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Design of tasks

The design of experiments (DOE or DOX), also known as experiment design 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. 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 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." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must be held constant to prevent external factors from affecting the results. Experimental design involves not only the selection of suitable independent, dependent, and control variables, but planning the delivery of the experiment under statistically optimal conditions given the constraints of available resources. There are multiple approaches for determining the set of design points (unique combinations of the settings of the independent variables) to be used in the experiment. 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 independent variable, 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, with design of experiments methodology recognised as a key tool in the successful implementation of a Quality by Design (QbD) framework. Other applications include marketing and policy making. The study of the design of experiments is an important topic in metascience.

A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883), two publications that emphasized the importance of randomization based inference in statistics.

Charles S. Peirce randomly assigned volunteers to a blinded, repeated measures design to evaluate their ability to discriminate weights. Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1800s. A pioneering optimal design for polynomial regression was suggested by Gergonne in 1815. In 1918, Kirstine Smith published optimal designs for polynomials of degree six (and less).

The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered by Abraham Wald in the context of sequential tests of statistical hypotheses. Herman Chernoff wrote an overview of optimal sequential designs, One specific type of sequential design is the "two armed bandit", generalized to the multi armed bandit, on which early work was done by Herbert Robbins in 1952.

In the pure experimental design, the independent (predictor) variable is manipulated by the researcher – that is – every participant of the research is chosen randomly from the population, and each participant chosen is assigned randomly to conditions of the independent variable. Only when this is done is it possible to certify with high probability that the reason for the differences in the outcome variables are caused by the different conditions. Therefore, researchers should choose the experimental design over other design types whenever possible. However, the nature of the independent variable does not always allow for manipulation. In those cases, researchers must be aware of not certifying about causal attribution when their design doesn't allow for it. For example, in observational designs, participants are not assigned randomly to conditions, and so if there are differences found in outcome variables between conditions, it is likely that there is something other than the differences between the conditions that causes the differences in outcomes, that is – a third variable. The same goes for studies with correlational design (Adér & Mellenbergh, 2008).

It is best that a process be in reasonable statistical control prior to conducting designed experiments. When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments. To control for nuisance variables, researchers institute control checks as additional measures. Investigators should ensure that uncontrolled influences (e. g., source credibility perception) do not skew the findings of the study. A manipulation check is one example of a control check. Manipulation checks allow investigators to isolate the chief variables to strengthen support that these variables are operating as planned. One of the most important requirements of experimental research designs is the necessity of eliminating the effects of spurious, intervening, and antecedent variables. In the most basic model, cause (X) leads to effect (Y). But there could be a third variable (Z) that influences (Y), and X might not be the true cause at all. Z is said to be a spurious variable and must be controlled for. The same is true for intervening variables (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (a variable prior to the supposed cause (X) that is the true cause). When a third variable is involved and has not been controlled for, the relation is said to be a zero order relationship. In most practical applications of experimental research designs there are several causes (X1, X2, X3). In most designs, only one of these causes is manipulated at a time.

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. About the same time, C. R. Rao introduced the concepts of orthogonal arrays as experimental designs. 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. His methods were successfully applied and adopted by Japanese and Indian industries and subsequently were also embraced by US industry albeit with some reservations. In 1950, Gertrude Mary Cox and William Gemmell Cochran published the book Experimental Designs, which became the major reference work on the design of experiments for statisticians for years afterwards. Developments of the theory of linear models have encompassed and surpassed the cases that concerned early writers. Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics. 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. Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, R. C. Bose, A. C. Atkinson, R. A. Bailey, D. R. Cox, G. E. P. Box, W. G. Cochran, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. Kiefer, O. Kempthorne, J. A. Nelder, Andrej Pázman, Friedrich Pukelsheim, D. Raghavarao, C. R. Rao, Shrikhande S. S., J. N. Srivastava, William J. Studden, G. Taguchi and H. P. Wynn. The textbooks of D. Montgomery, R. Myers, and G. Box/W. Hunter/J. S. Hunter have reached generations of students and practitioners. Some discussion of experimental design in the context of system identification (model building for static or dynamic models) is given in and.