Stats andersondarling ksample

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AndersonDarling.KSample

Tests whether several samples come from one distribution, scipy.stats.anderson_ksamp.

public static AndersonResult KSample(double[][] samples)

public static AndersonResult KSample(AndersonKSampleVariant variant, double[][] samples)

Parameters — samples are the samples, at least two, none empty, with at least two distinct values between them. variant is which form of the statistic, scipy's variant; AndersonKSampleVariant.Midrank by default.

Returns — an AndersonResult: the normalised statistic, the p-value interpolated from Scholz and Stephens' table and clamped to [0.001, 0.25], and the critical values at 25, 10, 5, 2.5, 1, 0.5, 0.1 percent.

Exceptions — ArgumentException when there are fewer than two samples, an empty one, a NaN, or fewer than two distinct values. ArgumentOutOfRangeException when variant is not declared.

Example — three machines: the same centre, different spreads, so different distributions.

using Lodestar.Stats;

double[] first = [20.1, 19.8, 20.3, 20.0, 19.9, 20.2, 20.1, 19.7];
double[] second = [20.4, 18.9, 21.2, 19.1, 21.0, 18.7, 20.8, 19.4];
double[] third = [20.0, 20.1, 19.9, 20.2, 19.8, 20.1, 20.0, 19.9];

AndersonResult result = AndersonDarling.KSample(first, second, third);

double statistic = Math.Round(result.Statistic, 6);   // => 1.560618
double pValue = Math.Round(result.PValue, 6);         // => 0.075272

Remarks — AndersonDarling.Test asks whether one sample is normal; this asks whether several share any distribution at all. scipy fits a quadratic in the critical values to the log of the levels and reads it at the statistic; outside the table it returns the table's end, 0.25 or 0.001, with a warning, which here is simply the clamped value. scipy's method=PermutationMethod() has no counterpart: its draws are random.

Applies to — net10.0, netstandard2.0.

See also — AndersonKSampleVariant, KolmogorovSmirnov for two samples.