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QuickStart Samples

Mean Tests QuickStart Sample (Visual Basic)

Illustrates how to use various tests for the mean of one or more sanples using classes in the Extreme.Statistics.Tests namespace in Visual Basic.

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Option Infer On

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

Namespace Extreme.Numerics.QuickStart.VB
    ' Illustrates hypothesis tests for the mean of a sample using classes 
    ' from the Extreme.Statistics.Tests namespace.
    Module MeanTests

        Sub Main()
            ' This QuickStart Sample uses the scores obtained by the students
            ' in two groups of students on a national test.
            ' 
            ' We want to know if the scores for these two groups of students
            ' are significantly different from the national average, and
            ' from each other.

            ' The mean and standard deviation of the complete population:
            Const nationalMean As Double = 79.3
            Const nationalStandardDeviation As Double = 7.3

            Console.WriteLine("Tests for group 1")

            ' First we create a NumericalVariable that holds the test scores.
            Dim group1Results = Vector.Create(New Double() _
                {62, 77, 61, 94, 75, 82, 86, 83, 64, 84, 68, 82, 72, 71, 85, 66, 61, 79, 81, 73})

            ' We can get the mean and standard deviation of the group right away:
            Console.WriteLine("Mean for the group: {0:F1}", group1Results.Mean)
            Console.WriteLine("Standard deviation: {0:F1}", group1Results.StandardDeviation)

            '
            ' One Sample z-test
            '

            Console.WriteLine(Environment.NewLine + "Using z-test:")
            ' We know the population standard deviation, so we can use the z-test,
            ' implemented by the OneSampleZTest group. We pass the sample variable
            ' and the population parameters to the constructor.
            Dim zTest As OneSampleZTest = _
                New OneSampleZTest(group1Results, nationalMean, nationalStandardDeviation)
            ' We can obtan the value of the test statistic through the Statistic property,
            ' and the corresponding P-value through the Probability property:
            Console.WriteLine("Test statistic: {0:F4}", zTest.Statistic)
            Console.WriteLine("P-value:        {0:F4}", zTest.PValue)

            ' The significance level is the default value of 0.05:
            Console.WriteLine("Significance level:     {0:F2}", zTest.SignificanceLevel)
            ' We can now print the test scores:
            Console.WriteLine("Reject null hypothesis? {0}", IIf(zTest.Reject(), "yes", "no"))
            ' We can get a confidence interval for the current significance level:
            Dim meanInterval As Interval = zTest.GetConfidenceInterval()
            Console.WriteLine("95% Confidence interval for the mean: {0:F1} - {1:F1}", _
                meanInterval.LowerBound, meanInterval.UpperBound)

            ' 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(zTest.Reject(0.01), "yes", "no"))
            ' The GetConfidenceInterval method needs the confidence level, which equals
            ' 1 - the significance level:
            meanInterval = zTest.GetConfidenceInterval(0.99)
            Console.WriteLine("99% Confidence interval for the mean: {0:F1} - {1:F1}", _
                meanInterval.LowerBound, meanInterval.UpperBound)


            ' 
            ' One sample t-test
            '

            Console.WriteLine(Environment.NewLine + "Using t-test:")
            ' Suppose we only know the mean of the national scores, 
            ' not the standard deviation. In this case, a t-test is 
            ' the appropriate test to use.
            Dim tTest As OneSampleTTest = New OneSampleTTest(group1Results, nationalMean)
            ' We can obtan the value of the test statistic through the Statistic property,
            ' and the corresponding P-value through the Probability property:
            Console.WriteLine("Test statistic: {0:F4}", tTest.Statistic)
            Console.WriteLine("P-value:        {0:F4}", tTest.PValue)

            ' The significance level is the default value of 0.05:
            Console.WriteLine("Significance level:     {0:F2}", tTest.SignificanceLevel)
            ' We can now print the test scores:
            Console.WriteLine("Reject null hypothesis? {0}", IIf(tTest.Reject(), "yes", "no"))
            ' We can get a confidence interval for the current significance level:
            meanInterval = tTest.GetConfidenceInterval()
            Console.WriteLine("95% Confidence interval for the mean: {0:F1} - {1:F1}", _
                meanInterval.LowerBound, meanInterval.UpperBound)


            ' 
            ' Two sample t-test
            '

            Console.WriteLine(Environment.NewLine + "Using two-sample t-test:")
            ' We want to compare the scores of the first group to the scores 
            ' of a second group from the same school. Once again, we start
            ' by creating a NumericalVariable containing the scores:
            Dim group2Results = Vector.Create(New Double() _
                {61, 80, 98, 90, 94, 65, 79, 75, 74, 86, 76, 85, 78, 72, 76, 79, 65, 92, 76, 80})

            ' To compare the means of the two groups, we need the two sample
            ' t test, implemented by the TwoSampleTTest group:
            Dim tTest2 As TwoSampleTTest = New TwoSampleTTest(group1Results, group2Results,
                SamplePairing.Paired, assumeEqualVariances:=False)
            ' We can obtan the value of the test statistic through the Statistic property,
            ' and the corresponding P-value through the Probability property:
            Console.WriteLine("Test statistic: {0:F4}", tTest2.Statistic)
            Console.WriteLine("P-value:        {0:F4}", tTest2.PValue)

            ' The significance level is the default value of 0.05:
            Console.WriteLine("Significance level:     {0:F2}", tTest2.SignificanceLevel)
            ' We can now print the test scores:
            Console.WriteLine("Reject null hypothesis? {0}", IIf(tTest2.Reject(), "yes", "no"))

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

    End Module

End Namespace