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Correlates the ranks of two paired samples.

public static TestResult Test(ReadOnlySpan<double> x, ReadOnlySpan<double> y, Alternative alternative = Alternative.TwoSided, NanPolicy nanPolicy = NanPolicy.Propagate)

Parameters — x and y are the two samples, of the same length; both spans are read, never modified. alternative says which tail the p-value covers. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate, and NanPolicy.Omit drops the pair rather than the value.

Returns — TestResult: rho, and the p-value. Fewer than two pairs, or a constant sample, leaves the correlation undefined and both numbers are NaN; so is the p-value alone at exactly two pairs, where the Student distribution has no degrees of freedom left.

Exceptions — ArgumentException when the samples differ in length, or when nanPolicy is NanPolicy.Raise and either sample holds a NaN. ArgumentOutOfRangeException when an option is outside its enumeration.

Example — the same eight tasting panels Pearson.Test measures.

using Lodestar.Stats;

double[] sugar = [4.0, 6.5, 5.0, 9.0, 7.5, 3.0, 8.0, 6.0];
double[] sweetness = [3.1, 5.9, 4.0, 7.4, 6.8, 2.2, 6.1, 5.2];

TestResult result = Spearman.Test(sugar, sweetness);

double rho = Math.Round(result.Statistic, 4);   // => 0.9762
double p = Math.Round(result.PValue, 6);        // => 3.3E-05

Remarks — ties take the mid-rank, as scipy.stats.rankdata gives them. Six values of which two are equal occupy ranks 1 to 6, and the tied pair takes the mean of the two places it spans rather than an arbitrary one of them. That is what keeps rho symmetric under a relabelling of equal observations.

There is no exact branch, because scipy has none. spearmanr approximates with t = rho · sqrt((n-2)/((1+rho)(1-rho))) on n - 2 degrees of freedom at every sample size, and so does this; a parameter with one legal value would be an API with nothing behind it. KendallTau.Test is the one of the three that does enumerate, and is the better reading on a short untied sample for exactly that reason.

Applies to — net10.0, netstandard2.0.

See also — Pearson.Test, KendallTau.Test, the Python equivalence table.