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{{Short description|Process involving chance used in research for allocating experimental subjects to groups}}

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'''Random assignment''' or '''random placement''' is an [[experiment]]al technique for assigning [[human subject research|human participants]] or [[animal testing|animal subjects]] to different groups in an experiment (e.g., [[treatment and control groups|a treatment group versus a control group]]) using [[wikt:randomization#Noun|randomization]], such as by a chance procedure (e.g., [[coin flipping|flipping a coin]]) or a [[random number generation|random number generator]].<ref name=":0">{{Cite book|last=Witte, Robert S.|title=Statistics|publisher=|others=Witte, John S.|date=5 January 2017|isbn=978-1-119-25451-5|edition=11|___location=Hoboken, NJ|pages=5|oclc=956984834}}</ref> This ensures that each participant or subject has an equal chance of being placed in any group.<ref name=":0" /> Random assignment of participants helps to ensure that any differences between and within the groups are not [[systematic error|systematic]] at the outset of the experiment.<ref name=":0" /> Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment.<ref name=":0" />

'''Random assignment''' or '''random placement''' is an [[experiment]]al technique for assigning subjects to different treatments (or no treatment). The thinking behind random assignment is that by randomizing treatment assignment, then the group attributes for the different treatments will be roughly equivalent and therefore any effect observed between treatment groups can be linked to the treatment effect and is not a characteristic of the individuals in the group.

Random assignment, [[blind experiment|blinding]], and [[scientific control|controlling]] are key aspects of the [[design of experiments]] because they help ensure that the results are not spurious or deceptive via [[confounding]]. This is why [[randomized controlled trial]]s are vital in [[clinical research]], especially ones that can be [[double-blinded]] and [[placebo-controlled]].

In [[Design of experiments|experimental design]], random assignment of participants in experiments or treatment and [[control group]]s help to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Random assignment does not guarantee that the groups are "matched" or equivalent, only that any differences are due to chance.

Mathematically, there are distinctions between randomization, [[pseudorandomness|pseudorandomization]], and [[low-discrepancy sequence|quasirandomization]], as well as between [[random number generation|random number generators]] and [[pseudorandom number generator]]s. How much these differences matter in experiments (such as [[clinical trial]]s) is a matter of [[design of experiments|trial design]] and [[statistics|statistical]] rigor, which affect [[levels of evidence|evidence grading]]. Studies done with pseudo- or quasirandomization are usually given nearly the same weight as those with true randomization but are viewed with a bit more caution.

==Example==

==Benefits of random assignment==

Consider an experiment with a treatment group and one control group. Suppose the experimenter has recruited a population of 50 people for the experiment--25 with blue eyes and 25 with brown eyes. If the experimenter were to assign all of the blue-eyed people to the treatment group and the brown-eyed people to the control group, this might might be bias the results. When analyzing the results, one might question whether an observed effect was due to the application of the experimental condition or was in fact due to eye color.

Imagine an experiment in which the participants are not randomly assigned; perhaps the first 10 people to arrive are assigned to the Experimental group, and the last 10 people to arrive are assigned to the Control group. At the end of the experiment, the experimenter finds differences between the Experimental group and the Control group, and claims these differences are a result of the experimental procedure. However, they also may be due to some other preexisting attribute of the participants, e.g. people who arrive early versus people who arrive late.

Imagine the experimenter instead uses a coin flip to randomly assign participants. If the coin lands heads-up, the participant is assigned to the Experimental group. If the coin lands tails-up, the participant is assigned to the Control group. At the end of the experiment, the experimenter finds differences between the Experimental group and the Control group. Because each participant had an equal chance of being placed in any group, it is unlikely the differences could be attributable to some other preexisting attribute of the participant, e.g. those who arrived on time versus late.

With random assignment, one would randomly assign individuals to either treatment or control and therefore have a better chance at detecting if an observed change is due to chance or due to the experimental treatment.

==Potential issues==

If a randomly assigned group is compared to the [[average|mean]] it may be discovered that statistically they differ, even though they were assigned from the same group. To express this same idea statistically - If a test of [[statistical significance]] is applied to randomly assigned groups to test the difference between sample [[average|mean]]s against the [[null hypothesis]] that they are equal to the same population mean (i.e., population mean of differences = 0), given the probability distribution, the null hypothesis will sometimes be "rejected," that is, deemed not plausible. That is, the groups will be sufficiently different on the variable tested to conclude statistically that they did not come from the same population, even though, procedurally, they were assigned from the same total group. In the example above using random assignment may create an assignment to groups that has 20 blue-eyed people and 5 brown-eyed people in one group. This is a rare event under random assignment, but it could happen, and when it does it might add some doubt to the causal agent in the experimental hypothesis.

