/// <summary>
/// Kruskal Wallis test is the extention of the Wilcoxon U test to more than two group
/// Another words it is designed to test the equakity of medians of multiple sample
/// </summary>
/// <param name="data">Value of the first dimension is number of groups, second - size of the group</param>
/// <param name="stat">H-statistic of the test</param>
/// <returns></returns>
public static double TestImpl(double[][] data, out double stat)
{
int i, j, counter = 0;
int[] arrN = new int[data.Length];
List <double> x = new List <double>();
for (i = 0; i < data.Length; i++)
{
arrN[i] = data[i].Length;
for (j = 0; j < arrN[i]; j++)
{
x.Add(data[i][j]);
}
}
int n = arrN.Sum();
List <double> dataRank = ArrayUtils.Rank(x, true).ToList();
List <int> numDuplicates = new List <int>();
double[] dataRankSorted = dataRank.OrderBy(a => a).ToArray();
for (i = 0; i < n; i++)
{
counter++;
if ((i == n - 1) || (dataRankSorted[i] != dataRankSorted[i + 1]))
{
if (counter > 1)
{
numDuplicates.Add(counter);
}
counter = 0;
}
}
j = 0;
double[] s = new double[data.Length];
for (i = 0; i < data.Length; i++)
{
s[i] = Math.Pow(dataRank.Skip(j).Take(arrN[i]).Select(d => d + 1).Sum(), 2) / arrN[i];
j += arrN[i];
}
stat = (12 * s.Sum() / (n * (n + 1)) - 3 * (n + 1)) / (1 - numDuplicates.Select(d => d * (d * d - 1)).Sum() / (Math.Pow(n, 3) - n));
int df = data.Length - 1;
return(1 - NumUtils.Gammq(stat * 0.5, df * 0.5));
}