---
tag: EHJ3R589ZX
kind: concept
name: Factorial experiment
msc: [62K15]
sources:
  - url: https://en.wikipedia.org/wiki/Factorial_experiment
same_as:
  wikidata: Q4116558
  wikipedia: 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|PBK2XY4M0A]] run only a chosen part of it.

## Explanations

### L1 human

To bake a better cake, one might vary the oven temperature (low or high) and the baking time (short or long).
A factorial experiment bakes all four combinations, instead of changing one thing at a time.
Every cake then says something about both temperature and time.
It also shows interactions: maybe a long time helps at low temperature but burns the cake at high temperature.