estimate the required effects, assuming three-factor and higher interactions are negligible. This design could be thought of as a three-quarter fraction.

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