FlignerKilleenTest Class

public sealed class FlignerKilleenTest : MultiSampleTest<double>

Public NotInheritable Class FlignerKilleenTest
	Inherits MultiSampleTest(Of Double)

public ref class FlignerKilleenTest sealed : public MultiSampleTest<double>

[<SealedAttribute>]
type FlignerKilleenTest = 
    class
        inherit MultiSampleTest<float>
    end

Inheritance

Object  →  HypothesisTest  →  MultiSampleTest<Double>  →  FlignerKilleenTest

Use the FlignerKilleenTest class to test whether a number of samples have the same variance. This property is called homogeneity of variance.

The null hypothesis of the Fligner-Killeen test is that all groups have the same variance. The test statistic is based on the ranks of absolute deviations from the group medians. This statistic follows a chi-square distribution.

The Fligner-Killeen test is a non-parametric test and is considered more robust than Levene's test or Bartlett's test when the data is not normally distributed.

The test works by using ranks of absolute deviations from the group medians, making it less sensitive to outliers and departures from normality.

Applications of the Fligner-Killeen test include comparing the variability of different groups in experimental data, quality control, and other fields where variance homogeneity is of interest.

For similar hypothesis tests, see LeveneTest and BartlettTest.

The following example demonstrates how to use the FlignerKilleenTest class to perform the test with non-trivial inputs and then shows using its properties and methods.

using Numerics.NET.DataAnalysis;  
using Numerics.NET.Statistics;  
using Numerics.NET.Statistics.Tests;  

// Example for the constructor with no arguments  
Vector<double>[] samples =  
{  
    [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 2.0 ],  
    [ 2.0, 3.0, 4.0, 5.0, 4.0, 3.0, 2.0, 2.0 ],  
    [ 3.0, 4.0, 5.0, 4.0, 5.0, 4.0, 3.0, 2.0 ]  
};  
FlignerKilleenTest test1 = new FlignerKilleenTest(samples);  
double statistic1 = test1.CalculateStatistic();  
double pValue1 = test1.GetPValue(HypothesisType.OneTailedUpper);  
Console.WriteLine($"Statistic: {statistic1}, P-Value: {pValue1}");  

// Example for the constructor with vector array and grouping  
Vector<double> sampleData = [ 1.0, 2.0, 3.0, 2.0, 3.0, 4.0, 3.0, 4.0, 5.0 ];  
var grouping = Grouping.ByQuantile(sampleData, 3);  
FlignerKilleenTest test2 = new FlignerKilleenTest(sampleData, grouping);  
double statistic2 = test2.CalculateStatistic();  
double pValue2 = test2.GetPValue(HypothesisType.OneTailedUpper);  
Console.WriteLine($"Statistic: {statistic2}, P-Value: {pValue2}");

Reference

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