Polychoric correlation


Polychoric correlation is the correlation between two ordinal variables or from their contingency table, under the assumption that the ordinal variables dissect continuous latent variables that are bivariate normal.

Items on self-report instruments such as personality tests and surveys that often use rating scales with a small number of response options (e.g., strongly disagree to strongly agree) are ordinal variable.

A special case of the polychoric correlation when both observed variables are dichotomous is called Tetrachoric correlation.

Either the maximum-likelihood estimator or a (possibly much) quicker “two-step” approximation is available.

Below is the sample input window




In the above example, only one list of variables in “Selected variable(s)” box was given, no “With variables (Options)” list, Empower will calculate correlation for any possible pairs of 2 variables.  If “With variables” is given, Empower will calculate correlation between each of “Selected variables” with each of the “With variables”.



Below is the sample output and explanation of the above model:


Polychoric correlation


 Polychoric correlation (Standard Error)




Polychoric Correlation, 2-step est. = 0.9067 (0.02071)


 Polychoric correlation (Standard Error)




Polychoric Correlation, 2-step est. = 0.6425 (0.05326)


 Polychoric correlation (Standard Error)




Polychoric Correlation, 2-step est. = 0.6034 (0.05405)


The number within parenthesis is the standard error of the correlation. Eg. the correlation between PHLEGM and WHEEZE is 0.6034, standard error is 0.05405.