, Volume 51, Issue 4, pp 549–557 | Cite as

Correlation coefficients for more than one scale type: An alternative to the Janson and Vegelius approach

  • Frits E. Zegers
  • Jos M. F. Ten Berge


Janson and Vegelius have recently suggested a family of correlations for variables of mixed scale types, including nominal scales. The resulting correlations areE-coefficients, which means that they are unity if the variables involved are identical up to permissible transformations, and that they can be considered as inner products in a Euclidian space. Some of the coefficients of the correlation family suggested by Janson and Vegelius are generalized squared product-moment correlations and some are not. In the present paper, a family of correlations for variables of mixed scale types is advocated all members of which are generalized squared product-moment correlations. Some practical advantages of the latter family are explained.

Key words

mixed levels of measurement association coefficients 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Daniels, H. E. (1944). The relation between measures of correlation in the universe of sample permutations.Biometrika, 36, 129–135.Google Scholar
  2. Gifi, A. (1981).Nonlinear multivariate analysis. University of Leiden, Department of Data Theory.Google Scholar
  3. Holley, J. W., & Guilford, J. P. (1964). A note on theG-index of agreement.Educational and Psychological Measurement, 24, 749–753.Google Scholar
  4. Janson, S., & Vegelius, J. (1978a). On the applicability of truncated principal component analysis based on correlation coefficients for nominal scales.Applied Psychological Measurement, 2, 135–145.Google Scholar
  5. Janson, S., & Vegelius, J. (1978b).Correlation coefficients for more than one scale type and symmetrization as a method of obtaining them (Research Report 78-2). Uppsala: University of Uppsala, Department of Statistics.Google Scholar
  6. Janson, S., & Vegelius, J. (1979). On generalizations of theG-index and the phi coefficient to nominal scales.Multivariate Behavioral Research, 14, 255–269.CrossRefGoogle Scholar
  7. Janson, S., & Vegelius, J. (1982a). Correlation coefficients for more than one scale type.Multivariate Behavioral Research, 17, 271–284.CrossRefGoogle Scholar
  8. Janson, S., & Vegelius, J. (1982b). TheJ-index as a measure of nominal scale response agreement.Applied Psychological Measurement, 6, 111–121.Google Scholar
  9. Kendall, M. G. (1955).Rank correlation methods (ed. 2). London: Griffin.Google Scholar
  10. ten Berge, J. M. F. (in press). Rotation to perfect congruence and the cross-validation of component weights across populations.Multivariate Behavioral Research,21, 41–61, 262–266.Google Scholar
  11. Tucker, L. R. (1978).A method for synthesis of factor analysis studies (Personnel Research Section Report No. 984). Washington, D. C.: Department of the Army.Google Scholar
  12. Vegelius, J. (1978). On the utility of theE-correlation coefficient concept in psychological research.Educational and Psychological Measurement, 38, 605–611.Google Scholar

Copyright information

© The Psychometric Society 1986

Authors and Affiliations

  • Frits E. Zegers
    • 1
  • Jos M. F. Ten Berge
    • 1
  1. 1.Department of PsychologyUniversity of GroningenGroningenThe Netherlands

Personalised recommendations