# VB Hypothesis Test Example

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```Imports System
Imports System.Collections

Imports CenterSpace.NMath.Core

Namespace CenterSpace.NMath.Examples.VisualBasic

A .NET example in Visual Basic 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 artherosclerotic
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 = "F7"
Dim Col2 As DFNumericColumn = New DFNumericColumn("Vit E")
Col2.NumericFormat = "F7"

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
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()

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")