Stats levene test

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Levene.Test

Compares the spread of two or more groups.

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

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

The centre and the policy come first because the groups are a params array and C# allows no parameter after one — the shape OneWayAnova.Test uses, for the same reason.

Parameters — groups are the samples to compare, at least two, each holding at least one value; scipy.stats.levene takes its samples the same way, one array per group, which groups is params for. center says which centre each group's deviations are measured from, defaulting to Center.Median as scipy's does. proportionToCut is how much of each end Center.Trimmed drops — scipy's proportiontocut, 0.05 by default and ignored by the other two centres. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

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

Exceptions — ArgumentException when there are fewer than two groups, a group is empty, or nanPolicy is NanPolicy.Raise and a group holds a NaN. ArgumentOutOfRangeException when proportionToCut would trim a group away entirely.

Example — three machines filling the same bottle, and the reason this test exists. One-way ANOVA says their means are indistinguishable. It is entitled to say that only if their variances match, and they do not: the second machine is all over the place.

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];

double meansAgree = Math.Round(OneWayAnova.Test(first, second, third).PValue, 4);  // => 0.9654
double spreadsDiffer = Math.Round(Levene.Test(first, second, third).PValue, 10);   // => 2.4E-08

A reader who ran only the ANOVA would report that the three machines agree. They agree on where they aim and disagree on how well they hold it, which for a bottling line is the whole question — and it is the assumption the ANOVA's own p-value rests on.

Remarks — the default centre is the median, which is Brown and Forsythe's test rather than Levene's own. scipy defaults the same way and for the same reason: centring on the mean lets one outlier inflate every deviation in its group, and the median does not notice it. The two give different statistics on the same data.

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];

double median = Math.Round(Levene.Test(first, second, third).Statistic, 4);
double mean = Math.Round(
    Levene.Test(Center.Mean, 0.05, NanPolicy.Propagate, first, second, third).Statistic, 4);

double brownForsythe = median;   // => 45.3383
double levenesOwn = mean;        // => 46.7262

Center.Trimmed drops int(n × proportionToCut) values from each end, which is scipy.stats.trim_mean's rule and truncates rather than rounds. At five values and the 0.05 default that is zero values, so Trimmed and Center.Mean agree exactly — scipy's behaviour, not an approximation of it.

Applies to — net10.0, netstandard2.0.

See also — Bartlett.Test for the same question under normality, OneWayAnova.Test, Center, the Python equivalence table.