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KruskalWallis.Test

Compares two or more groups by their ranks in the pooled sample.

public static TestResult Test(double[][] groups)

Parameters — groups are the samples to compare, at least two, each holding at least one value — scipy.stats.kruskal takes its samples the same way, one array per group, which groups is params for.

Returns — TestResult: the H statistic, and the upper-tail p-value.

Exceptions — ArgumentException when there are fewer than two groups, a group is empty, or every value in the pooled sample is tied.

Example — the same three shifts OneWayAnova.Test compares.

using Lodestar.Stats;

double[] morning = [12.0, 14.0, 11.0, 13.0, 15.0];
double[] afternoon = [16.0, 15.0, 18.0, 17.0, 14.0];
double[] evening = [21.0, 19.0, 22.0, 20.0, 23.0];

TestResult result = KruskalWallis.Test(morning, afternoon, evening);

double h = Math.Round(result.Statistic, 4);   // => 11.6215
double p = Math.Round(result.PValue, 6);      // => 0.002995

Remarks — a fully tied pooled sample throws, where OneWayAnova.Test's analogous input answers NaN.

using Lodestar.Stats;

string message = "nothing was thrown";
try
{
    KruskalWallis.Test([5.0, 5.0], [5.0, 5.0]);
}
catch (ArgumentException error)
{
    message = error.Message;
}

string what = message;   // => Every value in the pooled sample is tied…

The tie correction this statistic divides by is 1 - (t³ - t) / (n³ - n) for a tie group spanning t of the n pooled values; when every value is tied, t = n and the correction is exactly 0 — not close to zero, not a value a tolerance would need to catch — so the division that would follow is refused instead of silently producing an infinite or NaN statistic from ranks that carry no information at all.

A NaN propagates. There is no nan_policy here: a NaN anywhere in any group makes the statistic and the p-value NaN, checked before ranking — unguarded, Array.Sort sorts a NaN to the front and it would take a finite rank like any other value, the same failure mode MannWhitney.Test shares and guards against the same way.

Applies to — net10.0, netstandard2.0.

See also — OneWayAnova.Test for the parametric counterpart, MannWhitney.Test, the Python equivalence table.