Randomization
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Randomization is the process of making something random. It is remarkably difficult to make anything truly random, as most physical processes and human thoughts and actions, whilst subject to randomness, are much less random than is commonly supposed.
Randomization is used extensively in the field of gambling. 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.
Randomization is a core principle in the statistical theory of design of experiments. Its use was extensivly promoted by R.A. Fisher in his book Statistical Methods for Research Workers. Randomization involves randomly allocating the experimental units across the treatment groups. Thus, if the experiment compares a new drug against a standard drug used as a control, the patients should be allocated to new drug or control by a random process. Randomization is not haphazard; it serves a purpose in both frequentist and Bayesian statistics. A frequentist would say that randomization reduces bias by equalising other factors that have not been explictly accounted for in the experimental design. Considerations of bias are of little concern to Bayesians, who recommend randomization because it produces ignorable designs. In design of experiments, frequentists prefer Completely Randomized Designs. Other experimental designs are used when a full randomization is not possible. These cases include experiments that involve blocking and experiments that have hard-to-change factors (see Split-Plot Designs).
Randomization is also required in the generation of random numbers for scientific research and cryptography. Hardware random number generators are sometimes used for these purposes.
There are some difficulties associated with the use of random numbers in computers. Clearly, truly random numbers cannot be produced by algorithms. It would be possible to make use physical devices attached as peripherals, but this is inconvenient. Debugging of computer programs which make use of randomization also presents difficulties, as there no way of knowing the path that was taken through the algorithm on a particular run. The solution is pseudo-random number generators. They require a number as input, called a seed, and produce as output a sequence of numbers which pass statistical tests for randomness. If the seed is known the sequence of 'random' numbers can be reproduced. John von Neumann observed in 1951 that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin".
Methods used for randomization:
- 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
- etc.de:Randomisation