---
tag: 2TE42ZWJ3E
kind: concept
name: Design of experiments
msc: [62K99, 62K05]
sources:
  - url: https://en.wikipedia.org/wiki/Design_of_experiments
same_as:
  wikidata: Q2334061
  wikipedia: Design of experiments
---

## Summary

Design of experiments is the part of statistics that plans how data are collected when the experimenter controls the conditions.
Its aim is to answer the questions of interest validly and efficiently.
Its three classical principles, set out by Ronald Fisher, are [[randomization|734Q6Q51X7]], replication and local control by [[blocking|XCWKYS1DFA]].
Its main designs include completely randomized and block designs, Latin squares, [[factorial|EHJ3R589ZX]] and [[fractional factorial|PBK2XY4M0A]] designs, and response surface designs.
[[Optimal experimental design|PM5PQX6TVP]] chooses designs that make the estimates as precise as possible, and the data are usually analysed by [[analysis of variance|M9AQ5HKGP4]].

## Explanations

### L1 human

To learn whether a new fertiliser works, one could just look at farms that use it, but those farms may differ in many other ways.
In an experiment, the researcher decides which plots get which fertiliser, and that choice is the design.
A good design repeats each treatment several times, assigns treatments by chance, and compares treatments on similar plots.
Then a difference in yield can be credited to the fertiliser and not to something else.