# Design of experiments

The branch of mathematical statistics dealing with the rational organization of measurements subject to random errors. One usually considers the following scheme. A function $f(\theta,x)$ is measured with random errors, these being dependent on unknown parameters (the vector $\theta$) and on variables $x$, which, at the experimenter's choice, may take values from some admissible set $X$. The purpose of the experiment is usually either to estimate all or some of the parameters $\theta$ or functions of them, or else to test certain hypotheses concerning $\theta$. The purpose of the experiment is used in formulating a criterion for the design's optimality. The design of an experiment is understood to mean the set of values given to the variables $x$ in the experiment.

#### References

[1] | V.V. Nalimov, N.A. Chernova, "Statistical methods of designing extremal experiments" , Moscow (1965) (In Russian) |

[2] | V.V. Fedorov, "Theory of optimal experiments" , Acad. Press (1972) (Translated from Russian) |

[3] | C. Hicks, "Basic principles of experiment design" , Moscow (1967) (In Russian; translated from English) |

[4] | D. Finney, "An introduction to the theory of experimental design" , Univ. Chicago Press (1960) |

**How to Cite This Entry:**

Design of experiments.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Design_of_experiments&oldid=33940