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ON THE STRUCTURE OF PEARSON'S BISERIAL CORRELATION
Author(s) -
Hamdan M. A.
Publication year - 1979
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1979.tb01148.x
Subject(s) - contingency table , polychoric correlation , pearson product moment correlation coefficient , mathematics , statistics , estimator , correlation coefficient , correlation , stratified sampling , sample size determination , geometry
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.