A Monte Carlo Evaluation of the Tetrachoric Correlation Coefficient

• Published in: Educational and psychological measurement Vol. 63; no. 6; pp. 931 - 950
• Main Authors: Greer, Tammy, Dunlap, William P., Beatty, Gregory O.
• Format: Journal Article
• Language: English
• Published: London SAGE Publications 01.12.2003; Thousand Oaks, CA Sage; New Delhi SAGE PUBLICATIONS, INC
• Subjects: Biological and medical sciences; Correlation; Fundamental and applied biological sciences. Psychology; Monte Carlo simulation; Psychological tests; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Raw Scores; Statistics. Mathematics; dichotomization of continuous scores; tetrachoric correlation; Correlation coefficient; Statistical method; Monte Carlo method
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164403251318

The tetrachoric correlation coefficient (r tet), computed from a phi coefficient, approximates what the bivariate normal correlation would have been had the dichotomous variables been analyzed in their continuous form with underlying normal distributions. Although often used by early researchers to adjust phi when marginal distributions had extreme proportions, r tet, more commonly, has been regarded with suspicion. The purpose of these Monte Carlo simulationswas to investigate the inaccuracy of r tet. More specifically, the bias and standard error of r tet was examined for dichotomized scores computed from bivariate normal and lognormal continuous raw scores when the proportions of 0s and 1s ranged from somewhat to extremely skewed. Findings indicated that r tet tended to estimate what Pearson’s r may have been if symmetry in the marginal distributions of continuous rawscores had been induced by transformation and that in general (a) r tet exhibited little bias with standard errors slightly less than double those for Pearson’s r with proportions of 1s between .3 and .7, (b) r tet performed well with proportions more extreme than .3 and .7 provided there were no empty cells, (c) r tet resulted in less bias and smaller standard errors with larger sample sizes, and (d) the .5 adjustment further reduced bias and the standard error of r tet.