Research design features relating to the use of a binary response format to measure a continuous latent variable and to the arbitrary dichotomization of graduated data are discussed in connection with the advantages and disadvantages inherent in the use of the tetrachoric correlation. A FORTRAN IV program for computing the cosine-pi approximation to the tetrachoric correlation is described, and the nature and extent of systematic error found in that approximation are summarized.
Get full access to this article
View all access options for this article.
References
1.
Bouvier, E. A. , Perry, N. C., Michael, W. B., and Hertzka, A. F. (1954). A study of the error in the cosine-pi approximation to the tetrachoric coefficient of correlation. Educational and Psychological Measurement, 14, 690-699.
2.
Cohen, J. (1983). The cost of dichotomization. Applied Psychological Measurement, 7, 249-253.
3.
Gorsuch, R. L. (1983). Factor analysis. Hillsdale, NJ: Erlbaum.
4.
Guilford, J. P. and Fruchter, B. (1978). Fundamental statistics in psychology and education. New York, NY: McGraw-Hill.
5.
Hunter, J. E. and Schmidt, F. L. (1990). Methods of meta-analysis: Correcting error and bias in research findings. Newbury Park, CA: Sage.
6.
McNemar, Q. (1969). Psychological statistics. New York, NY: Wiley.
7.
Pearson, K. (1901). On the correlation of characters not quantitatively measureable. London: Transactions of the Royal Society, Series A, Vol. 195, 1-47.
