VB.NET Hypothesis Test Example

Imports System
Imports System.Collections

Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Stats

Namespace CenterSpace.NMath.Stats.Examples.VisualBasic

  ' A .NET example in VB.NET showing how to use the hypothesis test classes to test statistical
  ' hypotheses.

  ' 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.

  Module HypothesisTestExample

    Sub Main()

      ' 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.
      Dim DF As DataFrame = New DataFrame()
      Dim Col1 As DFNumericColumn = New DFNumericColumn("Baseline")
      Col1.NumericFormat = "F2"
      DF.AddColumn(Col1)
      Dim Col2 As DFNumericColumn = New DFNumericColumn("Vit E")
      Col2.NumericFormat = "F2"
      DF.AddColumn(Col2)
      DF.AddRow("Subject1", 0.66, 0.6)
      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", 0.7, 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.
      Dim Test As TwoSamplePairedTTest = 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()

    End Sub

  End Module

End Namespace