Bootstrap and Traditional Standard Errors of the Point-Biserial

Abstract

Because of the wide usage of the point-biserial, three methods of estimating the point-biserial correlation coefficient standard errors that involved (a) assuming normality, (b) not assuming normality, and (c) bootstrapping were compared. The findings suggest that the point-biserial standard errors estimated assuming normality are biased, with the direction of bias depending on item difficulty. However, the normal standard error estimates are less variable and much easier to compute than are the other two estimates. In practice, therefore, use of the normal standard errors might be warranted, despite the suspected untenability of the normality assumption.