The r-Point Biserial Limitation

Abstract

A study was made of the r-point biserial coefficient using four non-normal distributions for the continuous variable: rectangular, bimodal-normal, bimodal-peaked, and bimodal-peaked and skewed. Ns of 10,30, and 100 were used. It was argued that linearity was the main assumption required when using Pearson correlations and that the usual maximum r -point biserial of .798 could be exceeded when the shape of the continuous variable more nearly approached that of the dichotomized variable. Correlations were found over .80 with rectangular distributions, and over .90 with bimodal-peaked distributions.