Correlation coefficients from 2 × 2 tables and from biserial data

Abstract

Various measures of correlation between two quantities x and y are discussed, and it is shown that the phi coefficient is a logically unacceptable measure except perhaps when both x and y are purely qualitative two-valued attributes. For biserial data, a new measure of correlation is proposed which is free from the shortcomings of the biserial coefficient and the point biserial coefficient.