Hostname: page-component-6bf8c574d5-rwnhh Total loading time: 0 Render date: 2025-02-27T02:24:29.706Z Has data issue: false hasContentIssue false
  • English
  • Français

An Inter-Battery Method of Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker
Ledyard R Tucker*
Affiliation:
Educational Testing Service and Princeton University
Get access Rights & Permissions [Opens in a new window]

Abstract

The inter-battery method of factor analysis was devised to provide information relevant to the stability of factors over different selections of tests. Two batteries of tests, postulated to depend on the same common factors, but not parallel tests, are given to one sample of individuals. Factors are determined from the correlation of the tests in one battery with the tests in the other battery. These factors are only those that are common to the two batteries. No communality estimates are required. A statistical test is provided for judging the minimum number of factors involved. Rotation of axes is carried out independently for the two batteries. A final step provides the correlation between factors determined by scores on the tests in the two batteries. The correlations between corresponding factors are taken as factor reliability coefficients.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 2 , June 1958 , pp. 111 - 136
Copyright
Copyright © 1958 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This research was jointly supported by Princeton University and the Office of Naval Research under contract N6onr-270-20 and the National Science Foundation under grant NSF G-642; Harold Gulliksen, principal investigator. The preparation of this paper and the accompanying material has been aided by the Educational Testing Service. The author is grateful to Professors Harold Gulliksen and Samuel S. Wilks for their many most helpful comments and suggestions.

References

Bartlett, M. S. Internal and external factor analysis. Brit. J. Psychol., Statist. Sect., 1948, 1, 73–81.CrossRefGoogle Scholar
Bartlett, M. S. Tests of significance in factor analysis. Brit. J. Psychol., Statist. Sect., 1950, 3, 77–85.CrossRefGoogle Scholar
Bartlett, M. S. The effect of standardization on a x 2 approximation in factor analysis. Biometrika, 1951, 38, 337–344.Google Scholar
Bartlett, M. S. A further note on tests of significance in factor analysis. Brit. J. Psychol., Statist. Sect., 1951, 4, 1–2.CrossRefGoogle Scholar
Burt, C. A comparison of factor analysis and analysis of variance. Brit. J. Psychol., Statist. Sect., 1947, 1, 3–26.CrossRefGoogle Scholar
Burt, C. Tests of significance in factor analysis. Brit. J. Psychol., Statist. Sect., 1952, 5, 109–133.CrossRefGoogle Scholar
Cattell, R. B. A universal index for psychological factors. Advance Publication No. 3, Dec. 1953. Laboratory of Personality Assessment and Group Behavior, Dept. Psychology, Univ. Illinois.Google Scholar
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Emmett, W. G. Factor analysis by Lawley's method of maximum likelihood. Brit. J. Psychol., Statist. Sect., 1949, 2, 90–97.CrossRefGoogle Scholar
Fisher, R. A. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 1915, 10, 507–521.Google Scholar
French, J. W. The description of aptitude and achievement factors in terms of rotated factors. Psychometric Monogr. No. 5, Chicago: Univ. Chicago Press, 1951.Google Scholar
French, J. W. The selection of standard tests for factor analysis. Amer. Psychologist, 1952, 7, 297–297. (Abstract)Google Scholar
French, J. W. Kit of selected tests for reference aptitude and achievement factors, Princeton: Educational Testing Service, 1954.Google Scholar
Henrysson, S. The significance of factor loadings. Brit. J. Psychol., Statist. Sect., 1950, 3, 159–165.CrossRefGoogle Scholar
Hoel, P. G. A significance test for minimum rank in factor analysis. Psychometrika, 1939, 4, 149–158.CrossRefGoogle Scholar
Hotelling, H. The most predictable criterion. J. educ. Psychol., 1935, 26, 139–142.CrossRefGoogle Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proc. Roy. Soc. Edin., 1940, 60, 64–82.CrossRefGoogle Scholar
Lawley, D. N. Further investigations in factor estimation. Proc. Roy. Soc. Edin., 1942, 61, 176–185.Google Scholar
Lawley, D. N. Problems in factor analysis. Proc. Roy. Soc. Edin., 1949, 62, 394–399.Google Scholar
Lawley, D. N. Factor analysis by maximum likelihood: a correction. Brit. J. Psychol., Statist. Sect., 1950, 3, 76–76.CrossRefGoogle Scholar
McNemar, Q. On the sampling errors of factor loadings. Psychometrika, 1941, 6, 141–152.CrossRefGoogle Scholar
McNemar, Q. On the number of factors. Psychometrika, 1942, 7, 9–18.CrossRefGoogle Scholar
McNemar, Q. The factors in factoring behavior. Psychometrika, 1951, 16, 353–359.CrossRefGoogle Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Rippe, D. D. Application of a large sampling criterion to some sampling problems in factor analysis. Psychometrika, 1953, 18, 191–205.CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Thurstone, L. L. and Thurstone, T. G. Factorial studies of intelligence. Psychometric Monogr. No. 2, Chicago: Univ. Chicago Press, 1941.Google Scholar
Wold, H. Some artificial experiments in factor analysis. In: Uppsala Symposium on Psychological Factor Analysis, 17–19, March 1953. Nordisk Psykologi's Monograph Series No. 3. Pp. 43–64.Google Scholar
Young, G. Maximum likelihood estimation and factor analysis. Psychometrika, 1941, 6, 49–53.CrossRefGoogle Scholar