C# Hypothesis Test Example

using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Examples.CSharp
{
  /// <summary>
  /// A .NET example in C# showing how to use the hypothesis test classes to test statistical
  /// hypotheses.
  /// </summary>
  /// <remarks>
  /// Hypothesis tests use statistics to determine the probability that a
  /// given hypothesis is true. For example, could the differences between two
  /// sample means be explained away as sampling error? NMath Stats provides
  /// classes for many common hypothesis tests, such as the z-test, t-test,
  /// F-test, and Kolmogorov-Smirnov test, with calculation of p-values,
  /// critical values, and confidence intervals. All hypothesis test classes
  /// share substantially the same interface. Once you learn how to use one
  /// test, it’s easy to use any of the others.
  /// </remarks>
  public class HypothesisTestExample
  {

    static void Main( string[] args )
    {
      // Suppose we measure the thickness of plaque (mm) in the carotid
      // artery of 10 randomly selected patients with mild artherosclerotic
      // disease. Two measurements are taken: before treatment with
      // Vitamin E (baseline), and after two years of taking Vitamin E daily.
      var df = new DataFrame();
      var col1 = new DFNumericColumn( "Baseline" );
      col1.NumericFormat = "F7";
      df.AddColumn( col1 );
      var col2 = new DFNumericColumn( "Vit E" );
      col2.NumericFormat = "F7";
      df.AddColumn( col2 );
      df.AddRow( "Subj1", 0.66, 0.60 );
      df.AddRow( "Subj2", 0.72, 0.65 );
      df.AddRow( "Subj3", 0.85, 0.79 );
      df.AddRow( "Subj4", 0.62, 0.63 );
      df.AddRow( "Subj5", 0.59, 0.54 );
      df.AddRow( "Subj6", 0.63, 0.55 );
      df.AddRow( "Subj7", 0.64, 0.62 );
      df.AddRow( "Subj8", 0.70, 0.67 );
      df.AddRow( "Subj9", 0.73, 0.68 );
      df.AddRow( "Subj10", 0.68, 0.64 );

      // Display the data
      Console.WriteLine();
      Console.WriteLine( df );
      Console.WriteLine();

      // Construct a TwoSamplePairedTTest from the two columns of data.
      var test = new TwoSamplePairedTTest( df["Baseline"], df["Vit E"] );

      // Display the results
      Console.WriteLine( test );
      Console.WriteLine();

      // Change test type and alpha level, and display new results.
      test.Type = HypothesisType.Right;
      test.Alpha = 0.05;
      Console.WriteLine( test );
      Console.WriteLine();

      // Modify the data.
      df[5, 1] = 0.56;
      df.AddRow( "Subj11", 0.65, 0.64 );
      Console.WriteLine( df );
      Console.WriteLine();

      // Update the test, and display new results.
      test.Update( df["Baseline"], df["Vit E"] );
      test.Type = HypothesisType.TwoSided;
      Console.WriteLine( test );
      Console.WriteLine();

      // Properties provide programmatic access to individual elements in the test.
      Console.WriteLine( "Properties" );
      Console.WriteLine( "number of pairs = " + test.N );
      Console.WriteLine( "mean difference between pairs = " + test.Xbar );
      Console.WriteLine( "standard deviation of differences between pairs = " + test.S );
      Console.WriteLine( "deg of freedom = " + test.DegreesOfFreedom );
      Console.WriteLine( "t-statistic = " + test.Statistic );
      Console.WriteLine( "test type = " + test.Type );
      Console.WriteLine( "alpha level = " + test.Alpha );
      Console.WriteLine( "p-value = " + test.P );
      Console.WriteLine( "critical values: " + test.LeftCriticalValue + " " +
        test.RightCriticalValue );
      Console.WriteLine( "reject the null hypothesis? " + test.Reject );
      Console.WriteLine( "confidence interval: " + test.LowerConfidenceLimit + " " +
        test.UpperConfidenceLimit );

      Console.WriteLine();
      Console.WriteLine( "Press Enter Key" );
      Console.Read();

    }  // Main

  }  // class

}  // namespace