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] [3] The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. [4] 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. [5] [6]

Contents

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. [7] Randomization is widely applied in various fields, especially in scientific research, statistical analysis, and resource allocation, to ensure fairness and validity in the outcomes. [8] [9] [10]

In various contexts, randomization may involve

Randomization has many uses in gambling, political use, statistical analysis, art, cryptography, gaming and other fields.

In gambling

Shuffling playing cards Shuffling cards.jpg
Shuffling playing 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. [11] 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. [12] 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. [13]

In summary, randomization in gambling is not just a technical necessity; it is 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

In politics

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. [14] [15] Central to this system was the principle of random selection, seen as a cornerstone for fair representation. [14] 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. [15]

USCAR Court selecting a jury by sortition USCAR Court select juries by sortition.JPG
USCAR Court selecting a jury by sortition

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. [16] 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. [17] The ongoing study and debate surrounding the use of sortition reflect its enduring relevance and potential as a tool for political innovation and integrity.

Randomization in statistical 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). Its application in statistical methodologies is multifaceted and includes critical processes such as randomized controlled experiments, survey sampling and simulations.

Randomized controlled experiment

Educational tools used to extract a random sample from a pool Sampling experiments.jpg
Educational tools used to extract a random sample from a pool

In the realm of scientific research, particularly within clinical study designs, constraints such as limited manpower, material resources, financial backing, and time necessitate a selective approach to participant inclusion. [2] [4] Despite the broad spectrum of potential participants who fulfill the inclusion criteria, it is impractical to incorporate every eligible individual in the target population due to these constraints. Therefore, a representative subset of treatment groups is chosen based on the specific requirements of the research. [8] A randomized sampling method is employed to ensure the integrity and representativeness of the study. This method ensures that all qualified subjects within the target population have an equal opportunity to be selected. Such a strategy is pivotal in mirroring the overall characteristics of the target population and in mitigating the risk of selection bias.

The selected samples (or continuous non-randomly sampled samples) are grouped using randomization methods so that all research subjects in the sample have an equal chance of entering the experimental group or the control group and receiving corresponding treatment. In particular, the random grouping after the research subjects are stratified can make the known or unknown influencing factors between the groups basically consistent, thereby enhancing the comparability between the groups. [4]

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. It randomly displays the answer options to survey participants, which prevents order bias caused by the tendency of respondents to choose the first option when the same order is presented to different respondents. [18] To overcome this, researchers can give the answer options in a random order so that the respondents allocate some time to read all the options and choose an honest answer. For example, consider an automobile dealer who wants to conduct a feedback survey and ask the respondents to select their preferred automobile brand. The user can create a study with randomized answers to display the different automobile brands so that the respondents do not see them in the same order.

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.

Simulation

In many scientific and engineering fields, computer simulations of real phenomena are commonly used. When the real phenomena are affected by unpredictable processes, such as radio noise or day-to-day weather, these processes can be simulated using random or pseudo-random numbers. One of the most prominent uses of randomization in simulations is in Monte Carlo methods. These methods rely on repeated random sampling to obtain numerical results, typically to model probability distributions or to estimate uncertain quantities in a system.

Randomization also allows for the testing of models or algorithms against unexpected inputs or scenarios. This is essential in fields like machine learning and artificial intelligence, where algorithms must be robust against a variety of inputs and conditions. [19]

In cryptography

In art

Randomization plays a fascinating and often underappreciated role in literature, music, and art, where it introduces elements of unpredictability and spontaneity. Here is how it manifests in each of these creative fields:

Literature

A sentence generator using random words at the Sci-Port Discovery Center Random Words Make A Sentence.jpg
A sentence generator using random words at the Sci-Port Discovery Center

Pioneered by surrealists and later popularized by writers like William S. Burroughs, automatic writing and cut-up techniques involve randomly rearranging text to create new literary forms. It disrupts linear narratives, fostering unexpected connections and meanings. [20]

Music

In aleatoric music, elements of the composition are left to chance or the performer's discretion. Composers like John Cage used randomization to create music where certain elements are unforeseeable, resulting in each performance being uniquely different. Modern musicians sometimes employ computer algorithms that generate music based on random inputs. These compositions can range from electronic music to more classical forms, where randomness plays a key role in creating harmony, melody, or rhythm.

Art

Some artists in abstract expressionism movement, like Jackson Pollock, used random methods (like dripping or splattering paint) to create their artworks. This approach emphasizes the physical act of painting and the role of chance in the artistic process.Also, contemporary artists often use algorithms and computer-generated randomness to create visual art. This can result in intricate patterns and designs that would be difficult or impossible to predict or replicate manually.

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.

Common randomization methods including

See also

Related Research Articles

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event has occurred less frequently than expected, it is more likely to happen again in the future. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes.

<span class="mw-page-title-main">Shuffling</span> Procedure used to randomize a deck of playing cards

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.

A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Simply put, the problem is that many of the sources of randomness available to humans rely on physical processes not readily available to computer programs.

<span class="mw-page-title-main">Statistics</span> Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

In statistics, survey sampling describes the process of selecting a sample of elements from a target population to conduct a survey. The term "survey" may refer to many different types or techniques of observation. In survey sampling it most often involves a questionnaire used to measure the characteristics and/or attitudes of people. Different ways of contacting members of a sample once they have been selected is the subject of survey data collection. The purpose of sampling is to reduce the cost and/or the amount of work that it would take to survey the entire target population. A survey that measures the entire target population is called a census. A sample refers to a group or section of a population from which information is to be obtained.

