Skip to main content
SpringerLink
Log in

A comparison of computer routines for the calculation of the tetrachoric correlation coefficient

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

In calculations of the discriminating-power parameter of the normal ogive model, Bock and Lieberman compared estimates derived from their maximum-likelihood solution with those derived from the heuristic solution. The two sets of estimates were in excellent agreement provided the heuristic solution used accurate tetrachoric correlation coefficients. Three computer methods for the calculation of the tetrachoric correlation were examined for accuracy and speed. The routine by Saunders was identified as an acceptably accurate method for calculating the tetrachoric correlation coefficient.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abramowitz, M., & Stegun, I. (Eds.),Handbook of mathematical functions. Washington, D. C.: U. S. Government Printing Office, 1967. pp. 966–970.

    Google Scholar 

  2. Bock, R. D., & Lieberman, M., Fitting a response model forn dichotomous items.Psychometrika, 1970. (In press)

  3. Buhler, R., Tetrachoric program inP-stat, version 45 source listing. (Generated from P-stat program tape at The University of Chicago Computation Center, May 17, 1968). pp. 143–148.

  4. Carroll, J. B., The nature of the data or how to choose a correlation coefficient.Psychometrika, 1961,26, 47–372.

    Google Scholar 

  5. Castellan, N., On the estimation of the tetrachoric correlation coefficient.Psychometrika, 1966,31, 67–73.

    Google Scholar 

  6. Castellan, N., & Link, S., Tetrachoric correlation program for the IBM 709/7090.Behavioral Science, 1964,9, 292.

    Google Scholar 

  7. Charap, M., Tetrachoric correlation. (An Educational Testing Service program write-up, dated December 1957).

  8. Kuki, H.,Mathematical functions. (The University of Chicago Computation Center report, 1966). p. 103.

  9. Owen, D., Tables for computing bivariate normal probabilities.The Annals of Mathematical Statistics, 1956,27, 1075–1090.

    Google Scholar 

  10. Pearson, K., Mathematical contributions to the theory of evolution. VII: On the correlation of characters not quantitatively measurable.Philosophical Transactions of the Royal Society, London, 1901,195A, 1–47.

    Google Scholar 

  11. Tucker, L.,Notes on the approximation of tetrachoric correlation. (Unpublished notes, dated April 4, 1960).

  12. U. S. Bureau of Standards,Tables of the bivariate normal distribution function and related functions. Washington, D. C.: U. S. Government Printing Office, 1956. (Applied Math Series No. 50).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Chicago, USA

    Ernest C. Froemel

Authors
  1. Ernest C. Froemel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by NSF Grant E 1930 to The University of Chicago. The author wishes to thank Dr. David R. Saunders and Dr. Ledyard Tucker for the use of their original materials and Dr. R. Darrell Bock for his many helpful suggestions and his ready counsel throughout the course of this investigation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Froemel, E.C. A comparison of computer routines for the calculation of the tetrachoric correlation coefficient. Psychometrika 36, 165–174 (1971). https://doi.org/10.1007/BF02291396

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02291396

Keywords

Search

Navigation