Random assignment does not guarantee that the groups are matched or equivalent. The groups may still differ on some preexisting attribute due to chance. The use of random assignment cannot eliminate this possibility, but it greatly reduces it.

To express this same idea statistically - If a randomly assigned group is compared to the [[average|mean]] it may be discovered that statistically they differ, even though they were assigned from the same group. To express this same idea statistically - If a test of [[statistical significance]] is applied to randomly assigned groups to test the difference between sample [[average|mean]]s against the [[null hypothesis]] that they are equal to the same population mean (i.e., population mean of differences = 0), given the probability distribution, the null hypothesis will sometimes be "rejected," that is, deemed not plausible. That is, the groups will be sufficiently different on the variable tested to conclude statistically that they did not come from the same population, even though, procedurally, they were assigned from the same total group. In theFor example above, using random assignment may create an assignment to groups that has 20 blue-eyed people and 5 brown-eyed people in one group. This is a rare event under random assignment, but it could happen, and when it does it might add some doubt to the causal agent in the experimental hypothesis.

Because most basic statistical tests require the hypothesis of an independent randomly sampled population, random assignment is the desired assignment method because it provides control for all attributes of the members of the samples--in contrast to matching on only one or more variables--and provides the mathematical basis for estimating the likelihood of group equivalence for characteristics one is interested in, both for pretreatment checks on equivalence and the evaluation of posttreament results using inferential statistics. More advanced statistical modeling can be used to adapt the inference to the sampling method.

==Random sampling==

Random sampling is a related, but distinct, process.<ref name="socialresearchmethods.net">{{cite web|url=http://www.socialresearchmethods.net/kb/random.php|title=Social Research Methods - Knowledge Base - Random Selection & Assignment}}</ref> Random sampling is recruiting participants in a way that they represent a larger population.<ref name="socialresearchmethods.net"/> Because most basic statistical tests require the hypothesis of an independent randomly sampled population, random assignment is the desired assignment method because it provides control for all attributes of the members of the samples--insamples—in contrast to matching on only one or more variables--andvariables—and provides the mathematical basis for estimating the likelihood of group equivalence for characteristics one is interested in, both for pretreatment checks on equivalence and the evaluation of posttreamentpost treatment results using inferential statistics. More advanced statistical modeling can be used to adapt the inference to the sampling method.

==History==

Randomization was emphasized in the theory of statistical inference of [[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). Peirce applied randomization in the Peirce-[[Joseph Jastrow|Jastrow]] experiment on weight perception.

Charles S. Peirce randomly assigned volunteers to a [[blind experiment|blinded]], [[repeated measures design|repeated-measures design]] to evaluate their ability to discriminate weights.<ref name="smalldiff">{{cite journal| author=[[Charles Sanders Peirce]] and [[Joseph Jastrow]]|year=1885|title=On Small Differences in Sensation|url=http://psychclassics.yorku.ca/Peirce/small-diffs.htm| journal=Memoirs of the National Academy of Sciences|volume=3|pages=73–83}}</ref><ref name="telepathy">{{cite journal|author=Ian Hacking| title=Telepathy: Origins of Randomization in Experimental Design|journal=[[Isis (journal)|Isis]] |volume=79|issue=3|date=September 1988 |pages=427–451|doi=10.1086/354775| s2cid=52201011| author-link=Ian Hacking}}</ref><ref name="stigler">{{cite journal|doi=10.1086/444032|author=Stephen M. Stigler|title=A Historical View of Statistical Concepts in Psychology and Educational Research| journal=American Journal of Education| volume=101|issue=1|date=November 1992|pages=60–70|s2cid=143685203|author-link=Stephen M. Stigler}}</ref><ref name="dehue">{{cite journal|doi=10.1086/383850|author=Trudy Dehue|title=Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design|journal=[[Isis (journal)|Isis]]|volume=88|issue=4|date=December 1997|pages=653–673|pmid=9519574|s2cid=23526321|url=https://www.rug.nl/research/portal/files/71855616/237831.pdf}}</ref>

Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of [[randomized experiment]]s in laboratories and specialized textbooks in the eighteen-hundreds.<ref name="smalldiff"/><ref name="telepathy"/><ref name="stigler"/><ref name="dehue"/>

[[Jerzy Neyman]] advocated randomization in survey sampling (1934) and in experiments (1923).<ref name="Neyman">

