Randomization: Difference between revisions
Thatsme314 (talk | contribs) Importing Wikidata short description: "Process of making something random" |
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{{Short description|Process of making something random}} |
{{Short description|Process of making something random}} |
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'''Randomization''' is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups<ref name=":0" /><ref>{{Citation |last=Bespalov |first=Anton |title=Blinding and Randomization |date=2020 |url=https://doi.org/10.1007/164_2019_279 |work=Good Research Practice in Non-Clinical Pharmacology and Biomedicine |pages=81–100 |editor-last=Bespalov |editor-first=Anton |access-date=2023-12-10 |series=Handbook of Experimental Pharmacology |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/164_2019_279 |isbn=978-3-030-33656-1 |last2=Wicke |first2=Karsten |last3=Castagné |first3=Vincent |editor2-last=Michel |editor2-first=Martin C. |editor3-last=Steckler |editor3-first=Thomas}}</ref>. The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing [[selection bias]] and enhancing the [[Validity (statistics)|statistical validity]]<ref>{{Cite journal |last=Saghaei |first=Mahmoud |date=2011 |title=An Overview of Randomization and Minimization Programs for Randomized Clinical Trials |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3317766/ |journal=Journal of Medical Signals and Sensors |volume=1 |issue=1 |pages=55–61 |issn=2228-7477 |pmc=3317766 |pmid=22606659}}</ref>. It facilitates the objective comparison of treatment effects in [[Design of experiments|experimental design]], as it equates groups statistically by balancing both known and unknown factors at the outset of the study. In statistical terms, it underpins the principle of probabilistic equivalence among groups, allowing for the unbiased estimation of treatment effects and the generalizability of conclusions drawn from sample data to the broader population<ref>{{Cite journal |last=Desharnais |first=Josée |last2=Laviolette |first2=François |last3=Zhioua |first3=Sami |date=2013-06-01 |title=Testing probabilistic equivalence through Reinforcement Learning |url=https://www.sciencedirect.com/science/article/pii/S0890540113000163 |journal=Information and Computation |volume=227 |pages=21–57 |doi=10.1016/j.ic.2013.02.002 |issn=0890-5401}}</ref><ref>{{Cite journal |last=Sedgwick |first=Philip |date=2011-11-23 |title=Random sampling versus random allocation |url=https://www.bmj.com/content/343/bmj.d7453 |journal=BMJ |language=en |volume=343 |pages=d7453 |doi=10.1136/bmj.d7453 |issn=0959-8138}}</ref>. |
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'''Randomization''' is the process of making something [[random]]. Randomization is not haphazard; instead, a [[stochastic process|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 [[Arbitrariness|arbitrary]] individuals are selected. |
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Randomization is not haphazard; instead, a [[stochastic process|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 distribution|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 [[Arbitrariness|arbitrary]] individuals are selected. A [[Wald–Wolfowitz runs test|runs test]] can be used to determine whether the occurrence of a set of measured values is random<ref>{{Cite journal |last=Alhakim |first=A |last2=Hooper |first2=W |date=2008 |title=A non-parametric test for several independent samples |url=https://www.tandfonline.com/doi/abs/10.1080/10485250801976741 |journal=Journal of Nonparametric Statistics |volume=20 |issue=3 |pages=253–261 |citeseerx=10.1.1.568.6110 |doi=10.1080/10485250801976741}}</ref>. Randomization is widely applied in various fields, especially in scientific research, statistical analysis, and resource allocation, to ensure fairness and validity in the outcomes<ref>{{Citation |last=Fowler |first=Kathryn L. |title=Chapter 58 - Principles and methods of randomization in research |date=2023-01-01 |url=https://www.sciencedirect.com/science/article/pii/B9780323903004000380 |work=Translational Surgery |pages=353–358 |editor-last=Eltorai |editor-first=Adam E. M. |access-date=2023-12-10 |series=Handbook for Designing and Conducting Clinical and Translational Research |publisher=Academic Press |isbn=978-0-323-90300-4 |last2=Fleming |first2=Martin D. |editor2-last=Bakal |editor2-first=Jeffrey A. |editor3-last=Newell |editor3-first=Paige C. |editor4-last=Osband |editor4-first=Adena J.}}</ref><ref>{{Cite journal |last=Berger |first=Vance W. |last2=Bour |first2=Louis Joseph |last3=Carter |first3=Kerstine |last4=Chipman |first4=Jonathan J. |last5=Everett |first5=Colin C. |last6=Heussen |first6=Nicole |last7=Hewitt |first7=Catherine |last8=Hilgers |first8=Ralf-Dieter |last9=Luo |first9=Yuqun Abigail |last10=Renteria |first10=Jone |last11=Ryeznik |first11=Yevgen |last12=Sverdlov |first12=Oleksandr |last13=Uschner |first13=Diane |date=2021-08-16 |title=A roadmap to using randomization in clinical trials |url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8366748/ |journal=BMC Medical Research Methodology |volume=21 |pages=168 |doi=10.1186/s12874-021-01303-z |issn=1471-2288 |pmc=8366748 |pmid=34399696}}</ref><ref>{{Cite journal |last=Toroyan |first=Tami |last2=Roberts |first2=Ian |last3=Oakley |first3=Ann |date=2000-10-01 |title=Randomisation and resource allocation: a missed opportunity for evaluating health care and social interventions |url=https://jme.bmj.com/content/26/5/319 |journal=Journal of Medical Ethics |language=en |volume=26 |issue=5 |pages=319–322 |doi=10.1136/jme.26.5.319 |issn=0306-6800 |pmid=11055032}}</ref>. |
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In various contexts, randomization may involve: |
