Fractional factorial design

Summary

A fractional factorial design runs only a chosen fraction of the combinations of a factorial experiment. An example is $2^{k-p}$ of the $2^k$ runs of a two-level design. The fraction is chosen by a defining relation, so that the main effects and low-order interactions can still be estimated. The price is that they are aliased with higher-order interactions. The resolution of the design measures how severe the aliasing is. Such designs make screening experiments with many factors affordable, on the assumption that high-order interactions are negligible.