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QuickStart Samples

# Non-Parametric Tests QuickStart Sample (Visual Basic)

Illustrates how to perform non-parametric tests like the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test in Visual Basic.

```Option Infer On

Imports System.Data
Imports Extreme.Mathematics
Imports Extreme.Statistics
Imports Extreme.Statistics.Tests

Namespace Extreme.Numerics.QuickStart.VB
' Demonstrates how to use non-parametric hypothesis tests
' like the Mann-Whitney (Wilcoxon) rank sum test and the
' Kruskal-Wallis test.
Module MeanTests

Sub Main()

'
' Mann-Whitney test
'

Console.WriteLine("Mann-Whitney Test")
Console.WriteLine()

' The Mann-Whitney test compares to samples to see if they were
' drawn from the same distribution.

' We use an example from McDonald, et.al. (1996), who compared
' the geographic variation in oyster DNA to the variation in
' proteins. A significant difference in the samples would suggest
' that natural selection played a role in the oyster diversification.

' There are two ways to create a test with multiple samples.

' The first is to put all the data in one variable,
' and use a second variable to group the data in the first.
Console.WriteLine("Using grouping variable:")

Dim values = Vector.Create(
-0.005, 0.116, -0.006, 0.095, 0.053, 0.003,
-0.005, 0.016, 0.041, 0.016, 0.066,
0.163, 0.004, 0.049, 0.006, 0.058,
-0.002, 0.015, 0.044, 0.024)
Dim groups = Vector.CreateCategorical({
Group.Dna, Group.Dna, Group.Dna, Group.Dna, Group.Dna, Group.Dna,
Group.Protein, Group.Protein, Group.Protein, Group.Protein, Group.Protein,
Group.Protein, Group.Protein, Group.Protein, Group.Protein, Group.Protein,
Group.Protein, Group.Protein, Group.Protein, Group.Protein})

' With this data, we can create the test:
Dim mw As New MannWhitneyTest(Of Double)(values, groups)

' We can obtan the value of the test statistic through the Statistic property,
' and the corresponding P-value through the PValue property:
Console.WriteLine("Test statistic: {0:F4}", mw.Statistic)
Console.WriteLine("P-value:        {0:F4}", mw.PValue)

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

' We can get the same scores 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}", IIf(mw.Reject(), "yes", "no"))
Console.WriteLine()

' The second method is to put the data in different variables
Console.WriteLine("Using multiple variables:")

Dim dnaValues = Vector.Create(-0.005, 0.116, -0.006, 0.095, 0.053, 0.003)
Dim proteinValues = Vector.Create(
-0.005, 0.016, 0.041, 0.016, 0.066,
0.163, 0.004, 0.049, 0.006, 0.058,
-0.002, 0.015, 0.044, 0.024)

' With this data, we can create the test:
mw = New MannWhitneyTest(Of Double)(dnaValues, proteinValues)

' We can obtan the value of the test statistic through the Statistic property,
' and the corresponding P-value through the PValue property:
Console.WriteLine("Test statistic: {0:F4}", mw.Statistic)
Console.WriteLine("P-value:        {0:F4}", mw.PValue)

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

'
' Kruskal-Wallis test
'

Console.WriteLine()
Console.WriteLine("Kruskal-Wallis Test")
Console.WriteLine()

' The Kruskal-Wallis test is a generalization of the Mann-Whitney test
' to more than 2 groups.

' The following example was taken from the NIST Engineering Statistics Handbook
' at http:'www.itl.nist.gov/div898/handbook/prc/section4/prc41.htm

' The data represents percentage quarterly growth
' in 4 investment funds:
Dim aValues = Vector.Create(4.2, 4.6, 3.9, 4.0)
Dim bValues = Vector.Create(3.3, 2.4, 2.6, 3.8, 2.8)
Dim cValues = Vector.Create(1.9, 2.4, 2.1, 2.7, 1.8)
Dim dValues = Vector.Create(3.5, 3.1, 3.7, 4.1, 4.4)

' We simply pass these variables to the constructor:
Dim kw As New KruskalWallisTest(aValues, bValues, cValues, dValues)

' We can obtan the value of the test statistic through the Statistic property,
' and the corresponding P-value through the PValue property:
Console.WriteLine("Test statistic: {0:F4}", kw.Statistic)
Console.WriteLine("P-value:        {0:F4}", kw.PValue)

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

'
' Runs test
'

Console.WriteLine()
Console.WriteLine("Runs Test")
Console.WriteLine()

' The runs test is a test of randomness.

' It compares the lengths of runs of the same value
' in a sample to what would be expected.

' In numerical data, it uses the runs of successively
' increasing or decreasing values

Dim genders = Vector.Create(
Gender.Male, Gender.Male, Gender.Male, Gender.Female, Gender.Female,
Gender.Female, Gender.Male, Gender.Male, Gender.Male, Gender.Male,
Gender.Female, Gender.Female, Gender.Male, Gender.Male, Gender.Male,
Gender.Female, Gender.Female, Gender.Female, Gender.Female, Gender.Female,
Gender.Female, Gender.Female, Gender.Male, Gender.Male, Gender.Female,
Gender.Male, Gender.Male, Gender.Female, Gender.Female, Gender.Female,
Gender.Female).AsCategorical()

Dim rt As New RunsTest(Of Gender)(genders)

' We can obtan the value of the test statistic through the Statistic property,
' and the corresponding P-value through the PValue property:
Console.WriteLine("Test statistic: {0:F4}", rt.Statistic)
Console.WriteLine("P-value:        {0:F4}", rt.PValue)

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

Console.WriteLine("Press Enter key to continue.")
Console.ReadLine()
End Sub

Enum Group
Dna
Protein
End Enum

Enum Gender
Male
Female
End Enum

End Module

End Namespace```