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Compares a sample of differences against a median of zero.

public static TestResult OneSample(ReadOnlySpan<double> differences, ZeroMethod zeroMethod = ZeroMethod.Wilcox, Alternative alternative = Alternative.TwoSided, Continuity continuity = Continuity.None, ExactMethod method = ExactMethod.Auto, NanPolicy nanPolicy = NanPolicy.Propagate)

Parameters — differences is the sample, which answers NaN for both when empty, given or left by omission, as scipy's does; the span is read, never modified. zeroMethod says what to do with differences that are exactly zero. alternative says which tail the p-value covers. continuity says whether the normal approximation gets the half-unit correction. method chooses the exact null distribution, the exhaustive permutation test, its normal approximation, or a choice between them by the number of non-zero differences. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

Returns — TestResult: the signed-rank statistic and the p-value. Two-sided, the statistic is the smaller of the two rank sums; under Alternative.Less or Alternative.Greater it is the sum of the positive ranks, which can be the larger one — scipy's wilcoxon reports the same.

Exceptions — ArgumentException when nanPolicy is NanPolicy.Raise and the sample holds a NaN. ArgumentOutOfRangeException when method is ExactMethod.Exact and the zero-method-processed sample exceeds 500 values. ArgumentOutOfRangeException when an option is outside its enumeration.

Example — seven differences, two of them exactly zero.

using Lodestar.Stats;

double[] differences = [2.0, 0.0, 3.0, 0.0, 2.0, 3.0, 3.0];

TestResult result = Wilcoxon.OneSample(differences);

double w = result.Statistic;   // => 0
double p = result.PValue;      // => 0.0625

Remarks — every difference tied at zero is a defined answer, not an error. When zeroMethod leaves nothing to rank — ZeroMethod.Wilcox drops every value — the statistic is 0.0. The exact and permutation nulls put all their mass there, a p-value of 1.0; the normal approximation, asked for or chosen by Auto past 13 values, has no variance and answers NaN, as scipy's does. Pratt's zeros answer NaN from the normal approximation too, their exact null's own p-value under Exact, and 1 from the permutation null Auto takes up to 13 values; ZSplit ranks the zeros and answers as scipy does.

Under NanPolicy.Propagate, a NaN reaches the statistic and the p-value. The check runs before ranking — a NaN difference is neither greater than, less than nor equal to zero, so unguarded it would fall into the zero group along with every genuine tie at zero.

The exact route has a size bound this package added. scipy's own signed-rank table is exact for any n, but its total, 2^n, overflows a double to +Infinity past n = 1023, and every p-value it then divides would silently come out as exactly 0.0. ExactMethod.Exact above 500 ranked values is refused with ArgumentOutOfRangeException instead, comfortably inside that margin; ExactMethod.Auto never reaches the bound on its own, since it turns unconditionally asymptotic above 50 values.

Applies to — net10.0, netstandard2.0.

See also — Wilcoxon.Paired, TTest.OneSample for the parametric counterpart, ZeroMethod, ExactMethod, the Python equivalence table.