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Randomization

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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[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 Random Permutations: This is essential in various situations, such as shuffling cards. By randomly rearranging the sequence, it ensures fairness and unpredictability in games and experiments.
  • Selecting Random Samples from Populations: In statistical sampling, this method is vital for obtaining representative samples. By randomly choosing a subset of individuals, biases are minimized, ensuring that the sample accurately reflects the larger population.
  • Random Allocation in Experimental Design: Random assignment of experimental units to treatment or control conditions is fundamental in scientific studies. This approach ensures that each unit has an equal chance of receiving any treatment, thereby reducing systematic bias and improving the reliability of experimental results.
  • Generating Random Numbers: The process of random number generation is central to simulations, cryptographic applications, and statistical analysis. These numbers form the basis for simulations, model testing, and secure data encryption.
  • Data Stream Transformation: In telecommunications, randomization is used to transform data streams. Techniques like scramblers randomize the data to prevent predictable patterns, which is crucial for securing communication channels and enhancing transmission reliability."

Applications

Randomness has many uses in gambling, political use, art, statistics, cryptography, gaming, gambling and other fields.

Gambling

Shuffling cards

In the world of gambling, the integrity and fairness of games hinge significantly on effective randomization. This principle serves as a cornerstone in gambling, ensuring that each game outcome is unpredictable and not manipulable. The necessity for advanced randomization methods stems from the potential for skilled gamblers to exploit weaknesses in poorly randomized systems. High-quality randomization thwarts attempts at prediction or manipulation, maintaining the fairness of games. A quintessential example of randomization in gambling is the shuffling of playing cards. This process must be thoroughly random to prevent any predictability in the order of cards[10]. Casinos often employ automatic shuffling machines, which enhance randomness beyond what manual shuffling can achieve.

With the rise of online casinos, digital random number generators (RNGs) have become crucial. These RNGs use complex algorithms to produce outcomes that are as unpredictable as their real-world counterparts[11]. The gambling industry invests heavily in research to develop more effective randomization techniques. To ensure that gambling games are fair and random, regulatory bodies rigorously test and certify shuffling and random number generation methods. This oversight is vital in maintaining trust in the gambling industry, ensuring that players have equal chances of winning.

The unpredictability inherent in randomization is also a key factor in the psychological appeal of gambling. The thrill and suspense created by the uncertainty of outcomes contribute significantly to the allure and excitement of gambling games[12].

In summary, randomization in gambling is not just a technical necessity; it's a fundamental principle that upholds the fairness, integrity, and thrill of the games. As technology advances, so too do the methods to ensure that this randomization remains effective and beyond reproach

Political use

The concept of randomization in political systems, specifically through the method of allotment or sortition, has ancient roots and contemporary relevance, significantly impacting the evolution and practice of democracy.

In the fifth century BC, Athenian democracy was pioneering in its approach to ensuring political equality, or isonomia[13][14]. Central to this system was the principle of random selection, seen as a cornerstone for fair representation[13]. The unique structure of Greek democracy, which translates to "rule by the people," was exemplified by administrative roles being rotated among citizens, selected randomly through lot. This method was perceived as more democratic than elections, which the Athenians argued could lead to inequalities. They believed that elections, which often favored candidates based on merit or popularity, contradicted the principle of equal rights for all citizens. Furthermore, the random allotment of positions like magistrates or jury members served as a deterrent to vote-buying and corruption, as it was impossible to predict who would be chosen for these roles[14].

In modern times, the concept of allotment, also known as sortition, is primarily seen in the selection of jurors within Anglo-Saxon legal systems, such as those in the UK and the United States. However, its political implications extend further. There have been various proposals to integrate sortition into government structures. The idea is that sortition could introduce a new dimension of representation and fairness in political systems, countering issues associated with electoral politics[15]. This concept has garnered academic interest, with scholars exploring the potential of random selection in enhancing the democratic process, both in political frameworks and organizational structures[16]. The ongoing study and debate surrounding the use of sortition reflect its enduring relevance and potential as a tool for political innovation and integrity.

Statistics analysis

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.[17][1]

Randomized experiments

Main article: Randomized experiment
Main article: Randomized controlled trial

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

Main article: Resampling (statistics)

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.

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:

See also

References

  1. ^ a b Oxford English Dictionary "randomization"
  2. ^ 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, vol. 257, Cham: Springer International Publishing, pp. 81–100, doi:10.1007/164_2019_279, ISBN 978-3-030-33656-1, PMID 31696347, S2CID 207956615, retrieved 2023-12-10
  3. ^ Saghaei, Mahmoud (2011). "An Overview of Randomization and Minimization Programs for Randomized Clinical Trials". Journal of Medical Signals and Sensors. 1 (1): 55–61. doi:10.4103/2228-7477.83520. ISSN 2228-7477. PMC 3317766. PMID 22606659.
  4. ^ 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.
  5. ^ Sedgwick, Philip (2011-11-23). "Random sampling versus random allocation". BMJ. 343: d7453. doi:10.1136/bmj.d7453. ISSN 0959-8138. S2CID 71545281.
  6. ^ 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. S2CID 123493589.
  7. ^ 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
  8. ^ 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 (1): 168. doi:10.1186/s12874-021-01303-z. ISSN 1471-2288. PMC 8366748. PMID 34399696.
  9. ^ 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. PMC 1733281. PMID 11055032.
  10. ^ Liu, Michael (2023-04-22). "Expert reveals the fascinating link between math and card shuffling". News and Events. Retrieved 2023-12-10.
  11. ^ Lugrin, Thomas (2023), Mulder, Valentin; Mermoud, Alain; Lenders, Vincent; Tellenbach, Bernhard (eds.), "Random Number Generator", Trends in Data Protection and Encryption Technologies, Cham: Springer Nature Switzerland, pp. 31–34, doi:10.1007/978-3-031-33386-6_7, ISBN 978-3-031-33386-6, retrieved 2023-12-10
  12. ^ Clark, Luke; Averbeck, Bruno; Payer, Doris; Sescousse, Guillaume; Winstanley, Catharine A.; Xue, Gui (2013-11-06). "Pathological Choice: The Neuroscience of Gambling and Gambling Addiction". The Journal of Neuroscience. 33 (45): 17617–17623. doi:10.1523/JNEUROSCI.3231-13.2013. ISSN 0270-6474. PMC 3858640. PMID 24198353.
  13. ^ a b Hansen, Mogens Herman. The Athenian Democracy in the Age of Demosthenes. ISBN 1-85399-585-1.
  14. ^ a b Saxonhouse, Arlene W. (1993). "Athenian Democracy: Modern Mythmakers and Ancient Theorists". PS: Political Science & Politics. 26 (3): 486–490. doi:10.2307/419988.
  15. ^ Stone, Peter (July 2010). "The Political Potential of Sortition". The Philosophical Quarterly. 60 (240): 664–666. doi:10.1111/j.1467-9213.2010.660_11.x.
  16. ^ Lever, Annabelle (2023-07-20). "Democracy: Should We Replace Elections with Random Selection?". Danish Yearbook of Philosophy. 56 (2): 136–153. doi:10.1163/24689300-bja10042. ISSN 0070-2749.
  17. ^ Fisher RA. The arrangement of field experiments. J Min Agri GB 1926; 33: 700-725.
  • RQube - Generate quasi-random stimulus sequences for experimental designs
  • RandList - Randomization List Generator
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