Methods for Determining the Tetrachoric Correlation Coefficient for Binary Variables

Abstract

The tetrachoric correlation coefficient (rt) is a special case of the statistical covariation between two variables measured on a dichotomous scale, but assuming an underlying bivariate normal distribution. Our goal was to provide an analysis of seven different methods used to calculate rt. The rt approximation was then used to derive its standard error and its associated confidence interval. Computation of rt is not straightforward and is usually not available in standard statistical packages. This paper introduces seven methods for computing the rt value and three methods used to provide the standard error estimation {SE(rt)}. These methods were illustrated using data from questionnaires that were used to evaluate public awareness regarding Electronic Waste hazards. The different algorithmic/mathematical methods used to estimate rt and SE(rt) yielded values that were equal to (or very close to) each other and the estimates obtained from SAS statistical analysis software. Method 6 and Method 1 used to estimate rt and SE(rt) work very well, the equations are easy to understand, are computationally simple and are ideally suited for use. Additionally, the width of the confidence intervals for these methods are equal to (or closely approximates) the widths calculated by the SAS statistical analysis computer program.