Importance of Random Assignment
When designing controlled experiments, such as testing the effects of a new drug, statisticians often use the experimental design technique of random assignment. Random assignment, or random placement, is an experimental technique used to assign subjects either to different treatments or to a control group (no treatment). The thinking is that by placing subjects into groups by chance, any effect observed between treatment groups can be linked to the treatment effect and cannot be considered a characteristic of the individuals in the group .
Control Group
Take identical growing plants, randomly assign them to two groups, and give fertilizer to one of the groups. If there are differences between the fertilized plant group and the unfertilized "control" group, these differences may be due to the fertilizer.
In experimental design, random assignment of participants in experiments or treatment and control groups help to ensure that any differences between or 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.
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.
Random Assignment Example
Consider an experiment with one 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, the results may turn out to be biased. 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.
With random assignment, one would randomly assign individuals to either the treatment or control group, and therefore have a better chance at detecting if an observed change were due to chance or due to the experimental treatment itself.
If a randomly assigned group is compared to the mean, it may be discovered that they differ statistically, 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 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 implausible. In other words, the groups would be sufficiently different on the variable tested to conclude statistically that they did not come from the same population, even though they were assigned from the same total group. In the example above, using random assignment may create groups that result in 20 blue-eyed people and 5 brown-eyed people in the same 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.
History of Random Assignment
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. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights. His experiment inspired other researchers in psychology and education, and led to a research tradition of randomized experiments in laboratories and specialized textbooks in the nineteenth century.