randomize

Randomization is the process of making something random; this means:

• Generating a random permutation of a sequence (such as when shuffling cards).
• Selecting a random sample of a population (important in statistical sampling).
• Generating random numbers: see Random number generation.
• Transforming a data stream using a scrambler in telecommunications.

Applications

Randomization is used extensively in the field of gambling (or generally being random). Imperfect randomization may allow a skilled gambler to have an advantage, so much research has been devoted to effective randomization. A classic example of randomization is shuffling playing cards.

Statistics

Randomization is a core principle in statistical theory, whose importance was emphasized by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). Randomization-based inference is especially important in experimental design and in survey sampling.

Randomized experiments

In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.

Randomized experimentation is not haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also because it produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, the simplest design for comparing treatments is the Completely Randomized Design. Some "restriction on randomization" can occur with blocking and experiments that have hard-to-change factors; additional restrictions on randomization can occur when a full randomization is infeasible or when it is desirable to reduce the variance of estimators of selected effects.

Randomization of treatment in clinical trials pose ethical problems. In some cases, randomization reduces the therapeutic options for both physician and patient, and so randomization requires clinical equipoise regarding the treatments.

Randomized experiments were institutionalized in psychology and education in the late eighteen-hundreds, following the invention of randomized experiments by C. S. Peirce.^[1] Outside of psychology and education, randomized experiments were popularized by R.A. Fisher in his book Statistical Methods for Research Workers, which also introduced additional principles of experimental design.

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.

See also: Applications of randomness

Techniques

Although historically "manual" randomization techniques (such as shuffling cards, drawing pieces of paper from a bag, spinning a roulette wheel) were common, nowadays automated techniques are mostly used. As both selecting random samples and random permutations can be reduced to simply selecting random numbers, random number generation methods are now most commonly used, both hardware random number generators and pseudo-random number generators.

Non-algorithmic randomization methods include:

• Casting yarrow stalks (for the I Ching)
• Throwing dice
• Drawing straws
• Shuffling cards
• Roulette wheels
• Drawing pieces of paper or balls from a bag
• "Lottery machines"
• Observing atomic decay using a radiation counter

See also

• Randomized algorithm

References

1. ^
   • Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences 3: pp. 73-83.  http://psychclassics.yorku.ca/Peirce/small-diffs.htm
   • Ian Hacking (September 1988). "Telepathy: Origins of Randomization in Experimental Design". Isis (A Special Issue on Artifact and Experiment) 79 (3): pp. 427-451. 
   • Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology and Educational Research". American Journal of Education 101 (1): pp. 60-70. 
   • Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design". Isis 88 (4): pp. 653-673. 

External links

• RANDI2 - Open source Randomization tool for clinical trials / research
• RQube - Generate quasi-random stimulus sequences for experimental designs
• RandList - Randomization List Generator