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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. 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 is a related, but distinct process. More advanced statistical modeling can be used to adapt the inference to the sampling method.

Randomization was emphasized in the theory of statistical inference of Charles S. 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. Jerzy Neyman advocated randomization in survey sampling and in experiments Fisher advocated randomization in his book on experimental design From Wikipedia, the free encyclopedia.

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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Memoirs of the National Academy of Sciences. Origins of Randomization in Experimental Design". American Journal of Education. Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments.

Grouped data Frequency distribution Contingency table. Sampling stratified cluster Standard error Opinion poll Questionnaire. Observational study Natural experiment Quasi-experiment. Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator.

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