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Factor Analysis Calculations by Tabulating Machines

Published online by Cambridge University Press:  01 January 2025

D. M. Hall ,
E. L. Welker  and
Isabelle Crawford
D. M. Hall
Affiliation:
University of Illinois
E. L. Welker
Affiliation:
University of Illinois
Isabelle Crawford
Affiliation:
University of Illinois
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Abstract

I.B.M. tabulating equipment can be of considerable help in reducing the time and increasing the accuracy of multiple factor analysis, even if used for only a part of the calculations. Once the plugboard is wired and those cards punched which are used over and over again, problems involving any number of variables can be handled with dispatch. The correlation matrix is listed, the totals verified, and the signs changed on the tabulator. Then the factors and the residual coefficients are calculated by means of a calculator. Tucker's procedure has been modified by using a calculator instead of a multiplying punch, by reducing the number of cards used, by simplifying checks on calculations, by simplifying plugboard wiring, and by preparing work sheets on tabulator paper. Extraction of factors from 24 variables at the rate of one in four hour's time seems to justify the use of the tabulating equipment on small problems.

Type
Original Paper
Information
Psychometrika , Volume 10 , Issue 2 , June 1945 , pp. 93 - 125
Copyright
Copyright © 1945 The Psychometric Society

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Footnotes

*

Assistant Professor of Agricultural Extension, College of Agriculture; Associate in Mathematics, College of Liberal Arts and Sciences; and Senior Office Appliance Operator, University of Illinois, Urbana, Illinois, respectively.

†

Tucker, Ledyard R. The centroid method of factor analysis by punch cards. Microfilm Negative No. 1623, Department of Psychology, University of Chicago.

References

* All figures and tables are segregated at the end of this article.

† The number in parenthesis refer to card columns.

* The x-control is sometimes known as the 11 punch.