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.
