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In statistics, polychoric correlation [1] is a technique for estimating the correlation between two hypothesised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous .
Another choice is the tetrachoric correlation coefficient but it is only applicable to 2 × 2 tables. Polychoric correlation is an extension of the tetrachoric correlation to tables involving variables with more than two levels. Tetrachoric correlation assumes that the variable underlying each dichotomous measure is normally distributed. [5]
The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
The bulk of the chapter considers mathematical issues, including the rank of a matrix and methods for estimating the commonalities of the correlation matrix (the diagonal elements). Chapter III: The Centroid Method. A computation method is developed for factoring a correlation matrix, which is a symmetric matrix of real elements. After a ...
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X , we have the covariance of a variable with itself (i.e. σ X X {\displaystyle \sigma _{XX}} ), which is called the variance and is more commonly denoted as σ X 2 , {\displaystyle ...
Aickin's α; Andres and Marzo's delta; Bangdiwala's B; Bennett, Alpert, and Goldstein’s S; Brennan and Prediger’s κ; Coefficient of colligation - Yule's Y; Coefficient of consistency
Correlation does not imply causation; Correlation function; Cross-correlation matrix; Correlation function (astronomy) Correlation function (quantum field theory) Correlation function (statistical mechanics) Correlation ratio; Coskewness; Covariance; Covariance function; Covariance matrix; Covariance operator; Cramér's V; Cross-correlation ...