Hostname: page-component-5b777bbd6c-f9nfp Total loading time: 0 Render date: 2025-06-18T23:36:47.396Z Has data issue: false hasContentIssue false
  • English
  • Français

The Unit Hierarchy and its Properties

Published online by Cambridge University Press:  01 January 2025

Cyril Burt
Cyril Burt*
Affiliation:
Psychological Laboratory, University College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

A correlation matrix may be expanded as the weighted sum of a series of ‘unit hierarchies’. The properties of the ‘unit hierarchy’ are not only of theoretical interest for themselves, but lead to simpler modes of practical calculation. The analysis is analogous to a spectral set of projective operations in quantum-theory: and the analogy itself suggests many further problems and solutions.

Type
Original Paper
Information
Psychometrika , Volume 3 , Issue 3 , September 1938 , pp. 151 - 168
Copyright
Copyright © 1938 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.)

Article purchase

Temporarily unavailable

References

Burt, C., Memorandum on the Analysis of Examination Marks. In ap. Hartog, P., Rhodes, E. C.(Eds.), Marks of Examiners, London: Macmillan and Co., 1936.Google Scholar
Burt, C., Correlations between Persons. Brit. Journ. Psychol., 1937, 28, 56–96.Google Scholar
Burt, C., Factor Analysis with and without Successive Approximations. Brit. Journ. Educ. Psychol., 1937, 7, 172–195.CrossRefGoogle Scholar
Fisher, R. A., Statistical Methods for Research Workers, London: Oliver & Boyd, 1934.Google Scholar
Kelley, T. L., The Essential Traits of Mental Life, Cambridge, Mass.: Harvard University Press, 1935.Google Scholar
Stephenson, W., Introduction to Inverted Factor Analysis. Journ. Educ. Psychol., 1936, 27, 353–367.CrossRefGoogle Scholar
Thurstone, L. L., The Vectors of Mind, Chicago: University of Chicago Press, 1935.Google Scholar
Fisher, R. A., The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 1936, 7, 179–188.CrossRefGoogle Scholar
Kelley, T. L., Statistical Method, New York: Macmillan, 1923.Google Scholar
Courant, R., and Hilbert, D., Methoden der Mathematischen Physik I. 2 te Auflage, Berlin: J. Springer, 1931.CrossRefGoogle Scholar
Cullis, C. E., Matrices and Determinoids, vol. III, Cambridge: University Press, 1925.Google Scholar
Turnbull, H. W., and Aitken, A. C., An Introduction to the Theory of Canonical Matrices, London: Blackie, 1932.Google Scholar
Weyl, H., The Theory of Groups and Quantum Mechanics, London: Methuen, 1931.Google Scholar
Neumann, J. V., Mathematische Grundlagen der Quantenmechanik, Berlin: J. Springer, 1932.Google Scholar
Stone, ., Resolvents, Spectra, and Reducibility, Chap. IV.Google Scholar
Stern, O., and Gerlach, W., Zeitschr. für Physik, 1921, 7, 249–249.CrossRefGoogle Scholar
Katz, D., The World of Colour, London: Kegan Paul, 1935.Google Scholar
Burt, C., Distribution & Relations of Educational Abilities, London: P. S. King, 1917.Google Scholar
Hotelling, H., Analysis of a Complex of Statistical Variables into Principal Components. Journ. Educ. Psychol., 1933, 24, 417–441.CrossRefGoogle Scholar
Hotelling, H., Simplified Calculation of Principal Components. Psychometrika, 1936, 1, 27–35.CrossRefGoogle Scholar
Burt, C., The Analysis of Temperament. Brit. J. Med. Psych., 1938, 17, 158–188.CrossRefGoogle Scholar