Randomization is the process of making something
random. Randomization is not haphazard; instead, a
random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with
nonprobability sampling where
arbitrary individuals are selected.
In various contexts, randomization may involve:
* generating a
random permutation of a sequence (such as when
shuffling cards);
* selecting a
random sample of a population (important in
statistical sampling);
* allocating experimental units via
random assignment to a treatment or control condition;
* generating random numbers (
random number generation); or
* transforming a
data stream (such as when using a
scrambler in
telecommunications
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than tha ...
).
Applications
Randomization is used in statistics and in gambling.
Statistics
Randomization is a core principle in
statistical theory, whose importance was emphasized by
Charles S. Peirce in "
Illustrations of the Logic of Science" (1877–1878) and "
A Theory of Probable Inference" (1883). 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. The first use of "randomization" listed in the ''
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
'' is its use by
Ronald Fisher in 1926.
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
"randomization"
Randomized experiments
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. 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. Randomization reduces confounding by equalising so-called factors (
independent variables) that have not been accounted for in the experimental design.
Survey sampling
Survey sampling uses randomization, following the criticisms of previous "representative methods" by
Jerzy Neyman in his 1922 report to the
International Statistical Institute.
Resampling
Some important methods of statistical inference use
resampling from the observed data. Multiple alternative versions of the data-set that "might have been observed" are created by randomization of the original data-set, the only one observed. The variation of statistics calculated for these alternative data-sets is a guide to the uncertainty of statistics estimated from the original data.
Gambling
Randomization is used extensively in the field of
gambling
Gambling (also known as betting or gaming) is the wagering of something of Value (economics), value ("the stakes") on a Event (probability theory), random event with the intent of winning something else of value, where instances of strategy (ga ...
. Because poor randomization may allow a skilled gambler to take advantage, much research has been devoted to effective randomization. A classic example of randomizing is
shuffling playing cards.
Techniques
Although historically "manual" randomization techniques (such as shuffling cards, drawing pieces of paper from a bag, spinning a
roulette wheel) were common, nowadays automated techniques are mostly used. As both selecting
random samples and
random permutations can be reduced to simply selecting random numbers,
random number generation methods are now most commonly used, both
hardware random number generators and
pseudo-random number generators.
Optimization
Randomization is used in optimization to alleviate the computational burden associated to robust control techniques: a sample of values of the uncertainty parameters is randomly drawn and robustness is enforced for these values only. This approach has gained popularity by the introduction of rigorous theories that permit one to have control on the probabilistic level of robustness, see
scenario optimization.
Non-algorithmic randomization methods include:
* Casting
yarrow stalks (for the
I Ching)
* Throwing
dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing ...
* Flipping a coin
* Drawing straws
*
Shuffling cards
*
Roulette wheels
* Drawing pieces of paper or balls from a bag
* "
Lottery machines"
* Observing
atomic decay using a radiation counter
See also
*
Randomized algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performa ...
References
External links
RQube
- Generate quasi-random stimulus sequences for experimental designs
RandList
- Randomization List Generator
{{Statistics, collection, state=collapsed
Random number generation
Design of experiments