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Alternative

Which tail of the null distribution a test's p-value covers.

public enum Alternative { TwoSided, Less, Greater }

Members — TwoSided asks whether the samples differ, in either direction; scipy's 'two-sided'. Less asks whether the first sample's distribution is shifted below the second's; scipy's 'less'. Greater asks whether it is shifted above; scipy's 'greater'.

Example — the same test, on the same data, asked three different questions.

using Lodestar.Stats;

double[] sample = [12.1, 9.4, 15.0, 11.2, 8.8, 13.9, 10.5];

TTestResult twoSided = TTest.OneSample(sample, 10.0, Alternative.TwoSided);
TTestResult greater = TTest.OneSample(sample, 10.0, Alternative.Greater);
TTestResult less = TTest.OneSample(sample, 10.0, Alternative.Less);

double twoSidedP = Math.Round(twoSided.PValue, 4);   // => 0.1205
double greaterP = Math.Round(greater.PValue, 4);     // => 0.0603
double lessP = Math.Round(less.PValue, 4);           // => 0.9397

Remarks — a one-sided p-value is not half of the two-sided one, except by coincidence. The statistic here is positive, so Greater reads the tail the sample actually leans toward, and its 0.0603 is very nearly twoSidedP / 2; Less reads the opposite tail and its 0.9397 is not 1 - greaterP by accident but because the t distribution is symmetric around zero. Neither relationship survives on an asymmetric or discrete null distribution — the exact routes of MannWhitney.Test and Wilcoxon.Paired round each tail separately rather than deriving one from the other, which is why Alternative is a genuine argument to every test in this package rather than a display option layered on top of one two-sided computation.

scipy spells this alternative and defaults it to 'two-sided' everywhere this package does too.

Applies to — net10.0, netstandard2.0.