Skip to main content
Log in

Estimation of the correlation coefficient in contingency tables with possibly nonmetrical characters

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

A method of estimating the product moment correlation from the polychoric series is developed. This method is shown to be a generalization of the method which uses the tetrachoric series to obtain the tetrachoric correlation. Although this new method involves more computational labor, it is shown to be superior to older methods for data grouped into a small number of classes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bernstein, S. Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes.Math. Annalen, 1926,97, 1–59.

    Google Scholar 

  2. Irwin, J. O. On the distribution of a weighted estimate of variance and on analysis of variance in certain cases of unequal weighting.J. roy. statist. Soc., 1942,105, 115–118.

    Google Scholar 

  3. Lancaster, H. O. The derivation and partition ofx 2 in certain discrete distributions.Biometrika, 1949,36, 117–129.

    Google Scholar 

  4. Lancaster, H. O. The structure of bivariate distributions.Ann. math. Statist., 1958,29, 719–736.

    Google Scholar 

  5. Mehler, F. G. Uber die Entwicklung einer Funktion von beliebig vielen Variablen nach Laplaceschen Funktionen höherer Ordnung.J. f. Mathematik, 1866,66, 161–176.

    Google Scholar 

  6. Pearson, K. On a criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.Phil. Mag., 1900a,50, 157–175.

    Google Scholar 

  7. Pearson, K. Mathematical contribution to the theory of evolution VII: On the correlation of characters not quantitatively measurable.Philos. Trans. roy. Soc. London, 1900b,195A, 1–47.

    Google Scholar 

  8. Pearson, K. Mathematical contribution to the theory of evolution XIII: On the theory of contingency and its relation to association and normal correlation.Drapers Company Research Memoirs, Biometric Series No. 1, 1904.

  9. Pearson, K. On the measurement of the influence of “broad categories” on correlation.Biometrika, 1913,9, 116–139.

    Google Scholar 

  10. Pearson, K. and Heron, D. On theories of association.Biometrika, 1913,9, 159–315.

    Google Scholar 

  11. Pearson, K. and Lee, A. On the laws of inheritance in man.Biometrika, 1903,2, 357–462.

    Google Scholar 

  12. Pearson, K. and Pearson, E. S. On polychoric coefficients of correlation.Biometrika, 1922,14, 127–156.

    Google Scholar 

  13. Ritchie-Scott, A. The correlation coefficient of a polychoric table.Biometrika, 1918,12, 93–133

    Google Scholar 

  14. Szegö, G.Orthogonal polynomials. Colloquium Publ. No. 23, Amer. Math. Soc., 1959.

  15. Tschuprow, A. A.Grundbegriffe und Grundproblem der Korrelationtheorie. Leipzig: Teubner, 1925. Translated asPrinciples of the Mathematical Theory of Correlation. London: Hodge, 1939.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lancaster, H.O., Hamdan, M.A. Estimation of the correlation coefficient in contingency tables with possibly nonmetrical characters. Psychometrika 29, 383–391 (1964). https://doi.org/10.1007/BF02289604

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289604

Keywords

Navigation