{{citation|last=Neyman|first=Jerzy|author-link=Jerzy Neyman|orig-year=1923|year=1990|title=On the application of probability theory to agricultural experiments: Essay on principles (Section 9)|journal=Statistical Science|volume=5|number=4|pages=465–472|edition=Translated from (1923) Polish|editor1-first=Dorota&nbsp;M.|editor1-last=Dabrowska|editor1-link= Dorota Dabrowska |editor2-first=Terence&nbsp;P.|editor2-last=Speed|editor2-link=Terence Speed|doi=10.1214/ss/1177012031|mr=1092986|doi-access=free}}

</ref> [[Ronald A. Fisher]] advocated randomization in his [[The Design of Experiments|book]] on [[experimental design]] ([[The Design of Experiments|1935]]).

==See also==

*[[Asymptotic theory (statistics)]]

==References==

<references/>

*''Basic Psychology'' by Gleitman, Fridlund, and Reisberg.

* {{cite book |author1 = Caliński, Tadeusz

*"What statistical testing is, and what it is not," ''Journal of Experimental Education'', 1993, vol 61, pp. 293-316 by Shaver.

|author2 = Kageyama, Sanpei

|name-list-style = amp

|title = Block designs: A Randomization approach, Volume '''I''': Analysis

|series = Lecture Notes in Statistics

|volume = 150

|publisher = Springer-Verlag

|___location = New York

|year = 2000

|isbn = 0-387-98578-6

|url-access = registration

|url = https://archive.org/details/blockdesignsrand0002cali

}}

*{{cite book

|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]

|year=2008

|title=Design and Analysis of Experiments

|volume=I and II

|edition=Second

|publisher=Wiley

|isbn=978-0-470-38551-7}}

**{{cite book

|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]

|year=2008

|title=Design and Analysis of Experiments, Volume I: Introduction to Experimental Design

|edition=Second

|publisher=Wiley

|isbn=978-0-471-72756-9

}}

**{{cite book

|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]

|year=2005

|title=Design and Analysis of Experiments, Volume 2: Advanced [http://www.australiabesttutors.com/Help-with-Assignment Assignment] Experimental Design

|edition=First

|publisher=Wiley

|isbn=978-0-471-55177-5

}}

* [[Charles Sanders Peirce|Charles S. Peirce]], "[[Charles Sanders Peirce bibliography#illus|Illustrations of the Logic of Science]]" (1877–1878)

* [[Charles Sanders Peirce|Charles S. Peirce]], "[[Charles Sanders Peirce bibliography#SIL|A Theory of Probable Inference]]" (1883)

* {{cite journal| author=[[Charles Sanders Peirce]] and [[Joseph Jastrow]]|year=1885|title=On Small Differences in Sensation| journal=Memoirs of the National Academy of Sciences|volume=3|pages=73–83|url=http://psychclassics.yorku.ca/Peirce/small-diffs.htm}} http://psychclassics.yorku.ca/Peirce/small-diffs.htm

* {{cite journal |doi=10.1086/354775 |first=Ian |last=Hacking |author-link=Ian Hacking |title=Telepathy: Origins of Randomization in Experimental Design|journal=[[Isis (journal)|Isis]] |issue=3 |volume=79 |date=September 1988 |pages=427–451 | mr = 1013489 |jstor=234674|s2cid=52201011 }}

* {{cite journal |doi=10.1086/444032 |author=Stephen M. Stigler |title=A Historical View of Statistical Concepts in Psychology and Educational Research |journal=American Journal of Education |volume=101 |issue=1 |date=November 1992 |pages=60–70|s2cid=143685203 |author-link=Stephen M. Stigler }}

* {{cite journal |doi=10.1086/383850 |author=Trudy Dehue |title=Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design |journal=[[Isis (journal)|Isis]] |volume=88 |issue=4 |date=December 1997 |pages=653–673 |pmid=9519574|s2cid=23526321 |url=https://www.rug.nl/research/portal/files/71855616/237831.pdf }}

*''Basic Psychology'' by Gleitman, Fridlund, and Reisberg.

*"What statistical testing is, and what it is not," ''Journal of Experimental Education'', 1993, vol 61, pp. 293-316&nbsp;293–316 by Shaver.

== External links ==

* Experimental Random Assignment Tool: {{usurped|1=[https://web.archive.org/web/20130620135427/http://researchtool.org/ Random assignment tool - Experimental]}}

{{Statistics|collection|state=collapsed}}

{{Experimental design}}

[[Category:ExperimentalCausal designinference]]

[[Category:Design of experiments]]

[[Category:Experiments]]