tetrachoric correlation coefficient

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An estimate of the correlation coefficient in a sample drawn from a population having a bivariate normal distribution. Consider the two-by-two table (see two-way table) where a, b, c, d are cell frequencies. Now suppose that the classifying random variables X and Y have a bivariate normal distribution with unknown parameters. The values of X and Y have been reported with respect to some cut-off values of interest (e.g. ‘< 1’), and the precise values are not available. The question of interest is the value of the correlation coefficient, ρ, in the population. One approximate estimate of ρ is provided by Yule's Q (see association). A better approximation, proposed by Karl Pearson, is the tetrachoric correlation coefficient If there are more than two rows or columns then the corresponding statistic is called the polychoric correlation coefficient.

Subjects: Probability and Statistics.

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