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OneWayAnova.Test

Compares the means of two or more groups.

public static TestResult Test(double[][] groups)

public static TestResult Test(NanPolicy nanPolicy, double[][] groups)

The policy comes first because the groups are a params array and C# allows no parameter after one — the shape string.Join uses, for the same reason.

Parameters — groups are the samples to compare, at least two, each holding at least one value, and at least one holding more than one — scipy.stats.f_oneway takes its samples the same way, one array per group, which groups is params for. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

Returns — TestResult: the F statistic, and the upper-tail p-value.

Exceptions — ArgumentException when there are fewer than two groups, a group is empty, or every group holds exactly one value.

Example — three shifts, fifteen measurements in all.

using Lodestar.Stats;

double[] morning = [12.0, 14.0, 11.0, 13.0, 15.0];
double[] afternoon = [16.0, 15.0, 18.0, 17.0, 14.0];
double[] evening = [21.0, 19.0, 22.0, 20.0, 23.0];

TestResult result = OneWayAnova.Test(morning, afternoon, evening);

double f = Math.Round(result.Statistic, 4);   // => 32.6667
double p = Math.Round(result.PValue, 8);      // => 1.396E-05

Remarks — a fully degenerate input answers NaN, not an exception. Groups that are each internally constant, and constant at the same value, leave no variation to compare. Constancy is read off the values, as scipy's f_oneway does, not off the sums of squares: three copies of 0.1 average to 0.10000000000000002, which leaves the within-group sum at 1e-33 rather than zero.

using Lodestar.Stats;

TestResult degenerate = OneWayAnova.Test([5.0, 5.0], [5.0, 5.0]);

bool isNaN = double.IsNaN(degenerate.Statistic);   // => True
bool alsoNaN = double.IsNaN(OneWayAnova.Test([0.1, 0.1, 0.1], [0.1, 0.1, 0.1]).Statistic);   // => True

No variation within and none between has no ratio, and scipy's own f_oneway returns the same NaN on the same input — the honest answer, not a guard this package chose to skip. Compare KruskalWallis.Test, which throws on the analogous all-tied input: an ANOVA on constants is a well-formed question with an undefined answer, where the rank-based statistic's inputs there are provably meaningless rather than merely indeterminate.

Groups each constant at different values are a perfect separation: the statistic is PositiveInfinity and the p-value an exact 0, as scipy's.

using Lodestar.Stats;

TestResult separated = OneWayAnova.Test([0.1, 0.1, 0.1], [0.2, 0.2, 0.2]);

bool infinite = double.IsPositiveInfinity(separated.Statistic);   // => True
double p = separated.PValue;                                      // => 0

Applies to — net10.0, netstandard2.0.

See also — KruskalWallis.Test for the rank-based counterpart, TTest.Independent, MultipleComparisons for correcting the many pairwise tests an ANOVA's rejection invites, the Python equivalence table.