tetrachoric correlation
Học thuậtThân thiện
Definition
Noun: A tetrachoric correlation is a specific type of correlation coefficient. It is used to estimate the correlation between two theoretical, continuous variables that are assumed to follow a normal (bell-shaped) distribution, based on data where both variables have been measured or expressed as a simple dichotomy (i.e., divided into two categories, such as yes/no, pass/fail, or present/absent).
Usage
The term is used primarily in specialized fields like psychometrics, statistics, and the social sciences. It is applied when researchers want to understand the relationship between two underlying continuous traits, but their measurement tools have only produced binary (two-category) data for each trait.
Examples
- The researcher calculated a tetrachoric correlation to estimate the relationship between the underlying continuous traits of "mathematical aptitude" and "spatial reasoning," based on students' pass/fail results on two separate tests.
- In the analysis, a high tetrachoric correlation was found between the dichotomized measures, suggesting a strong association between the two normally distributed latent variables.
- When both variables are dichotomous, the tetrachoric correlation coefficient provides a better estimate of the true continuous relationship than the phi coefficient, under the assumption of bivariate normality.
Advanced Usage
- The calculation of a tetrachoric correlation relies on the assumption that a latent, continuous, and normally distributed variable exists behind each observed dichotomy. The point where the continuous variable is cut to create the two categories is called the threshold.
- It is often contrasted with other correlation coefficients for binary data, such as the or the . The tetrachoric correlation is specifically for when variables are artificially or naturally dichotomized from an assumed normal distribution.
Variants and Related Words
- Tetrachoric correlation coefficient: The full technical name; often used interchangeably with "tetrachoric correlation."
- Polychoric correlation: A generalization of the tetrachoric correlation used when the observed variables are ordinal with more than two categories, but are assumed to be based on underlying continuous normal distributions.
Synonyms
- Tetrachoric r (informal abbreviation within statistical reporting).
Related Concepts (Not Synonyms)
- Phi coefficient: A measure of association for two true dichotomous variables (not assumed to be from underlying normal distributions).
- Biserial correlation: A correlation between one continuous variable and one dichotomous variable assumed to be from an underlying normal distribution.
- Pearson correlation: The standard correlation coefficient for two continuous variables. The tetrachoric correlation is an estimate of what the Pearson correlation if the continuous variables were directly observed.
Noun
- a correlation coefficient computed for two normally distributed variables that are both expressed as a dichotomy