public void BivariateNullAssociation()
{
Random rng = new Random(314159265);
// Create sample sets for our three test statisics
Sample PS = new Sample();
Sample SS = new Sample();
Sample KS = new Sample();
// variables to hold the claimed distribution of teach test statistic
Distribution PD = null;
Distribution SD = null;
Distribution KD = null;
// generate a large number of bivariate samples and conduct our three tests on each
for (int j = 0; j < 100; j++) {
BivariateSample S = new BivariateSample();
// sample size should be large so that asymptotic assumptions are justified
for (int i = 0; i < 100; i++) {
double x = rng.NextDouble();
double y = rng.NextDouble();
S.Add(x, y);
}
TestResult PR = S.PearsonRTest();
PS.Add(PR.Statistic);
PD = PR.Distribution;
TestResult SR = S.SpearmanRhoTest();
SS.Add(SR.Statistic);
SD = SR.Distribution;
TestResult KR = S.KendallTauTest();
KS.Add(KR.Statistic);
KD = KR.Distribution;
}
// do KS to test whether the samples follow the claimed distributions
//Console.WriteLine(PS.KolmogorovSmirnovTest(PD).LeftProbability);
//Console.WriteLine(SS.KolmogorovSmirnovTest(SD).LeftProbability);
//Console.WriteLine(KS.KolmogorovSmirnovTest(KD).LeftProbability);
Assert.IsTrue(PS.KolmogorovSmirnovTest(PD).LeftProbability < 0.95);
Assert.IsTrue(SS.KolmogorovSmirnovTest(SD).LeftProbability < 0.95);
Assert.IsTrue(KS.KolmogorovSmirnovTest(KD).LeftProbability < 0.95);
}
public void PearsonRDistribution()
{
Random rng = new Random(1);
// pick some underlying distributions for the sample variables, which must be normal but can have any parameters
NormalDistribution xDistribution = new NormalDistribution(1, 2);
NormalDistribution yDistribution = new NormalDistribution(3, 4);
// try this for several sample sizes, all low so that we see the difference from the normal distribution
// n = 3 maxima at ends; n = 4 uniform; n = 5 semi-circular "mound"; n = 6 parabolic "mound"
foreach (int n in new int[] { 3, 4, 5, 6, 8 }) {
Console.WriteLine("n={0}", n);
// find r values
Sample rSample = new Sample();
for (int i = 0; i < 100; i++) {
// to get each r value, construct a bivariate sample of the given size with no cross-correlation
BivariateSample xySample = new BivariateSample();
for (int j = 0; j < n; j++) {
xySample.Add(xDistribution.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
double r = xySample.PearsonRTest().Statistic;
rSample.Add(r);
}
// check whether r is distributed as expected
TestResult result = rSample.KolmogorovSmirnovTest(new PearsonRDistribution(n));
Console.WriteLine("P={0}", result.LeftProbability);
Assert.IsTrue(result.LeftProbability < 0.95);
}
}
