BartlettTest Class

public sealed class BartlettTest : MultiSampleTest<double>

Public NotInheritable Class BartlettTest
	Inherits MultiSampleTest(Of Double)

public ref class BartlettTest sealed : public MultiSampleTest<double>

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

Inheritance

Object  →  HypothesisTest  →  MultiSampleTest<Double>  →  BartlettTest

Bartlett's test is used to test the null hypothesis that multiple samples have the same variance. This property is called homogeneity of variance. The test is based on the assumption that the samples are normally distributed. It is sensitive to violations of this assumption.

The test statistic for Bartlett's test is a chi-square statistic. The distribution of this test statistic under the null hypothesis follows a chi-square distribution with degrees of freedom equal to the number of samples minus one.

Bartlett's test is commonly used in statistical procedures such as Analysis of Variance (ANOVA), which assume that variances are the same across groups. However, it cannot adequately distinguish between violation of homogeneity of variances and violation of the normality assumption. In such cases, Levene's test gives more meaningful results.

The following example demonstrates how to perform Bartlett's test using different constructors and how to use its properties and methods.

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

// Example using the default constructor
Vector<double> data1 = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
Vector<double> data2 = [ 2.0, 3.0, 4.0, 6.0, 8.0 ];
Vector<double>[] samples = [ data1, data2 ];
BartlettTest test1 = new BartlettTest(samples);
double statistic1 = test1.CalculateStatistic();
double pValue1 = test1.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic1}, P-Value: {pValue1}");

// Example using the Vector and grouping constructor
Vector<double> data2 = [ 1.0, 2.0, 3.0, 4.0, 5.0, 2.0, 3.0, 4.0, 6.0, 8.0 ];
Vector<int> groups = [ 1, 1, 1, 1, 1, 2, 2, 2, 2, 2 ];
var grouping = groups.AsCategorical();
BartlettTest test2 = new BartlettTest(data2, grouping);
double statistic2 = test2.CalculateStatistic();
double pValue2 = test2.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic2}, P-Value: {pValue2}");

Reference