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December, 1949 Concerning Compound Randomization in the Binary System
John E. Walsh
Ann. Math. Statist. 20(4): 580-589 (December, 1949). DOI: 10.1214/aoms/1177729950


Let us consider a set of approximately random binary digits obtained by some experimental process. This paper outlines a method of compounding the digits of this set to obtain a smaller set of binary digits which is much more nearly random. The method presented has the property that the number of digits in the compounded set is a reasonably large fraction (say of the magnitude $\frac{1}{3}$ or $\frac{1}{4}$) of the original number of digits. If a set of very nearly random decimal digits is required, this can be obtained by first finding a set of very nearly random binary digits and then converting these digits to decimal digits. The concept of "maximum bias" is introduced to measure the degree of randomness of a set of digits. A small maximum bias shows that the set is very nearly random. The question of when a table of approximately random digits can be considered suitable for use as a random digit table is investigated. It is found that a table will be satisfactory for the usual types of situations to which a random digit table is applied if the reciprocal of the number of digits in the table is noticeably greater than the maximum bias of the table.


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John E. Walsh. "Concerning Compound Randomization in the Binary System." Ann. Math. Statist. 20 (4) 580 - 589, December, 1949.


Published: December, 1949
First available in Project Euclid: 28 April 2007

zbMATH: 0036.09105
MathSciNet: MR32156
Digital Object Identifier: 10.1214/aoms/1177729950

Rights: Copyright © 1949 Institute of Mathematical Statistics

Vol.20 • No. 4 • December, 1949
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