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QuickStart Samples

# Variance Tests QuickStart Sample (F#)

Illustrates how to perform hypothesis tests involving the standard deviation or variance using classes in our .NET statistical library in F#.

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#light open System open Extreme.Mathematics open Extreme.Statistics open Extreme.Statistics.Tests // Demonstrates how to use hypothesis tests for the variance // of one or two distributions. // </summary> // 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 variance of the scores is greater than // a specific value. We use the one sample Chi-square test for this // purpose. printfn "Tests for class 1" // First we create a NumericalVariable that holds the test results. let group1Results = Vector.Create( [| 62.0; 77.0; 61.0; 94.0; 75.0; 82.0; 86.0; 83.0; 64.0; 84.0; 68.0; 82.0; 72.0; 71.0; 85.0; 66.0; 61.0; 79.0; 81.0; 73.0 |]) // We can get the mean and standard deviation of the class right away: printfn "Mean for the class: %.1f" (group1Results.Mean()) printfn "Standard deviation: %.1f" (group1Results.StandardDeviation()) // // One Sample Chi-square Test // printfn "\nUsing chi-square test:" // We want to know if the standard deviation is larger than 15. // Therefore, we use a one-tailed chi-square test: let chiSquareTest = OneSampleChiSquareTest(group1Results, 225.0, HypothesisType.OneTailedUpper) // We can obtan the value of the test statistic through the Statistic property, // and the corresponding P-value through the Probability property: printfn "Test statistic: %.4f" chiSquareTest.Statistic printfn "P-value: %.4f" chiSquareTest.PValue // The significance level is the default value of 0.05: printfn "Significance level: %.2f" chiSquareTest.SignificanceLevel // We can now print the test results: printfn "Reject null hypothesis? %s" (if chiSquareTest.Reject() then "yes" else "no") // We can get a confidence interval for the current significance level: let varianceInterval = chiSquareTest.GetConfidenceInterval() printfn "95%% Confidence interval for the variance: %.1f - %1f" varianceInterval.LowerBound varianceInterval.UpperBound // We can get the same results for the 0.01 significance level by explicitly // passing the significance level as a parameter to these methods: printfn "Significance level: %.2f" 0.01 printfn "Reject null hypothesis? %s" (if chiSquareTest.Reject(0.01) then "yes" else "no") // The GetConfidenceInterval method needs the confidence level, which equals // 1 - the significance level: let varianceInterval2 = chiSquareTest.GetConfidenceInterval(0.99) printfn "99%% Confidence interval for the variance: %.1f - %.1f" varianceInterval2.LowerBound varianceInterval2.UpperBound // // Two sample F-test // printfn "\nUsing F-test:" // We want to compare the scores of the first group to the scores // of a second group from another school. We want to verify that the // variances of the scores from the two schools are equal. Once again, // we start by creating a NumericalVariable, this time containing // the scores for the second group: let group2Results = Vector.Create( [| 61.0; 80.0; 98.0; 90.0; 94.0; 65.0; 79.0; 75.0; 74.0; 86.0; 76.0; 85.0; 78.0; 72.0; 76.0; 79.0; 65.0; 92.0; 76.0; 80.0 |]) // To compare the variances of the two groups, we need the two sample // F test, implemented by the FTest class: let fTest = FTest(group1Results, group2Results) // We can obtan the value of the test statistic through the Statistic property, // and the corresponding P-value through the Probability property: printfn "Test statistic: %.4f" fTest.Statistic printfn "P-value: %.4f" fTest.PValue // The significance level is the default value of 0.05: printfn "Significance level: %.2f" fTest.SignificanceLevel // We can now print the test results: printfn "Reject null hypothesis? %s" (if fTest.Reject() then "yes" else "no") printf "Press any key to exit." Console.ReadLine() |> ignore

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