Tetrachoric correlation of bilateral nonmetric traits: a defect in the conventional procedure and a proposal for two alternative estimation methods

The individual-count method of bilateral nonmetric traits has been widely used despite its apparent defects in both theory and practice. Logically, its use means adopting the false concept of ‘two thresholds’ based on the single-liability model. This conceptual defect can create actual problems, in cluding that of conventional ‘tetrachoric correlation.’ The correlation coefficient calculated by formally applying the tetrachoric procedure to the individual-count frequencies is mathematically meaningless because there exists no true liability and threshold that can explain such data. Moreover, it considerably underestimates the correlation if it is used as the estimate of the correlation between the individual-specific components of liability because it neglects the contribution of the inter-side component in the variance of total liability. Two statistical methods are proposed to estimate the correlation coefficient between inter-individual components of liability and its confidence interval. Some selected data from the database published by Ossenberg on the Internet were used to illustrate the utility of the new methods and to examine the problem of the conventional method. The method of estimation of the correlation between the inter-individual components of liability based on the combination of two dual-liability mod els provided, as a by-product, substantial support for the standard threshold model based on data. Be cause the conventional ‘tetrachoric correlations’ proved to seriously underestimate the correlations, the results of almost all studies using Mahalanobis distances based on nonmetric traits so far published may require re-evaluation. It is also argued that a fundamental problem exists in the use of the individu -al-count method itself. Adopting an incorrect method for maintaining comparability is a vicious cycle. It is necessary to emphasize improving the reliability of future studies based on true statistics rather than keeping the comparability between less reliable results based on the false concept of threshold.