The **design of experiments** (**DOE**, **DOX**, or **experimental design**) is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with true experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in whichnatural conditions that influence the variation are selected for observation.

In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is reflected in a variable called the predictor. The change in the predictor is generally hypothesized to result in a change in the second variable, hence called the outcome variable. Experimental design involves not only the selection of suitable predictors and outcomes, but planning the delivery of the experiment under statistically optimal conditions given the constraints of available resources.

Main concerns in experimental design include the establishment of validity, reliability, and replicability. For example, these concerns can be partially addressed by carefully choosing the predictor, reducing the risk of measurement error, and ensuring that the documentation of the method is sufficiently detailed. Related concerns include achieving appropriate levels of statistical power and sensitivity.

Correctly designed experiments advance knowledge in the natural and social sciences and engineering. Other applications include marketing and policy making.

# Design of Experiments (DOE)

## Outline

**Introduction****Preparation****Components of Experimental Design****Purpose of Experimentation****Design Guidelines****Design Process****One Factor Experiments****Multi-factor Experiments****Taguchi Methods**

In the design of experiments, **optimal designs** (or **optimum designs**^{[2]}) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.^{[3]}^{[4]}

In the design of experiments for estimating statistical models, **optimal designs** allow parameters to be estimated without bias and withminimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the sameprecision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation.

The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding ofstatistical theory and practical knowledge with designing experiments.