In science

Scientific method

Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling

Survey sampling

In statistics, survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.A survey may refer to many different types or techniques of observation, but in the context of survey sampling it most often involves a questionnaire used to...

.

Applications

In the statistical theory of design of experiments

Design of experiments

In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...

, randomization involves randomly allocating the experimental units across the treatment groups

Treatment groups

In the design of experiments, treatments are applied to experimental units in the treatment group, while no treatments would be applied to members of a control group....

. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.

Randomized experimentation is not haphazard. Randomization reduces bias

Bias

Bias is an inclination to present or hold a partial perspective at the expense of alternatives. Bias can come in many forms.-In judgement and decision making:...

 by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers

Law of large numbers

In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...

). Randomization also produces ignorable designs

Ignorability

In statistics, ignorability refers to an experiment design where the method of data collection do not depend on the missing data...

, which are valuable in model

Statistical model

A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...

-based statistical inference

Statistical inference

In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...

, especially Bayesian

Bayesian inference

In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

 or likelihood

Likelihood function

In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...

-based. In the design of experiments, the simplest design for comparing treatments is the "completely randomized design". Some "restriction on randomization" can occur with blocking

Blocking

Blocking may refer to:- Telecommunications and computing :*Block , a sequence of bytes or bits, having a nominal length*Block , technical measures to restrict users' access to certain internet resources...

 and experiments that have hard-to-change factors; additional restrictions on randomization can occur when a full randomization is infeasible or when it is desirable to reduce the variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

 of estimators of selected effects.

Randomization of treatment in clinical trials pose ethical problems. In some cases, randomization reduces the therapeutic options for both physician and patient, and so randomization requires clinical equipoise

Clinical equipoise

Clinical equipoise, also known as the principle of equipoise, provides the ethical basis for medical research involving patients assigned to different treatment arms of a clinical trial...

 regarding the treatments.

History

Randomized experiments were institutionalized in psychology and education in the late eighteen-hundreds, following the invention of randomized experiments by C. S. Peirce.
Outside of psychology and education, randomized experiments were popularized by R.A. Fisher in his book Statistical Methods for Research Workers

Statistical Methods for Research Workers

Statistical Methods for Research Workers is a classic 1925 book on statistics by the statistician R.A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods. According to ,...

, which also introduced additional principles of experimental design.