science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence ...

, randomized experiments are the

experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...

s that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in

experimental design 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. The term is generally associ ...

and in survey sampling.

Overview

In the statistical theory of

design of experiments 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. The term is generally associ ...

, randomization involves randomly allocating the experimental units across the

treatment groups In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one ...

. 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 is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...

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

law of large numbers In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials shou ...

). Randomization also produces ignorable designs, which are valuable in model-based

statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properti ...

, especially Bayesian or

likelihood The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...

-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 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 In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...

of estimators of selected effects. Randomization of treatment in

clinical trials Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dieta ...

pose ethical problems. In some cases, randomization reduces the therapeutic options for both physician and patient, and so randomization requires clinical equipoise regarding the treatments.

Online randomized controlled experiments

Web sites can run randomized controlled experiments to create a feedback loop. Key differences between offline experimentation and online experiments include: * Logging: user interactions can be logged reliably. * Number of users: large sites, such as Amazon, Bing/Microsoft, and Google run experiments, each with over a million users. * Number of concurrent experiments: large sites run tens of overlapping, or concurrent, experiments. * Robots, whether web crawlers from valid sources or malicious internet bots. * Ability to ramp-up experiments from low percentages to higher percentages. * Speed / performance has significant impact on key metrics. * Ability to use the pre-experiment period as an A/A test to reduce variance.

History

A controlled experiment appears to have been suggested in the Old Testament's Book of Daniel. King Nebuchadnezzar proposed that some Israelites eat "a daily amount of food and wine from the king's table." Daniel preferred a vegetarian diet, but the official was concerned that the king would "see you looking worse than the other young men your age? The king would then have my head because of you." Daniel then proposed the following controlled experiment: "Test your servants for ten days. Give us nothing but vegetables to eat and water to drink. Then compare our appearance with that of the young men who eat the royal food, and treat your servants in accordance with what you see". (Daniel 1, 12– 13). Randomized experiments were institutionalized in psychology and education in the late eighteen-hundreds, following the invention of randomized experiments by

C. S. Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for t ...

. 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'' is a classic book on statistics, written 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, together with his ''The ...

'', which also introduced additional principles of experimental design.

Statistical interpretation

The

Rubin Causal Model The Rubin causal model (RCM), also known as the Neyman–Rubin causal model, is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes, named after Donald Rubin. The name "Rubin causal model" was ...

provides a common way to describe a randomized experiment. While the Rubin Causal Model provides a framework for defining the causal parameters (i.e., the effects of a randomized treatment on an outcome), the analysis of experiments can take a number of forms. Most commonly, randomized experiments are analyzed using ANOVA,

student's t-test A ''t''-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of ...

regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

, or a similar statistical test.

Empirical evidence that randomization makes a difference

Empirically differences between randomized and non-randomized studies, and between adequately and inadequately randomized trials have been difficult to detect.

References