/// <summary>
/// Checks that (x-y) > threshold
/// </summary>
/// <remarks>Should be consistent with wilcox.test(x, y, mu=threshold, alternative="greater") from R</remarks>
public MannWhitneyResult IsGreater(double[] x, double[] y, Threshold threshold = null)
{
threshold = threshold ?? RelativeThreshold.Default;
double thresholdValue = threshold.GetValue(x);
int n = x.Length, m = y.Length;
if (Math.Min(n, m) < 3 || Math.Max(n, m) < 5)
{
return(null); // Test can't be applied
}
var xy = new double[n + m];
for (int i = 0; i < n; i++)
{
xy[i] = x[i];
}
for (int i = 0; i < m; i++)
{
xy[n + i] = y[i] + thresholdValue;
}
var index = new int[n + m];
for (int i = 0; i < n + m; i++)
{
index[i] = i;
}
Array.Sort(index, (i, j) => xy[i].CompareTo(xy[j]));
var ranks = new double[n + m];
for (int i = 0; i < n + m;)
{
int j = i;
while (j + 1 < n + m && Math.Abs(xy[index[j + 1]] - xy[index[i]]) < 1e-9)
{
j++;
}
double rank = (i + j + 2) / 2.0;
for (int k = i; k <= j; k++)
{
ranks[k] = rank;
}
i = j + 1;
}
double ux = 0;
for (int i = 0; i < n + m; i++)
{
if (index[i] < n)
{
ux += ranks[i];
}
}
ux -= n * (n + 1) / 2.0;
double uy = n * m - ux;
if (n + m <= BinomialCoefficientHelper.MaxAcceptableN)
{
double pValue = 1 - PValueForSmallN(n, m, ux - 1);
return(new MannWhitneyResult(ux, uy, pValue, threshold));
}
else
{
double mu = n * m / 2.0;
double su = Math.Sqrt(n * m * (n + m + 1) / 12.0);
double z = (ux - mu) / su;
double pValue = 1 - NormalDistribution.Gauss(z);
return(new MannWhitneyResult(ux, uy, pValue, threshold));
}
}