<span class="mw-page-title-main">Stratified sampling</span> Sampling from a population which can be partitioned into subpopulations

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.

<span class="mw-page-title-main">Monte Carlo method</span> Probabilistic problem-solving algorithm

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, physicist Stanislaw Ulam, was inspired by his uncle's gambling habits.

<span class="mw-page-title-main">Experiment</span> Scientific procedure performed to validate a hypothesis

An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies.

<span class="mw-page-title-main">Sampling (statistics)</span> Selection of data points in statistics.

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population and statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

<span class="mw-page-title-main">Randomized controlled trial</span> 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, diets or other medical treatments.

Nonprobability sampling is a form of sampling that does not utilise random sampling techniques where the probability of getting any particular sample may be calculated.

External validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can generalize or transport to other situations, people, stimuli, and times. Generalizability refers to the applicability of a predefined sample to a broader population while transportability refers to the applicability of one sample to another target population. In contrast, internal validity is the validity of conclusions drawn within the context of a particular study.

This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design.

Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized controlled trials helps scientists to test hypotheses, and random numbers or pseudorandom numbers help video games such as video poker.

<span class="mw-page-title-main">Random number generation</span> Producing a sequence that cannot be predicted better than by random chance

Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model. This would be in contrast to so-called "random number generations" done by pseudorandom number generators (PRNGs), which generate numbers that only look random but are in fact predetermined—these generations can be reproduced simply by knowing the state of the PRNG.

<span class="mw-page-title-main">Randomized experiment</span> 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.

<span class="mw-page-title-main">Fisher–Yates shuffle</span> Algorithm for generating a random permutation of a finite set

The Fisher–Yates shuffle is an algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and continually determines the next element in the shuffled sequence by randomly drawing an element from the list until no elements remain. The algorithm produces an unbiased permutation: every permutation is equally likely. The modern version of the algorithm takes time proportional to the number of items being shuffled and shuffles them in place.

<span class="mw-page-title-main">Randomness</span> Apparent lack of pattern or predictability in events

In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.

In governance, sortition is the selection of public officials or jurors at random, i.e. by lottery, in order to obtain a representative sample.

<span class="mw-page-title-main">Stratified randomization</span> Method of statistical sampling

In statistics, stratified randomization is a method of sampling which first stratifies the whole study population into subgroups with same attributes or characteristics, known as strata, then followed by simple random sampling from the stratified groups, where each element within the same subgroup are selected unbiasedly during any stage of the sampling process, randomly and entirely by chance. Stratified randomization is considered a subdivision of stratified sampling, and should be adopted when shared attributes exist partially and vary widely between subgroups of the investigated population, so that they require special considerations or clear distinctions during sampling. This sampling method should be distinguished from cluster sampling, where a simple random sample of several entire clusters is selected to represent the whole population, or stratified systematic sampling, where a systematic sampling is carried out after the stratification process.

References

  1. ↑ Oxford English Dictionary "randomization"
  2. 1 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
  3. 1 2 3 4 5 Kang, Minsoo; Ragan, Brian G; Park, Jae-Hyeon (2008). "Issues in Outcomes Research: An Overview of Randomization Techniques for Clinical Trials". Journal of Athletic Training. 43 (2): 215–221. doi:10.4085/1062-6050-43.2.215. ISSN   1062-6050. PMC   2267325 . PMID   18345348.
  4. 1 2 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.
  5. ↑ 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.
  6. ↑ Sedgwick, Philip (2011-11-23). "Random sampling versus random allocation". BMJ. 343: d7453. doi:10.1136/bmj.d7453. ISSN   0959-8138. S2CID   71545281.
  7. ↑ 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.
  8. 1 2 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
  9. ↑ 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.
  10. ↑ 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.
  11. ↑ Liu, Michael (2023-04-22). "Expert reveals the fascinating link between math and card shuffling". News and Events. Retrieved 2023-12-10.
  12. ↑ 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
  13. ↑ 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.
  14. 1 2 Hansen, Mogens Herman (18 December 1998). The Athenian Democracy in the Age of Demosthenes. Bloomsbury Academic. ISBN   1-85399-585-1.
  15. 1 2 Saxonhouse, Arlene W. (1993). "Athenian Democracy: Modern Mythmakers and Ancient Theorists". PS: Political Science & Politics. 26 (3): 486–490. doi:10.2307/419988. JSTOR   419988.
  16. ↑ 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.
  17. ↑ 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.
  18. ↑ Smith, T. M. F. (1976). "The Foundations of Survey Sampling: A Review". Journal of the Royal Statistical Society. Series A (General). 139 (2): 183–204. doi:10.2307/2345174. JSTOR   2345174.
  19. ↑ Pinot, Rafael (2020-12-02). On the impact of randomization on robustness in machine learning (phdthesis thesis). Université Paris sciences et lettres.
  20. ↑ babel (1920-12-12). "Dada Manifesto On Feeble Love And Bitter Love (1920) - Tristan Tzara". 391.org. Retrieved 2023-12-11.
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