[jira] [Created] (MATH-1453) Mann-Whitney U Test returns maximum of U1 and U2

["Nikos Katsipoulakis (JIRA)" <ji...@apache.org>]

Nikos Katsipoulakis created MATH-1453:
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             Summary: Mann-Whitney U Test returns maximum of U1 and U2
                 Key: MATH-1453
                 URL: https://issues.apache.org/jira/browse/MATH-1453
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 3.6.1
            Reporter: Nikos Katsipoulakis


Currently, I need to use Mann-Whitney U Test and I figured out that Apache Commons Math has it implemented. After consulting the [Wiki|https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test] presented in the Java Doc, it indicates that the U statistic of this test is the minimum among U1 and U2. However, when I look into Apache Commons Math {{MannWhitneyUTest.mannWhitneyU()}} method, it returns the maximum of U1 and U2. In fact, the code of this method is the following: 

 
{code:java}
public double mannWhitneyU(double[] x, double[] y) throws NullArgumentException, NoDataException {
  this.ensureDataConformance(x, y);
  double[] z = this.concatenateSamples(x, y);
  double[] ranks = this.naturalRanking.rank(z);
  double sumRankX = 0.0D;

  for(int i = 0; i < x.length; ++i) {
    sumRankX += ranks[i];
  }

  double U1 = sumRankX - (double)((long)x.length * (long)(x.length + 1) / 2L);
  double U2 = (double)((long)x.length * (long)y.length) - U1;
  return FastMath.max(U1, U2);
}
{code}
Also, in the Java Doc it is stated that the maximum value of U1 and U2 is returned.

 
My question is why Apache Commons returns the maximum of those two values, whereas all other sources I found online indicate returning the minimum? If this is not wrong, then shouldn't the Java Doc be updated to include a source that justifies that the maximum U should be returned.



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