## Randomassignment

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**Random selection** is how you draw the sample of people for your study from a population.

**Random**is how you assign the sample that you draw to different groups or treatments in your study.

*assignment*It is possible to have *both* random selection and assignment in a study. Let's say you drew a random sample of 100 clients from a population list of 1000 current clients of your organization. That is random sampling. Now, let's say you randomly assign 50 of these clients to get some new additional treatment and the other 50 to be controls. That's random assignment.

It is also possible to have *only one of these* (random selection or random assignment) but not the other in a study. For instance, if you do not randomly draw the 100 cases from your list of 1000 but instead just take the first 100 on the list, you do not have random selection. But you could still randomly assign this nonrandom sample to treatment versus control. Or, you could randomly select 100 from your list of 1000 and then nonrandomly (haphazardly) assign them to treatment or control.

And, it's possible to have *neither* random selection nor random assignment. In a typical nonequivalent groups design in education you might nonrandomly choose two 5th grade classes to be in your study. This is nonrandom selection. Then, you could arbitrarily assign one to get the new educational program and the other to be the control. This is nonrandom (or nonequivalent) assignment.

Random selection is related to sampling. Therefore it is most related to the external validity (or generalizability) of your results. After all, we would randomly sample so that our research participants better represent the larger group from which they're drawn. Random assignment is most related to design. In fact, when we randomly assign participants to treatments we have, by definition, an experimental design. Therefore, random assignment is most related to internal validity. After all, we randomly assign in order to help assure that our treatment groups are similar to each other (i.e., equivalent) prior to the treatment.

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Copyright ©2006, William M.K. Trochim, All Rights Reserved

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Last Revised: 10/20/2006

**Random assignment** or **random placement** is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. This ensures that each participant or subject has an equal chance of being placed in any group. Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment.

Random assignment, blinding, and 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 trials are vital in clinical research, especially ones that can be double-blinded and placebo-controlled.

Mathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. How much these differences matter in experiments (such as clinical trials) is a matter of trial design and statistical rigor, which affect 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.

## Benefits of random assignment[edit]

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.

## Potential issues[edit]

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 mean it may be discovered that they differ, even though they were assigned from the same group. If a test of statistical significance is applied to randomly assigned groups to test the difference between sample means 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. For example, 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 sampling[edit]

Random sampling is a related, but distinct process.^{[1]} Random sampling is recruiting participants in a way that they represent a larger population.^{[1]} 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 post treatment results using inferential statistics. More advanced statistical modeling can be used to adapt the inference to the sampling method.

## History[edit]

Randomization was emphasized in the theory of statistical inference of Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). Peirce applied randomization in the Peirce-Jastrow experiment on weight perception.

Charles S. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights.^{[2]}^{[3]}^{[4]}^{[5]} Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the eighteen-hundreds.^{[2]}^{[3]}^{[4]}^{[5]}

Jerzy Neyman advocated randomization in survey sampling (1934) and in experiments (1923).^{[6]}Ronald A. Fisher advocated randomization in his book on experimental design (1935).

## See also[edit]

## References[edit]

- ^
^{a}^{b}http://www.socialresearchmethods.net/kb/random.php. - ^
^{a}^{b}Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation".*Memoirs of the National Academy of Sciences*.**3**: 73–83. - ^
^{a}^{b}Ian Hacking (September 1988). "Telepathy: Origins of Randomization in Experimental Design".*Isis (A Special Issue on Artifact and Experiment)*.**79**(3): 427–451. doi:10.1086/354775. - ^
^{a}^{b}Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology and Educational Research".*American Journal of Education*.**101**(1): 60–70. doi:10.1086/444032. - ^
^{a}^{b}Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design".*Isis*.**88**(4): 653–673. doi:10.1086/383850. PMID 9519574. **^**Neyman, Jerzy (1990) [1923], Dabrowska, Dorota M.; Speed, Terence P., eds., "On the application of probability theory to agricultural experiments: Essay on principles (Section 9)",*Statistical Science*(Translated from (1923) Polish ed.),**5**(4): 465–472, doi:10.1214/ss/1177012031, MR 1092986

- Caliński, Tadeusz & Kageyama, Sanpei (2000).
*Block designs: A Randomization approach, Volume*. Lecture Notes in Statistics.**I**: Analysis**150**. New York: Springer-Verlag. ISBN 0-387-98578-6. - Hinkelmann, Klaus and Kempthorne, Oscar (2008).
*Design and Analysis of Experiments*. I and II (Second ed.). Wiley. ISBN 978-0-470-38551-7. - Charles S. Peirce, "Illustrations of the Logic of Science" (1877–1878)
- Charles S. Peirce, "A Theory of Probable Inference" (1883)
- Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation".
*Memoirs of the National Academy of Sciences*.**3**: 73–83. http://psychclassics.yorku.ca/Peirce/small-diffs.htm - Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design".
*Isis*.**79**(3): 427–451. doi:10.1086/354775. JSTOR 234674. MR 1013489. - Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology and Educational Research".
*American Journal of Education*.**101**(1): 60–70. doi:10.1086/444032. - Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design".
*Isis*.**88**(4): 653–673. doi:10.1086/383850. PMID 9519574. *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 by Shaver.

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