Stats bartlett test

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Bartlett.Test

Compares the variances 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.

Parameters — groups are the samples to compare, at least two, each holding at least two values, one array per group as scipy.stats.bartlett takes them. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

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

Exceptions — ArgumentException when there are fewer than two groups, a group holds fewer than two values — it would have no variance for the statistic's logarithm to read — or nanPolicy is NanPolicy.Raise and a group holds a NaN.

Example — the same three machines Levene.Test measures.

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];

TestResult result = Bartlett.Test(first, second, third);

double t = Math.Round(result.Statistic, 4);   // => 27.6477
double p = Math.Round(result.PValue, 10);     // => 9.917E-07

Remarks — which of the two variance tests to reach for is a question about the data, not about precision. Bartlett assumes each group is normal and is the more powerful test when that holds. It is also sensitive to departures from normality in a way that is indistinguishable from a difference in variance, so on a skewed or heavy-tailed sample it reports a difference that is not there. Levene.Test around the median assumes nothing about the shape and is the safer default; this one is the sharper instrument once normality has itself been checked, with AndersonDarling.Test or ShapiroWilk.Test.

The statistic is floored at zero after its p-value is taken, not before. Variances that agree to the last bits can drive the numerator a shade negative; scipy reports the floor together with the tail the unfloored value produced, and so does this.

Applies to — net10.0, netstandard2.0.

See also — Levene.Test, OneWayAnova.Test, AndersonDarling.Test, the Python equivalence table.