Development build. This page describes main, not a released package. The latest published Lodestar.Stats is 0.5.0 — read its documentation.

Home › Stats › Hypothesis tests

KruskalWallis.Test

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

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

public static TestResult Test(NanPolicy nanPolicy, double[][] groups)

The policy comes first because the groups are a params array and C# allows no parameter after one — the shape string.Join uses, for the same reason.

Parameters — groups are the samples to compare, at least two — scipy.stats.kruskal takes its samples the same way, one array per group, which groups is params for. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

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

Exceptions — ArgumentException when there are fewer than two groups. A fully tied pooled sample, and a null or empty group, given or left by omission, answer NaN for both. ArgumentOutOfRangeException when an option is outside its enumeration.

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 answers NaN, as OneWayAnova.Test's analogous input does.

using Lodestar.Stats;

TestResult tied = KruskalWallis.Test([5.0, 5.0], [5.0, 5.0]);

bool undefined = double.IsNaN(tied.Statistic);   // => True

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, so H is 0/0. Kruskal and Wallis leave that case undefined, and the answer is NaN (decision 0010), where this used to throw.

H can round a hair below zero, and the p-value is then NaN. When the groups' mean ranks are equal, H is zero in exact arithmetic, and rounding can leave it at -5.7e-14 — the values 1 to 148 split into two groups with equal rank sums do. The chi-squared tail is undefined below zero, so the p-value is NaN, as scipy's kruskal answers on the same split, and the statistic is returned as computed.

Under NanPolicy.Propagate, a NaN reaches the statistic and the p-value. The check runs 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.

Omission runs before this test's own requirements, which are unchanged by it — a pool left fully tied, or a group left empty, answers exactly as it would if passed directly.

Applies to — net10.0, netstandard2.0.

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