Editing Randomization (section)

== Randomization in statistical analysis ==
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).  Its application in statistical methodologies is multifaceted and includes critical processes such as [[Randomized controlled trial|randomized controlled experiments]], [[survey sampling]] and [[Simulation|simulations]].

=== Randomized controlled experiment ===
[[File:Sampling experiments.jpg|thumb|Educational tools used to extract a random sample from a pool]]
In the realm of scientific research, particularly within [[Clinical study design|clinical study designs]], constraints such as limited manpower, material resources, financial backing, and time necessitate a selective approach to participant inclusion.<ref name=":3" /><ref name=":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.<ref name=":5" /> A [[Random sampling|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.<ref name=":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.<ref>{{Cite journal |last=Smith |first=T. M. F. |date=1976 |title=The Foundations of Survey Sampling: A Review |url=https://www.jstor.org/stable/2345174 |journal=Journal of the Royal Statistical Society. Series A (General) |volume=139 |issue=2 |pages=183–204 |doi=10.2307/2345174|jstor=2345174 |url-access=subscription }}</ref> 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 ===
{{Main|Resampling (statistics)}}

Some important methods of statistical inference use [[Resampling (statistics)|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 ===
{{Main|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 method|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.<ref>{{Cite thesis |title=On the impact of randomization on robustness in machine learning |url=https://hal.science/tel-03121555 |publisher=Université Paris sciences et lettres |date=2020-12-02 |degree=phdthesis |language=en |first=Rafael |last=Pinot}}</ref>