| Abstract: | Pearson (1909) introduced a special method for estimating the correlation coefficient between a two-level variate X and a c-level variate Y , where it is assumed that the regression of Y on X is linear. Pearson's estimator, called biserial correlation, is thus obtained from a sample of size n from a 2 × c table. On the other hand, Lancaster and Hamdan (1964) introduced the polychoric estimator of the correlation between two variates X and Y from a sample available in the form of an r×c contingency table. Later, Hamdan (1968) proved that Pearson's (1900) tetrachoric estimator is a special case of Lancaster and Hamdan polychoric estimator. The present paper applies the orthonor-mal technique which underlies Lancaster's partition of chi-squared (1949) to show that Pearson's biserial correlation is a special form of Lancaster and Hamdan's polychoric estimator. |
