ShapiroWilkTest Class

public sealed class ShapiroWilkTest : OneSampleTest

Public NotInheritable Class ShapiroWilkTest
	Inherits OneSampleTest

public ref class ShapiroWilkTest sealed : public OneSampleTest

[<SealedAttribute>]
type ShapiroWilkTest = 
    class
        inherit OneSampleTest
    end

Inheritance

Object  →  HypothesisTest  →  OneSampleTest<Double>  →  OneSampleTest  →  ShapiroWilkTest

The Shapiro-Wilk test is a statistical test that checks whether a sample comes from a normal distribution. The null hypothesis for this test is that the sample is drawn from a normally distributed population.

The test statistic W is calculated based on the sample data. This statistic follows a specific distribution under the null hypothesis. A small p-value indicates that it is unlikely that the sample comes from a normal distribution, leading to the rejection of the null hypothesis.

The Shapiro-Wilk test is generally considered more reliable than the Anderson-Darling or Kolmogorov-Smirnov tests. It is valid for sample sizes between 3 and 5000.

Use the ShapiroWilkTest class to test whether a sample comes from a normal distribution. A small p-value indicates that it is unlikely that the sample comes from a normal distribution.

This example demonstrates how to perform the Shapiro-Wilk test on a sample and how to use its properties and methods.

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

// Sample data
Vector<double> data = [1.0, 2.0, 3.0, 4.0, 5.0];

// Perform the Shapiro-Wilk test
var test = new ShapiroWilkTest(data);
double statistic = test.CalculateStatistic();
double pValue = test.GetPValue(HypothesisType.OneTailedLower);

// Output the results
Console.WriteLine($"Test Statistic: {statistic}");
Console.WriteLine($"P-Value: {pValue}");

Reference