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ExactMethod

Whether a p-value comes from the exact null distribution or its normal approximation.

public enum ExactMethod { Auto, Exact, Asymptotic }

Members — Auto is exact when the sample is small and free of ties, asymptotic otherwise; scipy's 'auto'. Exact enumerates the null distribution whatever the sample; measured, scipy computes an exact p-value on tied data too rather than refusing, so this does the same. Asymptotic uses the normal (or Kolmogorov) approximation whatever the sample size.

Example — the same tied sample, exact and asymptotic disagreeing on the number.

using Lodestar.Stats;

double[] control = [7.0, 3.0, 6.0, 2.0, 8.0, 5.0];
double[] treated = [9.0, 12.0, 8.0, 11.0, 15.0, 10.0];

TestResult auto = MannWhitney.Test(control, treated);
TestResult exact = MannWhitney.Test(control, treated, method: ExactMethod.Exact);

double autoP = Math.Round(auto.PValue, 6);     // => 0.006392
double exactP = Math.Round(exact.PValue, 6);   // => 0.004329

Remarks — Auto never throws; an explicit Exact can. control and treated share a value, so Auto falls to the asymptotic route on its own — the two samples are otherwise small enough that Auto would have taken the exact route if they had been tie-free. Asking for Exact explicitly still answers, on a different number, because the exact table is built and read regardless of ties.

Choosing Exact is not free at every size. MannWhitney.Test refuses it past x.Length * y.Length > 20_000, and Wilcoxon.Paired and Wilcoxon.OneSample refuse it past 500 ranked values — both throwing ArgumentOutOfRangeException rather than building a table that would cost tens of seconds or overflow a double. Auto is bounded by the same limits internally, but never throws for it: past the bound it silently falls back to the asymptotic answer instead, because nothing the caller wrote asked for an exact result in the first place. KolmogorovSmirnov.TwoSample is the one exception — its exact route costs O(n · m), not the quadratic-or-worse cost the rank-based tests' tables do, so Exact there is honoured at any size.

Applies to — net10.0, netstandard2.0.

See also — MannWhitney.Test, Wilcoxon.Paired, KolmogorovSmirnov.TwoSample, the Python equivalence table.