**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)

COUGH with PHLEGM

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

Polychoric
correlation (Standard Error)

COUGH with WHEEZE

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

Polychoric
correlation (Standard Error)

PHLEGM with WHEEZE

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.