public void BivariateAssociationDiscreteNullDistribution()
{
Random rng = new Random(1);
// Pick very non-normal distributions for our non-parameteric tests
ContinuousDistribution xd = new FrechetDistribution(1.0);
ContinuousDistribution yd = new CauchyDistribution();
// Pick small sample sizes to get exact distributions
foreach (int n in TestUtilities.GenerateIntegerValues(4, 24, 4))
{
// Do a bunch of test runs, recording reported statistic for each.
List <int> spearmanStatistics = new List <int>();
List <int> kendallStatistics = new List <int>();
DiscreteDistribution spearmanDistribution = null;
DiscreteDistribution kendallDistribution = null;
for (int i = 0; i < 512; i++)
{
List <double> x = new List <double>();
List <double> y = new List <double>();
for (int j = 0; j < n; j++)
{
x.Add(xd.GetRandomValue(rng));
y.Add(yd.GetRandomValue(rng));
}
DiscreteTestStatistic spearman = Bivariate.SpearmanRhoTest(x, y).UnderlyingStatistic;
if (spearman != null)
{
spearmanStatistics.Add(spearman.Value);
spearmanDistribution = spearman.Distribution;
}
DiscreteTestStatistic kendall = Bivariate.KendallTauTest(x, y).UnderlyingStatistic;
if (kendall != null)
{
kendallStatistics.Add(kendall.Value);
kendallDistribution = kendall.Distribution;
}
}
// Test whether statistics are actually distributed as claimed
if (spearmanDistribution != null)
{
TestResult spearmanChiSquared = spearmanStatistics.ChiSquaredTest(spearmanDistribution);
Assert.IsTrue(spearmanChiSquared.Probability > 0.01);
}
if (kendallDistribution != null)
{
TestResult kendallChiSquared = kendallStatistics.ChiSquaredTest(kendallDistribution);
Assert.IsTrue(kendallChiSquared.Probability > 0.01);
}
}
}
public void BivariateNullAssociation()
{
Random rng = new Random(31415926);
// Create a data structure to hold the results of Pearson, Spearman, and Kendall tests.
FrameTable data = new FrameTable();
data.AddColumn <double>("r");
data.AddColumn <double>("ρ");
data.AddColumn <double>("τ");
// Create variables to hold the claimed distribution of each test statistic.
ContinuousDistribution PRD = null;
ContinuousDistribution SRD = null;
ContinuousDistribution KTD = null;
// Generate a large number of bivariate samples and conduct our three tests on each.
ContinuousDistribution xDistribution = new LognormalDistribution();
ContinuousDistribution yDistribution = new CauchyDistribution();
for (int j = 0; j < 100; j++)
{
List <double> x = new List <double>();
List <double> y = new List <double>();
for (int i = 0; i < 100; i++)
{
x.Add(xDistribution.GetRandomValue(rng));
y.Add(yDistribution.GetRandomValue(rng));
}
TestResult PR = Bivariate.PearsonRTest(x, y);
TestResult SR = Bivariate.SpearmanRhoTest(x, y);
TestResult KT = Bivariate.KendallTauTest(x, y);
PRD = PR.Statistic.Distribution;
SRD = SR.Statistic.Distribution;
KTD = KT.Statistic.Distribution;
data.AddRow(new Dictionary <string, object>()
{
{ "r", PR.Statistic.Value }, { "ρ", SR.Statistic.Value }, { "τ", KT.Statistic.Value }
});
}
Assert.IsTrue(data["r"].As <double>().KolmogorovSmirnovTest(PRD).Probability > 0.05);
Assert.IsTrue(data["ρ"].As <double>().KolmogorovSmirnovTest(SRD).Probability > 0.05);
Assert.IsTrue(data["τ"].As <double>().KolmogorovSmirnovTest(KTD).Probability > 0.05);
}
public static void Association()
{
double[] x = new double[] { -0.58, 0.92, 1.41, 1.62, 2.72, 3.14 };
double[] y = new double[] { 1.00, 0.00, 2.00, 16.00, 18.0, 20.0 };
TestResult pearson = Bivariate.PearsonRTest(x, y);
Console.WriteLine($"Pearson {pearson.Statistic.Name} = {pearson.Statistic.Value}");
Console.WriteLine($"{pearson.Type} P = {pearson.Probability}");
TestResult spearman = Bivariate.SpearmanRhoTest(x, y);
Console.WriteLine($"Spearman {spearman.Statistic.Name} = {spearman.Statistic.Value}");
Console.WriteLine($"{spearman.Type} P = {spearman.Probability}");
TestResult kendall = Bivariate.KendallTauTest(x, y);
Console.WriteLine($"Kendall {kendall.Statistic.Name} = {kendall.Statistic.Value}");
Console.WriteLine($"{kendall.Type} P = {kendall.Probability}");
}