Randomization
Encyclopedia
Randomization is the process of making something random; this means:
, 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 and in survey sampling
. The first use of "randomization" listed in the Oxford English Dictionary
is its use by Ronald Fisher
in 1926.
, 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.
Randomized experimentation is not haphazard. Randomization reduces bias
by equalising so-called factors ( independent variables
) that have not been accounted for in the experimental design.
uses randomization, following the criticisms of previous "representative methods" by Jerzy Neyman
in his 1922 report to the International Statistical Institute
.
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.
(or generally being random). 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
.
wheel) were common, nowadays automated techniques are mostly used. As both selecting random sample
s and random permutation
s can be reduced to simply selecting random numbers, random number generation
methods are now most commonly used, both hardware random number generator
s and pseudo-random number generators.
Non-algorithmic randomization methods include:
- Generating a random permutationRandom permutationA random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation...
of a sequence (such as when shuffling cardsShuffleShuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome.-Shuffling techniques:...
). - Selecting a random sampleRandom sampleIn statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...
of a population (important in statistical samplingSampling (statistics)In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
). - Generating random numberRandom numberRandom number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
s: see Random number generationRandom number generationA random number generator ) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random....
. - Transforming a data streamData streamIn telecommunications and computing, a data stream is a sequence of digitally encoded coherent signals used to transmit or receive information that is in the process of being transmitted....
(such as when using a scrambler in telecommunications).
Statistics
Randomization is a core principle in statistical theoryStatistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
, 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 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...
. The first use of "randomization" listed in the Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...
is its use by Ronald Fisher
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
in 1926.
Randomized experiments
In the statistical theory of design of experimentsDesign 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 so-called factors ( independent variables
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
) that have not been accounted for in the experimental design.
Survey sampling
Survey samplingSurvey 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...
uses randomization, following the criticisms of previous "representative methods" by Jerzy Neyman
Jerzy Neyman
Jerzy Neyman , born Jerzy Spława-Neyman, was a Polish American mathematician and statistician who spent most of his professional career at the University of California, Berkeley.-Life and career:...
in his 1922 report to the International Statistical Institute
International Statistical Institute
The International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
.
Resampling
Some important methods of statistical inference use resamplingResampling (statistics)
In statistics, resampling is any of a variety of methods for doing one of the following:# Estimating the precision of sample statistics by using subsets of available data or drawing randomly with replacement from a set of data points # Exchanging labels on data points when performing significance...
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 gamblingGambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
(or generally being random). 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
Shuffle
Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome.-Shuffling techniques:...
.
- See also: Applications of randomnessApplications of randomnessRandomness has many uses in gambling, statistics, cryptography, art, etc.These uses have different randomness requirements, which leads to the use of different randomization methods...
Techniques
Although historically "manual" randomization techniques (such as shuffling cards, drawing pieces of paper from a bag, spinning a rouletteRoulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
wheel) were common, nowadays automated techniques are mostly used. As both selecting random sample
Random sample
In statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...
s and random permutation
Random permutation
A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation...
s can be reduced to simply selecting random numbers, random number generation
Random number generation
A random number generator ) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random....
methods are now most commonly used, both hardware random number generator
Hardware random number generator
In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. Such devices are often based on microscopic phenomena that generate a low-level, statistically random "noise" signal, such as thermal noise or the photoelectric effect or other...
s and pseudo-random number generators.
Non-algorithmic randomization methods include:
- Casting yarrowYarrowAchillea millefolium or yarrow is a flowering plant in the family Asteraceae, native to the Northern Hemisphere. In New Mexico and southern Colorado, it is called plumajillo, or "little feather", for the shape of the leaves. In antiquity, yarrow was known as herbal militaris, for its use in...
stalks (for the I ChingI ChingThe I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
) - Throwing diceDiceA die is a small throwable object with multiple resting positions, used for generating random numbers...
- Drawing straws
- Shuffling cardsShuffleShuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome.-Shuffling techniques:...
- RouletteRouletteRoulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
wheels - Drawing pieces of paper or balls from a bag
- "LotteryLotteryA lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments...
machines" - Observing atomic decay using a radiation counter