Note on Rank Biserial Correlation

Abstract

variables, n consecutive ranks, a dichotomy, a trichotomy, etc. In this paper we shall be concerned with developing a measure of the correlation between one variable comprising n consecutive untied ranks and a second variable comprising a dichotomy. We shall regard the dichotomy (scored 0, 1) as having a ranking variable underlying it. In this regard it is analogous to the assumption made in biserial correlation that a normally distributed variable has been forced into a dichotomy. Of major interest is a surprising equivalence which results between the coefficient found in this paper and a coefficient due to Cureton (1956). It is to present and prove the equivalence of these two coefficients, which though quite different in origin and derivation are algebraically equivalent, that this paper is being written.