Abstract
The point-biserial correlation (rpb) coefficient is a measure of the
strength of association between a continuous-level variable and a
dichotomous (“naturally” or “artificially” dichotomized) variable.
The rpb is mathematically equivalent to Pearson correlation but has a
more intuitive formula which provides insights on what constitutes a
“good” association between continuous and dichotomous variable. In the
probabilistic forecasts verification system, skill scores are estimated
between issued forecast probabilities (continuous variable) and relative
observed category (whether or not the event; dichotomous variable). Most
of the existing skill scores for probabilistic forecasts focusing either
on the mean squared error in probabilistic space (Brier score) or degree
of correspondence between issued forecast probabilities and relative
observed frequencies (reliability diagrams) or the degree of correct
probabilistic discrimination in a set of forecasts. In this study, we
will introduce the use of rpb to verify probabilistic forecasts for
measuring the strength of association between issued forecast
probabilities and actual observed events. The proposed method will be
demonstrated in experimental evaluation with synthetic and real
precipitation forecasts.