The Annals of Mathematical Statistics

Concerning Compound Randomization in the Binary System

John E. Walsh

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177729950

Digital Object Identifier
doi:10.1214/aoms/1177729950

Mathematical Reviews number (MathSciNet)
MR32156

Zentralblatt MATH identifier
0036.09105

JSTOR
links.jstor.org

Citation

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


Export citation