Critical Values of the Rank-Biserial Correlation Coefficient

Abstract

For data with observations on variable Y restricted to consecutive and untied ranks 1,2... n, and with observations on X restricted to nominal classification into group 1 or 2, the Mann-Whitney U-test provides a test of group mean difference. It is shown below that the rank-biserial correlation coefficient r rb is a linear function of the U-statistic, so that a test of group mean difference is equivalent to a test of zero correlation for the rank-biserial coefficient. This provides a distribution theory for sample values of r rb when ρ rb = 0.