GrubbsTest Class

public sealed class GrubbsTest : OneSampleTest

Public NotInheritable Class GrubbsTest
	Inherits OneSampleTest

public ref class GrubbsTest sealed : public OneSampleTest

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

Inheritance

Object  →  HypothesisTest  →  OneSampleTest<Double>  →  OneSampleTest  →  GrubbsTest

The Grubbs test is used to detect a single outlier in a normally distributed sample. The null hypothesis is that there are no outliers in the data. The test statistic is the maximum absolute deviation from the mean, divided by the standard deviation. This statistic follows a Student's t distribution.

The test has two-sided and one-sided versions. In the one-sided version, the null hypothesis is that the smallest (one-tailed lower) or largest (one-tailed upper) value in the sample is not an outlier. In the two-sided version, the null hypothesis is that neither the smallest nor the largest value are outliers.

This test assumes that the sample is drawn from a normal distribution. It can only test for a single outlier. If you suspect there is more than one outlier, the GeneralizedEsdTest is the test of choice.

The following example demonstrates how to use the GrubbsTest class to detect a single outlier in a sample.

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

Vector<double> data = [ 1.0, 2.0, 3.0, 4.0, 100.0 ];  
GrubbsTest test = new GrubbsTest(data);  
double statistic = test.CalculateStatistic();  
bool isOutlier = test.Reject();  
Console.WriteLine($"Test Statistic: {statistic}");  
Console.WriteLine($"Is Outlier: {isOutlier}");

The following example demonstrates how to use the GrubbsTest class with a one-tailed upper hypothesis.

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

Vector<double> data = [ 1.0, 2.0, 3.0, 4.0, 100.0 ];  
GrubbsTest test = new GrubbsTest(data, HypothesisType.OneTailedUpper);  
double statistic = test.CalculateStatistic();  
bool isOutlier = test.Reject();  
Console.WriteLine($"Test Statistic: {statistic}");  
Console.WriteLine($"Is Outlier: {isOutlier}");

Reference