The tetrachoric correlation coefficient is a statistical measure used to quantify the relationship or association between two binary variables. Specifically, it is designed to assess the degree of correlation between two variables by estimating the correlation coefficient using data from two ordinal variables that have been binarized.
When dealing with ordinal data, it is often challenging to compute conventional correlation coefficients due to the nonlinearity and lack of normal distribution of the variables. Tetrachoric correlation overcomes this limitation by estimating the correlation coefficient using the joint distribution of the binary variables.
It assumes that the underlying continuous variables follow a bivariate normal distribution and that the observed binary values are generated by a threshold mechanism. The tetrachoric correlation coefficient estimates the latent correlations based on the thresholds, which are determined in a way that maximizes the likelihood of the observed binary data.
The coefficient ranges from -1 to +1, with 0 indicating no association, a positive value suggesting a positive association, and a negative value indicating a negative association. The magnitude of the coefficient represents the strength of the association, where values closer to -1 or +1 indicate a stronger relationship.
Tetrachoric correlation is commonly used in various fields, such as psychology, sociology, and education, to examine the relationship between dichotomous variables, such as yes/no responses, agree/disagree choices, or presence/absence of a characteristic. It allows researchers to understand and quantify the relationship between these variables, providing valuable insights for further analysis and interpretation.
