Hi there,

I found that the computation of rank-biserial correlation (RBC) is problematic. This is related to #417 and #424.

According to the cited paper, there are three ways to compute RBC. It seems you adopted the third method based on Hans Wendt (1972): r=1 – (2U)/ (n1 * n2). From the paper, U is the smaller number between U1 and U2:

Finding the test statistic U requires two steps. First, compute the number of favorable and unfavorable pairs; or what is the same thing, compute U1 and U2, as defined in Equations 1 and 2. Second, select the smaller of the two numbers; this smaller number is the test statistic U.

According to SciPy,

the Mann-Whitney U statistic corresponding with sample x; If U1 is the statistic corresponding with sample x, then the statistic corresponding with sample y is U2 = x.shape[axis] * y.shape[axis] - U1.

It seems that the returned U is not the smaller one in U1 and U2. And, it will result in a RBC value that is negative (according to the paper, this should always be positive). This is also demonstrated in my experiments.

Thanks!