# Design of experiments

**experimental designdesignExperimental techniquesdesigned experimentexperimentsexperimentaldesigned experimentsDOEexperimentexperimental designs**

The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation.wikipedia

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### Optimal design

**optimal experimental designoptimaloptimal design of experiments**

Charles S. Peirce also contributed the first English-language publication on an optimal design for regression models in 1876. A pioneering optimal design for polynomial regression was suggested by Gergonne in 1815.

In the design of experiments, optimal designs (or optimum designs ) are a class of experimental designs that are optimal with respect to some statistical criterion.

### Dependent and independent variables

**dependent variableindependent variableexplanatory variable**

In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables."

In an experiment, the variable manipulated by an experimenter is called an independent variable.

### Lady tasting tea

As a mundane example, he described how to test the lady tasting tea hypothesis, that a certain lady could distinguish by flavour alone whether the milk or the tea was first placed in the cup.

In the design of experiments in statistics, the lady tasting tea is a randomized experiment devised by Ronald Fisher and reported in his book The Design of Experiments (1935).

### Power (statistics)

**statistical powerpowerpowerful**

Related concerns include achieving appropriate levels of statistical power and sensitivity.

The design of an experiment or observational study often influences the power.

### Agricultural engineering

**agricultural engineerAgriculturalagrotechnology**

These methods have been broadly adapted in the physical and social sciences, are still used in agricultural engineering and differ from the design and analysis of computer experiments.

### Polynomial regression

**cubic regressionPolynomial fittingregression**

A pioneering optimal design for polynomial regression was suggested by Gergonne in 1815.

The first design of an experiment for polynomial regression appeared in an 1815 paper of Gergonne.

### Combinatorial design

**combinatorial design theoryDesign theory(''n'',''r'',''k'',''r'')-lotto design**

Many problems of the design of experiments involve combinatorial designs, as in this example and others. Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.

Combinatorial design theory can be applied to the area of design of experiments.

### The Design of Experiments

**book**

A methodology for designing experiments was proposed by Ronald Fisher, in his innovative books: The Arrangement of Field Experiments (1926) and The Design of Experiments (1935).

The Design of Experiments is a 1935 book by the English statistician Ronald Fisher about the design of experiments and is considered a foundational work in experimental design.

### Analysis of variance

**ANOVAanalysis of variance (ANOVA)corrected the means**

design of experiments.

### Orthogonal array

**Hyper-Graeco-Latin square design**

About the same time, C. R. Rao introduced the concepts of orthogonal arrays as experimental designs.

These arrays have many connections to other combinatorial designs and have applications in the statistical design of experiments, coding theory, cryptography and various types of software testing.

### Taguchi methods

**Taguchirobust designTaguchi design**

This concept played a central role in the development of Taguchi methods by Genichi Taguchi, which took place during his visit to Indian Statistical Institute in early 1950s.

Traditionally, statistical methods have relied on mean-unbiased estimators of treatment effects: Under the conditions of the Gauss–Markov theorem, least squares estimators have minimum variance among all mean-unbiased linear estimators.

### Algebraic statistics

**algebrastatistics**

Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.

Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.

### Bayesian experimental design

**BayesianBayesian design of experimentsdesigns**

As with other branches of statistics, experimental design is pursued using both frequentist and Bayesian approaches: In evaluating statistical procedures like experimental designs, frequentist statistics studies the sampling distribution while Bayesian statistics updates a probability distribution on the parameter space.

Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived.

### Randomization

**randomizedrandomizingrandomisation**

In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups.

### Statistical model

**modelprobabilistic modelstatistical modeling**

Charles S. Peirce also contributed the first English-language publication on an optimal design for regression models in 1876.

### Raj Chandra Bose

**R. C. BoseBoseBose, R. C.**

Some efficient designs for estimating several main effects were found independently and in near succession by Raj Chandra Bose and K. Kishen in 1940 at the Indian Statistical Institute, but remained little known until the Plackett–Burman designs were published in Biometrika in 1946. Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

Raj Chandra Bose (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him.

### Statistics

**statisticalstatistical analysisstatistician**

It typically involves the manipulation - perhaps unconsciously - of the process of statistical analysis and the degrees of freedom until they return a figure below the p

Fisher's most important publications were his 1918 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance, which was the first to use the statistical term, variance, his classic 1925 work Statistical Methods for Research Workers and his 1935 The Design of Experiments, where he developed rigorous design of experiments models.

### Ronald Fisher

**R.A. FisherR. A. FisherFisher**

A methodology for designing experiments was proposed by Ronald Fisher, in his innovative books: The Arrangement of Field Experiments (1926) and The Design of Experiments (1935). Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

His contributions to statistics include the maximum likelihood, fiducial inference, the derivation of various sampling distributions, founding principles of the design of experiments, and much more.

### John Nelder

**John Ashworth NelderNelderNelder, John**

Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

John Ashworth Nelder (8 October 1924 – 7 August 2010) was a British statistician known for his contributions to experimental design, analysis of variance, computational statistics, and statistical theory.

### Genichi Taguchi

**TaguchiTaguchi, GenichiDr. Genichi Taguchi**

This concept played a central role in the development of Taguchi methods by Genichi Taguchi, which took place during his visit to Indian Statistical Institute in early 1950s. Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

After the war, in 1948 he joined the Ministry of Public Health and Welfare, where he came under the influence of eminent statistician Matosaburo Masuyama, who kindled his interest in the design of experiments.

### Oscar Kempthorne

**Kempthorne, OscarKempthorneO. Kempthorne**

Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

Oscar Kempthorne (January 31, 1919 – November 15, 2000) was a British statistician and geneticist known for his research on randomization-analysis and the design of experiments, which had wide influence on research in agriculture, genetics, and other areas of science.

### Joseph Diez Gergonne

**Joseph Diaz GergonneGergonneJoseph Gergonne**

A pioneering optimal design for polynomial regression was suggested by Gergonne in 1815.

In 1815, Gergonne wrote the first paper on the optimal design of experiments for polynomial regression.

### George E. P. Box

**George BoxGeorge Edward Pelham BoxBox, George E. P.**

Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J. Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G. Taguchi.

George Edward Pelham Box FRS (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.

### System identification

**identificationmodel order reductionnonlinear system identification**

Some discussion of experimental design in the context of system identification (model building for static or dynamic models) is given in and.

System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction.

### Experiment

**experimentalexperimentationexperiments**

The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.

In the design of experiments, two or more "treatments" are applied to estimate the difference between the mean responses for the treatments.