The Annals of Mathematical Statistics

Concerning Compound Randomization in the Binary System

John E. Walsh

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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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Ann. Math. Statist., Volume 20, Number 4 (1949), 580-589.

First available in Project Euclid: 28 April 2007

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Walsh, John E. Concerning Compound Randomization in the Binary System. Ann. Math. Statist. 20 (1949), no. 4, 580--589. doi:10.1214/aoms/1177729950.

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