Factorial experiment

Summary

A factorial experiment studies several factors at once, each at a few levels, and runs every combination of levels. It estimates the main effect of each factor and the interactions between factors. An interaction shows whether the effect of one factor depends on the level of another. Each run contributes to the estimate of every main effect, so a factorial experiment is more efficient than changing one factor at a time. The $2^k$ design, with $k$ factors at two levels each, is the basic case, and fractional factorial designs run only a chosen part of it.