C# Hypothesis Test Example

using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Stats;

namespace HypothesisTestExample
{
  /// <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 atherosclerotic
      // disease. Two measurements are taken: before treatment with
      // Vitamin E (baseline), and after two years of taking Vitamin E daily.
      DataFrame df = new DataFrame();
      DFNumericColumn col1 = new DFNumericColumn("Baseline");
      col1.NumericFormat = "F2";
      df.AddColumn(col1);
      DFNumericColumn col2 = new DFNumericColumn("Vit E");
      col2.NumericFormat = "F2";
      df.AddColumn(col2);
      df.AddRow("Subject1", 0.66, 0.60);
      df.AddRow("Subject2", 0.72, 0.65);
      df.AddRow("Subject3", 0.85, 0.79);
      df.AddRow("Subject4", 0.62, 0.63);
      df.AddRow("Subject5", 0.59, 0.54);
      df.AddRow("Subject6", 0.63, 0.55);
      df.AddRow("Subject7", 0.64, 0.62);
      df.AddRow("Subject8", 0.70, 0.67);
      df.AddRow("Subject9", 0.73, 0.68);
      df.AddRow("Subject10", 0.68, 0.64);

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

      // Construct a TwoSamplePairedTTest from the two columns of data.
      TwoSamplePairedTTest 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("Subject11", 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