OneSampleTTest Class

public sealed class OneSampleTTest : OneSampleTest

Public NotInheritable Class OneSampleTTest
	Inherits OneSampleTest

public ref class OneSampleTTest sealed : public OneSampleTest

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

Inheritance

Object  →  HypothesisTest  →  OneSampleTest<Double>  →  OneSampleTest  →  OneSampleTTest

Use the OneSampleTTest to test the hypothesis that the mean of a variable is equal to a specified value. The variable is a sample from a population with a normal distribution.

The null hypothesis for the one-sample t-test is that the population mean is equal to the specified value. The test statistic follows a Student's t distribution with degrees of freedom equal to the sample size minus one.

This test is commonly used in situations where the population variance is unknown and the sample size is small. It is applicable in various fields such as psychology, medicine, and social sciences to determine if a sample mean significantly differs from a known or hypothesized population mean.

The sample data can be supplied either as a Vector<T>, or by specifying the SampleMean, SampleStandardDeviation and the SampleSize.

A confidence interval for the variance of the sample can be obtained using the GetConfidenceInterval(Double) method.

When the population variance is known, use a OneSampleZTest. To compare two sample means, use a TwoSampleTTest.

The following example demonstrates how to perform a one-sample t-test using the OneSampleTTest class. It creates a sample vector, performs the test, and then displays the test statistic, p-value, and confidence interval.

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

Vector<double> sampleData = [ 2.3, 2.5, 2.8, 3.0, 3.2 ];
double hypothesizedMean = 2.5;

var tTest = new OneSampleTTest(sampleData, hypothesizedMean);
double testStatistic = tTest.CalculateStatistic();
double pValue = tTest.GetPValue(HypothesisType.TwoTailed);
var confidenceInterval = tTest.GetConfidenceInterval(0.95);

Console.WriteLine($"Test Statistic: {testStatistic}");
Console.WriteLine($"P-Value: {pValue}");
Console.WriteLine($"95% Confidence Interval: [{confidenceInterval.LowerBound}, {confidenceInterval.UpperBound}]");

Reference