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An I.B.M. Technique for the Computation of ΣX2 and ΣXY

Published online by Cambridge University Press:  01 January 2025

Kurt Benjamin
Kurt Benjamin*
Affiliation:
Graduate Record Examination
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Abstract

Given I.B.M. cards punched with scores (or any numbers)—but not their squares—a method is presented of tabulating them (on the No. 405 alphameric I.B.M. tabulator) so as to obtain the sum of squares. The technique is also adaptable to summation of cross-products. The principle is an extension of the Mendenhall-Warren-Hollerith technique of vertical progressive digiting, without the necessity of manual addition or summary-punching, and is designed for machines not equipped with the “card cycle total transfer” device or “progressive total” device. Use is made of “counter rolling.” Efficient use of machine capacity is made only when intercorrelations between no more than two variables are required in addition to sums of squares. A resumé of some techniques now commonly employed is included.

Type
Original Paper
Information
Psychometrika , Volume 10 , Issue 1 , March 1945 , pp. 61 - 67
Copyright
Copyright © 1945 Psychometric Society

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Footnotes

*

The author is indebted to Dr. Paul Dwyer, Associate Professor of Mathematics, University of Michigan, for valuable criticism of the original draft; and to Mr. Alan Meacham, in charge of the University's Tabulating Station, for testing the method.

References

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