Goodness-Of-Fit Tests QuickStart Sample (C#)

Illustrates how to test for goodness-of-fit using classes in the Extreme.Statistics.Tests namespace in C#.

Visual Basic code F# code IronPython code Back to QuickStart Samples

using System;
using Extreme.Statistics;
using Extreme.Statistics.Distributions;
using Extreme.Statistics.Tests;
using Extreme.Mathematics;

namespace Extreme.Numerics.QuickStart.CSharp
{
	/// <summary>
	/// Illustrates the Chi Square, Kolmogorov-Smirnov and Anderson-Darling 
	/// tests for goodness-of-fit.
	/// </summary>
	class GoodnessOfFitTests
	{
		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		[STAThread]
		static void Main(string[] args)
		{
			// This QuickStart Sample illustrates the wide variety of goodness-of-fit
			// tests available.

			//
			// Chi-square Test
			//

			Console.WriteLine("Chi-square test.");

			// The Chi-square test is the simplest of the goodness-of-fit tests.
			// The results follow a binomial distribution with 3 trials (rolls of the dice):
			BinomialDistribution sixesDistribution = new BinomialDistribution(3, 1/6.0);

			// First, create a histogram with the expected results.
			Histogram expected = sixesDistribution.GetExpectedHistogram(100);

			// And a histogram with the actual results
			Histogram actual = new Histogram(0, 4);
			actual.SetTotals(new double[] {51, 35, 12, 2});
			ChiSquareGoodnessOfFitTest chiSquare = new ChiSquareGoodnessOfFitTest(actual, expected);
			chiSquare.SignificanceLevel = 0.01;

			// We can obtan the value of the test statistic through the Statistic property,
			// and the corresponding P-value through the Probability property:
			Console.WriteLine("Test statistic: {0:F4}", chiSquare.Statistic);
			Console.WriteLine("P-value:        {0:F4}", chiSquare.PValue);

			// We can now print the test results:
			Console.WriteLine("Reject null hypothesis? {0}", 
				chiSquare.Reject() ? "yes" : "no");

			//
			// One-sample Kolmogorov-Smirnov Test
			//

			Console.WriteLine("\nOne-sample Kolmogorov-Smirnov Test");

			// We will investigate a sample of 25 random numbers from a lognormal distribution
			// and investigate how well it matches a similar looking Weibull distribution.

			// We first create the two distributions:
			LognormalDistribution logNormal = new LognormalDistribution(0, 1);
			WeibullDistribution weibull = new WeibullDistribution(2, 1);

			// Then we generate the samples from the lognormal distribution:
			Vector logNormalData = Vector.Create(25);
			logNormal.Sample(new System.Random(), logNormalData);
			NumericalVariable logNormalSample = new NumericalVariable(logNormalData);

			// Finally, we construct the Kolmogorov-Smirnov test:
			OneSampleKolmogorovSmirnovTest ksTest = 
				new OneSampleKolmogorovSmirnovTest(logNormalSample, weibull);

			// We can obtan the value of the test statistic through the Statistic property,
			// and the corresponding P-value through the Probability property:
			Console.WriteLine("Test statistic: {0:F4}", ksTest.Statistic);
			Console.WriteLine("P-value:        {0:F4}", ksTest.PValue);

			// We can now print the test results:
			Console.WriteLine("Reject null hypothesis? {0}", 
				ksTest.Reject() ? "yes" : "no");

			//
			// Two-sample Kolmogorov-Smirnov Test
			//

			Console.WriteLine("\nTwo-sample Kolmogorov-Smirnov Test");

			// We once again investigate the similarity between a lognormal and 
			// a Weibull distribution. However, this time, we use 25 random
			// samples from each distribution.

			// We already have the lognormal samples.
			// Generate the samples from the Weibull distribution:
			Vector weibullData = Vector.Create(25);
			weibull.Sample(new System.Random(), weibullData);
			NumericalVariable weibullSample = new NumericalVariable(weibullData);

			// Finally, we construct the Kolmogorov-Smirnov test:
			TwoSampleKolmogorovSmirnovTest ksTest2 = 
				new TwoSampleKolmogorovSmirnovTest(logNormalSample, weibullSample);

			// We can obtan the value of the test statistic through the Statistic property,
			// and the corresponding P-value through the Probability property:
			Console.WriteLine("Test statistic: {0:F4}", ksTest2.Statistic);
			Console.WriteLine("P-value:        {0:F4}", ksTest2.PValue);

			// We can now print the test results:
			Console.WriteLine("Reject null hypothesis? {0}", 
				ksTest2.Reject() ? "yes" : "no");

			//
			// Anderson-Darling Test
			//

			Console.WriteLine("\nAnderson-Darling Test");

			// The Anderson-Darling is defined for a small number of
			// distributions. Currently, only the normal distribution
			// is supported.

			// We will investigate the distribution of the strength
			// of polished airplane windows. The data comes from 
			// Fuller, e.al. (NIST, 1993) and represents the pressure
			// (in psi).

			// First, create a numerical variable:
			NumericalVariable strength = new NumericalVariable(new double[] 
				{18.830, 20.800, 21.657, 23.030, 23.230, 24.050, 
					24.321, 25.500, 25.520, 25.800, 26.690, 26.770, 
					26.780, 27.050, 27.670, 29.900, 31.110, 33.200, 
					33.730, 33.760, 33.890, 34.760, 35.750, 35.910, 
					36.980, 37.080, 37.090, 39.580, 44.045, 45.290,
                    45.381});

			// Let's print some summary statistics:
			Console.WriteLine("Number of observations: {0}", strength.Length);
			Console.WriteLine("Mean:                   {0:F3}", strength.Mean);
			Console.WriteLine("Standard deviation:     {0:F3}", strength.StandardDeviation);

			// The most refined test of normality is the Anderson-Darling test.
			AndersonDarlingTest adTest = new AndersonDarlingTest(strength);

			// We can obtan the value of the test statistic through the Statistic property,
			// and the corresponding P-value through the Probability property:
			Console.WriteLine("Test statistic: {0:F4}", adTest.Statistic);
			Console.WriteLine("P-value:        {0:F4}", adTest.PValue);

			// We can now print the test results:
			Console.WriteLine("Reject null hypothesis? {0}", 
				adTest.Reject() ? "yes" : "no");

			Console.Write("Press any key to exit.");
			Console.ReadLine();
		}
	}
}