In various contexts, randomization may involve: |
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===Statistics=== |
===Statistics=== |
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Randomization is a core principle in [[statistical theory]], whose importance was emphasized by [[Charles Sanders Peirce|Charles S. Peirce]] in "[[Charles Sanders Peirce bibliography#illus|Illustrations of the Logic of Science]]" (1877–1878) and "[[Charles Sanders Peirce bibliography#SIL|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.<ref>Fisher RA. [http://digital.library.adelaide.edu.au/dspace/handle/2440/15191 The arrangement of field experiments]. J Min Agri GB 1926; 33: 700-725.</ref><ref>[[Oxford English Dictionary]] "randomization"</ref> |
Randomization is a core principle in [[statistical theory]], whose importance was emphasized by [[Charles Sanders Peirce|Charles S. Peirce]] in "[[Charles Sanders Peirce bibliography#illus|Illustrations of the Logic of Science]]" (1877–1878) and "[[Charles Sanders Peirce bibliography#SIL|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.<ref>Fisher RA. [http://digital.library.adelaide.edu.au/dspace/handle/2440/15191 The arrangement of field experiments]. J Min Agri GB 1926; 33: 700-725.</ref><ref name=":0">[[Oxford English Dictionary]] "randomization"</ref> |
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====Randomized experiments==== |
====Randomized experiments==== |
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Revision as of 03:27, 10 December 2023
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups[1][2]. The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity[3]. It facilitates the objective comparison of treatment effects in experimental design, as it equates groups statistically by balancing both known and unknown factors at the outset of the study. In statistical terms, it underpins the principle of probabilistic equivalence among groups, allowing for the unbiased estimation of treatment effects and the generalizability of conclusions drawn from sample data to the broader population[4][5].
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. A runs test can be used to determine whether the occurrence of a set of measured values is random[6]. Randomization is widely applied in various fields, especially in scientific research, statistical analysis, and resource allocation, to ensure fairness and validity in the outcomes[7][8][9].
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).
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 and in survey sampling. The first use of "randomization" listed in the Oxford English Dictionary is its use by Ronald Fisher in 1926.[10][1]
Randomized experiments
In the statistical theory of design of experiments, 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. 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
- 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
References
- ^ a b Oxford English Dictionary "randomization"
- ^ Bespalov, Anton; Wicke, Karsten; Castagné, Vincent (2020), Bespalov, Anton; Michel, Martin C.; Steckler, Thomas (eds.), "Blinding and Randomization", Good Research Practice in Non-Clinical Pharmacology and Biomedicine, Handbook of Experimental Pharmacology, Cham: Springer International Publishing, pp. 81–100, doi:10.1007/164_2019_279, ISBN 978-3-030-33656-1, retrieved 2023-12-10
- ^ Saghaei, Mahmoud (2011). "An Overview of Randomization and Minimization Programs for Randomized Clinical Trials". Journal of Medical Signals and Sensors. 1 (1): 55–61. ISSN 2228-7477. PMC 3317766. PMID 22606659.
- ^ Desharnais, Josée; Laviolette, François; Zhioua, Sami (2013-06-01). "Testing probabilistic equivalence through Reinforcement Learning". Information and Computation. 227: 21–57. doi:10.1016/j.ic.2013.02.002. ISSN 0890-5401.
- ^ Sedgwick, Philip (2011-11-23). "Random sampling versus random allocation". BMJ. 343: d7453. doi:10.1136/bmj.d7453. ISSN 0959-8138.
- ^ Alhakim, A; Hooper, W (2008). "A non-parametric test for several independent samples". Journal of Nonparametric Statistics. 20 (3): 253–261. CiteSeerX 10.1.1.568.6110. doi:10.1080/10485250801976741.
- ^ Fowler, Kathryn L.; Fleming, Martin D. (2023-01-01), Eltorai, Adam E. M.; Bakal, Jeffrey A.; Newell, Paige C.; Osband, Adena J. (eds.), "Chapter 58 - Principles and methods of randomization in research", Translational Surgery, Handbook for Designing and Conducting Clinical and Translational Research, Academic Press, pp. 353–358, ISBN 978-0-323-90300-4, retrieved 2023-12-10
- ^ Berger, Vance W.; Bour, Louis Joseph; Carter, Kerstine; Chipman, Jonathan J.; Everett, Colin C.; Heussen, Nicole; Hewitt, Catherine; Hilgers, Ralf-Dieter; Luo, Yuqun Abigail; Renteria, Jone; Ryeznik, Yevgen; Sverdlov, Oleksandr; Uschner, Diane (2021-08-16). "A roadmap to using randomization in clinical trials". BMC Medical Research Methodology. 21: 168. doi:10.1186/s12874-021-01303-z. ISSN 1471-2288. PMC 8366748. PMID 34399696.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Toroyan, Tami; Roberts, Ian; Oakley, Ann (2000-10-01). "Randomisation and resource allocation: a missed opportunity for evaluating health care and social interventions". Journal of Medical Ethics. 26 (5): 319–322. doi:10.1136/jme.26.5.319. ISSN 0306-6800. PMID 11055032.
- ^ Fisher RA. The arrangement of field experiments. J Min Agri GB 1926; 33: 700-725.
External links
- RQube - Generate quasi-random stimulus sequences for experimental designs
- RandList - Randomization List Generator
| Scientific method | |
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| Treatment and blocking | |
| Models and inference | |
| Designs Completely randomized | |
