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Factor Analysis I: Some Effects of Chance Error

Published online by Cambridge University Press:  01 January 2025

D. R. Saunders
D. R. Saunders*
Affiliation:
University of Illinois
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Abstract

Ignorance concerning the standard error of individual factor loadings and their differences has been a major obstacle to the proper interpretation of factorial results. The effects of three types of experimental error (selection of variables, selection of subjects and selection of scores) are here reported. In order to handle the errors of rotation systematically, it has been necessary to introduce a new semi-analytical criterion for the attainment of simple structure. Variability in results which may theoretically be eliminated is discussed under the heading of non-essential error.

Type
Original Paper
Information
Psychometrika , Volume 13 , Issue 4 , December 1948 , pp. 251 - 257
Copyright
Copyright © 1948 The Psychometric Society

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Footnotes

*

The author wishes to acknowledge the kind counsel and encouragement received from Professor R. B. Cattell during the preparation of this manuscript.

†

The following notational symbols will be used throughout this paper:

a = a factor loading

a1 =loading without correction for attenuation

h2 = communality

i = subscript denoting a variable of measurement

j = subscript denoting a variable of measurement

k = subscript denoting a factor

n = total number of variables

rij = correlation coefficient

rij = uncorrected correlation coefficient

ri = reliability coefficient

wik= weight of variable i for factor k

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