, Volume 23, Issue 4, pp 291–296 | Cite as

Some relations between guttman's principal components of scale analysis and other psychometric theory

  • Frederic M. Lord


Guttman's principal components for the weighting system are the item scoring weights that maximize the generalized Kuder-Richardson reliability coefficient. The principal component for any item is effectively the same as the factor loading of the item divided by the item standard deviation, the factor loadings being obtained from an ordinary factor analysis of the item intercorrelation matrix.


Standard Deviation Public Policy Factor Loading Statistical Theory Reliability Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cronbach, L. J. Coefficient alpha and the internal structure of tests.Psychometrika, 1951,16, 297–334.Google Scholar
  2. [2]
    Dressel, P. L. Some remarks on the Kuder-Richardson reliability coefficient.Psychometrika, 1940,5, 305–310.Google Scholar
  3. [3]
    Edgerton, H. A. and Kolbe, L. E. The method of minimum variation for the combination of criteria.Psychometrika, 1936,1, 183–187.Google Scholar
  4. [4]
    Gulliksen, H.Theory of mental tests. New York: Wiley, 1950.Google Scholar
  5. [5]
    Guttman, L. The quantification of a class of attributes: a theory and method of scale construction. In P. Horst (Ed.),The prediction of personal adjustment. Soc. Sci. Res. Council, Bull. 48, 1941. Pp. 321–345.Google Scholar
  6. [6]
    Guttman, L. A basis for analyzing test-retest reliability.Psychometrika, 1945,10, 225–282.Google Scholar
  7. [7]
    Horst, P. Obtaining a composite measure from a number of different measures of the same attribute.Psychometrika, 1936,1, 53–60.Google Scholar
  8. [8]
    Hoyt, C. J. and Stunkard, C. L. Estimation of test reliability for unrestricted item scoring methods.Educ. psychol. Measmt, 1952,12, 756–758.Google Scholar
  9. [9]
    Stouffer, S. A. (Ed.) Measurement and prediction.Studies in social psychology in World War II, Vol. IV. Princeton, N. J.: Princeton Univ. Press, 1950.Google Scholar
  10. [10]
    Thurstone, L. L.Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.Google Scholar
  11. [11]
    Tryon, R. C. Reliability and behavior domain validity: reformulation and historical critique.Psychol. Bull., 1957,54, 229–249.Google Scholar
  12. [12]
    Turnbull, H. W. and Aitken, A. C.An introduction to the theory of canonical matrices. Toronto: Blackie, 1950.Google Scholar
  13. [13]
    Wilks, S. S. Weighting systems for linear functions of correlated variables when there is no dependent variable.Psychometrika, 1938,3, 23–40.Google Scholar
  14. [14]
    Woodbury, M. A. and Lord, F. M. The most reliable composite with a specified true score.Brit. J. statist. Psychol., 1956,9, 21–28.Google Scholar

Copyright information

© Psychometric Society 1958

Authors and Affiliations

  • Frederic M. Lord
    • 1
  1. 1.Educational Testing ServiceUSA

Personalised recommendations