private static void CompareSamples()
{
List <double> a = new List <double>()
{
130.0, 140.0, 150.0, 150.0, 160.0, 190.0
};
List <double> b = new List <double>()
{
120.0, 150.0, 180.0, 170.0, 185.0, 175.0, 190.0, 200.0
};
TestResult student = Univariate.StudentTTest(a, b);
Console.WriteLine($"{student.Statistic.Name} = {student.Statistic.Value}");
Console.WriteLine($"{student.Type} P = {student.Probability}");
student.Type = TestType.LeftTailed;
Console.WriteLine($"{student.Type} P = {student.Probability}");
TestResult mannWhitney = Univariate.MannWhitneyTest(a, b);
Console.WriteLine($"{mannWhitney.Statistic.Name} = {mannWhitney.Statistic.Value}");
Console.WriteLine($"{mannWhitney.Type} P = {mannWhitney.Probability}");
TestResult kolmogorov = Univariate.KolmogorovSmirnovTest(a, b);
Console.WriteLine($"{kolmogorov.Statistic.Name} = {kolmogorov.Statistic.Value}");
Console.WriteLine($"{kolmogorov.Type} P = {kolmogorov.Probability}");
}
public void TwoSampleKolmogorovNullDistributionTest()
{
Random rng = new Random(4);
ContinuousDistribution population = new ExponentialDistribution();
int[] sizes = new int[] { 23, 30, 175 };
foreach (int na in sizes)
{
foreach (int nb in sizes)
{
Sample d = new Sample();
ContinuousDistribution nullDistribution = null;
for (int i = 0; i < 128; i++)
{
List <double> a = TestUtilities.CreateDataSample(rng, population, na).ToList();
List <double> b = TestUtilities.CreateDataSample(rng, population, nb).ToList();
TestResult r = Univariate.KolmogorovSmirnovTest(a, b);
d.Add(r.Statistic.Value);
nullDistribution = r.Statistic.Distribution;
}
// Only do full KS test if the number of bins is larger than the sample size, otherwise we are going to fail
// because the KS test detects the granularity of the distribution.
TestResult mr = d.KolmogorovSmirnovTest(nullDistribution);
if (AdvancedIntegerMath.LCM(na, nb) > d.Count)
{
Assert.IsTrue(mr.Probability > 0.01);
}
// But always test that mean and standard deviation are as expected
Assert.IsTrue(d.PopulationMean.ConfidenceInterval(0.99).ClosedContains(nullDistribution.Mean));
Assert.IsTrue(d.PopulationStandardDeviation.ConfidenceInterval(0.99).ClosedContains(nullDistribution.StandardDeviation));
// This test is actually a bit sensitive, probably because the discrete-ness of the underlying distribution
// and the inaccuracy of the asymptotic approximation for intermediate sample size make strict comparisons iffy.
}
}
}
public static void AnalyzingData()
{
FrameTable table;
Uri url = new Uri("https://raw.githubusercontent.com/dcwuser/metanumerics/master/Examples/Data/example.csv");
WebRequest request = WebRequest.Create(url);
using (WebResponse response = request.GetResponse()) {
using (StreamReader reader = new StreamReader(response.GetResponseStream())) {
table = FrameTable.FromCsv(reader);
}
}
FrameView view = table.WhereNotNull();
// Get the column with (zero-based) index 4.
FrameColumn column4 = view.Columns[4];
// Get the column named "Height".
FrameColumn heightsColumn = view.Columns["Height"];
// Even easier way to get the column named "Height".
FrameColumn alsoHeightsColumn = view["Height"];
IReadOnlyList <double> heights = view["Height"].As <double>();
SummaryStatistics summary = new SummaryStatistics(view["Height"].As <double>());
Console.WriteLine($"Count = {summary.Count}");
Console.WriteLine($"Mean = {summary.Mean}");
Console.WriteLine($"Standard Deviation = {summary.StandardDeviation}");
Console.WriteLine($"Skewness = {summary.Skewness}");
Console.WriteLine($"Estimated population mean = {summary.PopulationMean}");
Console.WriteLine($"Estimated population standard deviation = {summary.PopulationStandardDeviation}");
IReadOnlyList <double> maleHeights =
view.Where <string>("Sex", s => s == "M").Columns["Height"].As <double>();
IReadOnlyList <double> femaleHeights =
view.Where <string>("Sex", s => s == "F").Columns["Height"].As <double>();
TestResult test = Univariate.StudentTTest(maleHeights, femaleHeights);
Console.WriteLine($"{test.Statistic.Name} = {test.Statistic.Value}");
Console.WriteLine($"P = {test.Probability}");
TestResult maleHeightNormality = maleHeights.ShapiroFranciaTest();
TestResult totalHeightNormality = view["Height"].As <double>().ShapiroFranciaTest();
TestResult heightCompatibility = Univariate.KolmogorovSmirnovTest(maleHeights, femaleHeights);
LinearRegressionResult fit =
view["Weight"].As <double>().LinearRegression(view["Height"].As <double>());
Console.WriteLine($"Model weight = ({fit.Slope}) * height + ({fit.Intercept}).");
Console.WriteLine($"Model explains {fit.RSquared * 100.0}% of variation.");
ContingencyTable <string, bool> contingency =
Bivariate.Crosstabs(view["Sex"].As <string>(), view["Result"].As <bool>());
Console.WriteLine($"Male incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "M")}");
Console.WriteLine($"Female incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "F")}");
Console.WriteLine($"Log odds ratio = {contingency.Binary.LogOddsRatio}");
view.AddComputedColumn("Bmi", r => ((double)r["Weight"]) / MoreMath.Sqr((double)r["Height"] / 100.0));
view.AddComputedColumn("Age", r => (DateTime.Now - (DateTime)r["Birthdate"]).TotalDays / 365.24);
MultiLinearLogisticRegressionResult result =
view["Result"].As <bool>().MultiLinearLogisticRegression(
view["Bmi"].As <double>(),
view["Sex"].As <string, double>(s => s == "M" ? 1.0 : 0.0)
);
foreach (Parameter parameter in result.Parameters)
{
Console.WriteLine($"{parameter.Name} = {parameter.Estimate}");
}
TestResult spearman = Bivariate.SpearmanRhoTest(view["Age"].As <double>(), view["Result"].As <double>());
Console.WriteLine($"{spearman.Statistic.Name} = {spearman.Statistic.Value} P = {spearman.Probability}");
}