Computing the Point-biserial Correlation under Any Underlying Continuous Distribution

The connection between the point-biserial and biserial correlations is well-established when the underlying distribution is bivariate normal. For many other bivariate distributions, the formula that links these two quantities is not straightforward to derive or does not have a closed form. We propose a simple technique that enables researchers to compute one of these correlations when the other is specified. For this, we take advantage of the constancy of their ratio, which can be easily approximated for any distribution. We illustrate the proposed method using several examples and discuss its extension to the ordinal case. We believe that this approach is potentially useful in stochastic simulation..