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QuickStart Samples

Variance Tests QuickStart Sample (C#)

Illustrates how to perform hypothesis tests involving the standard deviation or variance using classes in our .NET statistical library in C#.

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using System;

using Extreme.Mathematics;
using Extreme.Statistics;
using Extreme.Statistics.Tests;

namespace Extreme.Numerics.QuickStart.CSharp
{
    /// <summary>
    /// Demonstrates how to use hypothesis tests for the variance 
    /// of one or two distributions.
    /// </summary>
    class VarianceTests
    {
        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            // This QuickStart Sample uses the scores obtained by the students
            // in two groups of students on a national test.
            // 
            // We want to know if the variance of the scores is greater than
            // a specific value. We use the one sample Chi-square test for this
            // purpose.

            Console.WriteLine("Tests for class 1");

            // First we create a NumericalVariable that holds the test results.
            var group1Results = Vector.Create(new double[]
                {62, 77, 61, 94, 75, 82, 86, 83, 64, 84, 
                 68, 82, 72, 71, 85, 66, 61, 79, 81, 73});
            
            // We can get the mean and standard deviation of the class right away:
            Console.WriteLine("Mean for the class: {0:F1}", group1Results.Mean());
            Console.WriteLine("Standard deviation: {0:F1}", group1Results.StandardDeviation());
            
            //
            // One Sample Chi-square Test
            //

            Console.WriteLine("\nUsing chi-square test:");

            // We want to know if the standard deviation is larger than 15.
            // Therefore, we use a one-tailed chi-square test:
            OneSampleChiSquareTest chiSquareTest = 
                new OneSampleChiSquareTest(group1Results, 225, HypothesisType.OneTailedUpper);
            
            // 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}", chiSquareTest.Statistic);
            Console.WriteLine("P-value:        {0:F4}", chiSquareTest.PValue);

            // The significance level is the default value of 0.05:
            Console.WriteLine("Significance level:     {0:F2}", 
                chiSquareTest.SignificanceLevel);
            // We can now print the test results:
            Console.WriteLine("Reject null hypothesis? {0}", 
                chiSquareTest.Reject() ? "yes" : "no");
            // We can get a confidence interval for the current significance level:
            Interval varianceInterval = chiSquareTest.GetConfidenceInterval();
            Console.WriteLine("95% Confidence interval for the variance: {0:F1} - {1:F1}", 
                varianceInterval.LowerBound, varianceInterval.UpperBound);

            // We can get the same results for the 0.01 significance level by explicitly
            // passing the significance level as a parameter to these methods:
            Console.WriteLine("Significance level:     {0:F2}", 0.01);
            Console.WriteLine("Reject null hypothesis? {0}", 
                chiSquareTest.Reject(0.01) ? "yes" : "no");
            
            // The GetConfidenceInterval method needs the confidence level, which equals
            // 1 - the significance level:
            varianceInterval = chiSquareTest.GetConfidenceInterval(0.99);
            Console.WriteLine("99% Confidence interval for the variance: {0:F1} - {1:F1}", 
                varianceInterval.LowerBound, varianceInterval.UpperBound);

            // 
            // Two sample F-test
            //

            Console.WriteLine("\nUsing F-test:");
            // We want to compare the scores of the first group to the scores 
            // of a second group from another school. We want to verify that the
            // variances of the scores from the two schools are equal. Once again, 
            // we start by creating a NumericalVariable, this time containing 
            // the scores for the second group:
            var group2Results = Vector.Create(new double[]
                {61, 80, 98, 90, 94, 65, 79, 75, 74, 86, 
                 76, 85, 78, 72, 76, 79, 65, 92, 76, 80});

            // To compare the variances of the two groups, we need the two sample
            // F test, implemented by the FTest class:
            FTest fTest = new FTest(group1Results, group2Results);
            // 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}", fTest.Statistic);
            Console.WriteLine("P-value:        {0:F4}", fTest.PValue);

            // The significance level is the default value of 0.05:
            Console.WriteLine("Significance level:     {0:F2}", fTest.SignificanceLevel);
            // We can now print the test results:
            Console.WriteLine("Reject null hypothesis? {0}", fTest.Reject() ? "yes" : "no");

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