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Compares the means of two independent samples.

public static TTestResult Independent(ReadOnlySpan<double> a, ReadOnlySpan<double> b, Alternative alternative = Alternative.TwoSided, Variance variance = Variance.Welch, NanPolicy nanPolicy = NanPolicy.Propagate)

Parameters — a and b are the two samples, each at least two values; both spans are read, never modified. alternative says which tail the p-value covers. variance says whether to pool the two sample variances. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

Returns — TTestResult: the t statistic, the p-value, and the degrees of freedom, which are fractional under Variance.Welch.

Exceptions — ArgumentException when either sample holds fewer than two values, or nanPolicy is NanPolicy.Raise and either sample holds a NaN.

Example — two samples with clearly different means.

using Lodestar.Stats;

double[] before = [102.0, 98.0, 110.0, 105.0, 99.0];
double[] after = [95.0, 92.0, 99.0, 91.0, 97.0];

TTestResult result = TTest.Independent(before, after);

bool significant = result.PValue < 0.05;   // => True

Remarks — the default is not scipy's. This defaults to Variance.Welch; scipy.stats.ttest_ind defaults to equal_var=True, which is Student's test. Pooling is only correct when the two populations really share a variance, and a default that is wrong in the common case costs more than a word at the call site. Pass Variance.Equal for scipy's default. Both are covered by tests/oracles/stats_ttest.json, and the divergence has a row in the equivalence table.

Applies to — net10.0, netstandard2.0.

See also — TTest.Paired, TTest.OneSample, MannWhitney.Test for the rank-based counterpart, the Python equivalence table.