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}");
}
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}");
}