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QuickStart Samples

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#.

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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.
            var expected = sixesDistribution.GetExpectedHistogram(100);

            // And a histogram with the actual results
            var actual = Vector.Create(new double[] {51, 35, 12, 2});
            var 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:
            var logNormalSample = logNormal.Sample(25);

            // Finally, we construct the Kolmogorov-Smirnov test:
            var 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:
            var weibullSample = weibull.Sample(25);

            // Finally, we construct the Kolmogorov-Smirnov test:
            var 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:
            var strength = Vector.Create(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();
        }
    }
}