Random assignment

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Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. [1] This ensures that each participant or subject has an equal chance of being placed in any group. [1] Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. [1] Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment. [1]


Random assignment, blinding, and controlling are key aspects of the design of experiments because they help ensure that the results are not spurious or deceptive via confounding. This is why randomized controlled trials are vital in clinical research, especially ones that can be double-blinded and placebo-controlled.

Mathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. How much these differences matter in experiments (such as clinical trials) is a matter of trial design and statistical rigor, which affect evidence grading. Studies done with pseudo- or quasirandomization are usually given nearly the same weight as those with true randomization but are viewed with a bit more caution.

Benefits of random assignment

Imagine an experiment in which the participants are not randomly assigned; perhaps the first 10 people to arrive are assigned to the Experimental group, and the last 10 people to arrive are assigned to the Control group. At the end of the experiment, the experimenter finds differences between the Experimental group and the Control group, and claims these differences are a result of the experimental procedure. However, they also may be due to some other preexisting attribute of the participants, e.g. people who arrive early versus people who arrive late.

Imagine the experimenter instead uses a coin flip to randomly assign participants. If the coin lands heads-up, the participant is assigned to the Experimental group. If the coin lands tails-up, the participant is assigned to the Control group. At the end of the experiment, the experimenter finds differences between the Experimental group and the Control group. Because each participant had an equal chance of being placed in any group, it is unlikely the differences could be attributable to some other preexisting attribute of the participant, e.g. those who arrived on time versus late.

Potential issues

Random assignment does not guarantee that the groups are matched or equivalent. The groups may still differ on some preexisting attribute due to chance. The use of random assignment cannot eliminate this possibility, but it greatly reduces it.

To express this same idea statistically - If a randomly assigned group is compared to the mean it may be discovered that they differ, even though they were assigned from the same group. If a test of statistical significance is applied to randomly assigned groups to test the difference between sample means against the null hypothesis that they are equal to the same population mean (i.e., population mean of differences = 0), given the probability distribution, the null hypothesis will sometimes be "rejected," that is, deemed not plausible. That is, the groups will be sufficiently different on the variable tested to conclude statistically that they did not come from the same population, even though, procedurally, they were assigned from the same total group. For example, using random assignment may create an assignment to groups that has 20 blue-eyed people and 5 brown-eyed people in one group. This is a rare event under random assignment, but it could happen, and when it does it might add some doubt to the causal agent in the experimental hypothesis.

Random sampling

Random sampling is a related, but distinct process. [2] Random sampling is recruiting participants in a way that they represent a larger population. [2] Because most basic statistical tests require the hypothesis of an independent randomly sampled population, random assignment is the desired assignment method because it provides control for all attributes of the members of the samples—in contrast to matching on only one or more variables—and provides the mathematical basis for estimating the likelihood of group equivalence for characteristics one is interested in, both for pretreatment checks on equivalence and the evaluation of post treatment results using inferential statistics. More advanced statistical modeling can be used to adapt the inference to the sampling method.


Randomization was emphasized in the theory of statistical inference of Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). Peirce applied randomization in the Peirce-Jastrow experiment on weight perception.

Charles S. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights. [3] [4] [5] [6] 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 eighteen-hundreds. [3] [4] [5] [6]

Jerzy Neyman advocated randomization in survey sampling (1934) and in experiments (1923). [7] Ronald A. Fisher advocated randomization in his book on experimental design (1935).

See also

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Statistical inference Process of using data analysis

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Experiment Scientific procedure performed to validate a hypothesis

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Randomized controlled trial Form of scientific experiment

A randomized controlled trial is a form of scientific experiment used to control factors not under direct experimental control. Examples of RCTs are clinical trials that compare the effects of drugs, surgical techniques, medical devices, diagnostic procedures or other medical treatments.

Experimental psychology

Experimental psychology refers to work done by those who apply experimental methods to psychological study and the processes that underlie it. Experimental psychologists employ human participants and animal subjects to study a great many topics, including sensation & perception, memory, cognition, learning, motivation, emotion; developmental processes, social psychology, and the neural substrates of all of these.


Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions".

Field experiment

Field experiments are experiments carried out outside of laboratory settings.

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In the design of experiments, treatments 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 treatment group, more than one control group, or both.

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Joseph Jastrow American psychologist

Joseph Jastrow was a Polish-born American psychologist, noted for inventions in experimental psychology, design of experiments, and psychophysics. He also worked on the phenomena of optical illusions, and a number of well-known optical illusions were either discovered or popularized in his work. Jastrow believed that everyone had their own, often incorrect, preconceptions about psychology. One of his goals was to use the scientific method to identify truth from error, and educate the layperson, which he did through speaking tours, popular print media, and radio.

Randomized experiment Experiment using randomness in some aspect, usually to aid in removal of bias

In science, 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.

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A quasi-experiment is an empirical interventional study used to estimate the causal impact of an intervention on target population without random assignment. Quasi-experimental research shares similarities with the traditional experimental design or randomized controlled trial, but it specifically lacks the element of random assignment to treatment or control. Instead, quasi-experimental designs typically allow the researcher to control the assignment to the treatment condition, but using some criterion other than random assignment.

Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. The evolution of statistics was, in particular, intimately connected with the development of European states following the peace of Westphalia (1648), and with the development of probability theory, which put statistics on a firm theoretical basis.

Oscar Kempthorne 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.

In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model.


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