public static void ContingencyTable()
{
ContingencyTable <string, bool> contingency = new ContingencyTable <string, bool>(
new string[] { "P", "N" }, new bool[] { true, false }
);
contingency["P", true] = 35;
contingency["P", false] = 65;
contingency["N", true] = 4;
contingency["N", false] = 896;
IReadOnlyList <string> x = new string[] { "N", "P", "N", "N", "P", "N", "N", "N", "P" };
IReadOnlyList <bool> y = new bool[] { false, false, false, true, true, false, false, false, true };
ContingencyTable <string, bool> contingencyFromLists = Bivariate.Crosstabs(x, y);
foreach (string row in contingency.Rows)
{
Console.WriteLine($"Total count of {row}: {contingency.RowTotal(row)}");
}
foreach (bool column in contingency.Columns)
{
Console.WriteLine($"Total count of {column}: {contingency.ColumnTotal(column)}");
}
Console.WriteLine($"Total counts: {contingency.Total}");
foreach (string row in contingency.Rows)
{
UncertainValue probability = contingency.ProbabilityOfRow(row);
Console.WriteLine($"Estimated probability of {row}: {probability}");
}
foreach (bool column in contingency.Columns)
{
UncertainValue probability = contingency.ProbabilityOfColumn(column);
Console.WriteLine($"Estimated probablity of {column}: {probability}");
}
UncertainValue sensitivity = contingency.ProbabilityOfRowConditionalOnColumn("P", true);
Console.WriteLine($"Chance of P result given true condition: {sensitivity}");
UncertainValue precision = contingency.ProbabilityOfColumnConditionalOnRow(true, "P");
Console.WriteLine($"Chance of true condition given P result: {precision}");
UncertainValue logOddsRatio = contingency.Binary.LogOddsRatio;
Console.WriteLine($"log(r) = {logOddsRatio}");
TestResult pearson = contingency.PearsonChiSquaredTest();
Console.WriteLine($"Pearson χ² = {pearson.Statistic.Value} has P = {pearson.Probability}.");
TestResult fisher = contingency.Binary.FisherExactTest();
Console.WriteLine($"Fisher exact test has P = {fisher.Probability}.");
}
public void BinaryContingencyTest()
{
// Create a table with significant association and test for it.
ContingencyTable e1 = CreateExperiment(0.50, 0.50, 0.75, 128);
Assert.IsTrue(e1.RowTotal(0) + e1.RowTotal(1) == e1.Total);
Assert.IsTrue(e1.ColumnTotal(0) + e1.ColumnTotal(1) == e1.Total);
UncertainValue lnr = e1.Binary.LogOddsRatio;
Assert.IsTrue(!lnr.ConfidenceInterval(0.95).ClosedContains(0.0));
UncertainValue r = e1.Binary.OddsRatio;
Assert.IsTrue(!r.ConfidenceInterval(0.95).ClosedContains(1.0));
// Chi square should detect association
TestResult p = e1.PearsonChiSquaredTest();
Assert.IsTrue(p.Probability < 0.05);
// Fisher exact should detect association
TestResult f = e1.Binary.FisherExactTest();
Assert.IsTrue(f.Probability < 0.05);
// Phi should be the same as Pearson correlation coefficient
List <double> x = new List <double>();
List <double> y = new List <double>();
for (int i = 0; i < e1[0, 0]; i++)
{
x.Add(0); y.Add(0);
}
for (int i = 0; i < e1[0, 1]; i++)
{
x.Add(0); y.Add(1);
}
for (int i = 0; i < e1[1, 0]; i++)
{
x.Add(1); y.Add(0);
}
for (int i = 0; i < e1[1, 1]; i++)
{
x.Add(1); y.Add(1);
}
double s = x.CorrelationCoefficient(y);
Assert.IsTrue(TestUtilities.IsNearlyEqual(s, e1.Binary.Phi));
}
public void ContingencyTableNamedOperations()
{
ContingencyTable t = new ContingencyTable(2, 3);
t.RowNames[0] = "Male";
t.RowNames[1] = "Female";
t.ColumnNames[0] = "Party 1";
t.ColumnNames[1] = "Party 2";
t.ColumnNames[2] = "Party 3";
t["Male", "Party 1"] = 10;
t["Male", "Party 2"] = 20;
t["Male", "Party 3"] = 30;
t["Female", "Party 1"] = 30;
t["Female", "Party 2"] = 20;
t["Female", "Party 3"] = 10;
}
public void ContingencyTableOperations()
{
ContingencyTable t = new ContingencyTable(4, 3);
Assert.IsTrue(t.RowCount == 4);
Assert.IsTrue(t.ColumnCount == 3);
Assert.IsTrue(t.RowTotal(2) == 0);
Assert.IsTrue(t.ColumnTotal(1) == 0);
Assert.IsTrue(t.Total == 0);
t[1, 1] = 2;
Assert.IsTrue(t.RowTotal(2) == 0);
Assert.IsTrue(t.ColumnTotal(1) == 2);
Assert.IsTrue(t.Total == 2);
}
public void Bug10()
{
// Fisher exact test didn't give same probability when rows were permuted.
// To compute the Fisher exact probability, we iterate over all contingency tables
// with the same marginal totals and count their probability if it is less than or
// equal to the probability of the observed matrix.
// In particular for the symmetric case, the "opposite" table has the exact
// same probability. But there is floating point noise, so sometimes it's
// calculated probability is infinitesimally larger and isn't counted.
// To fix this, we special-case the symmetric case.
ContingencyTable t1 = new ContingencyTable(new int[, ] {
{ 18, 16 }, { 12, 14 }
});
ContingencyTable t2 = new ContingencyTable(new int[, ] {
{ 12, 14 }, { 18, 16 }
});
Assert.IsTrue(TestUtilities.IsNearlyEqual(t1.Binary.FisherExactTest().Probability, t2.Binary.FisherExactTest().Probability));
}
public void McNemarTestDistribution()
{
// Define a population and the accuracy of two tests for a condition
double fractionPositive = 0.4;
double aAccuracy = 0.2;
double bAccuracy = 0.9;
// Form a bunch of samples; we will run a McNemar test on each
List <double> statistics = new List <double>();
ContinuousDistribution distribution = null;
Random rng = new Random(1);
for (int i = 0; i < 32; i++)
{
// Run a and b tests on each person.
List <bool> aResults = new List <bool>();
List <bool> bResults = new List <bool>();
for (int j = 0; j < 64; j++)
{
bool isPositive = rng.NextDouble() < fractionPositive;
bool aResult = rng.NextDouble() < aAccuracy ? isPositive : !isPositive;
aResults.Add(aResult);
bool bResult = rng.NextDouble() < bAccuracy ? isPositive : !isPositive;
bResults.Add(bResult);
}
// Do a McNemar test to determine whether tests are differently weighted.
// By our construction, they shouldn't be.
ContingencyTable <bool, bool> table = Bivariate.Crosstabs(aResults, bResults);
TestResult result = table.Binary.McNemarTest();
statistics.Add(result.Statistic.Value);
distribution = result.Statistic.Distribution;
}
// Since the null hypothesis is satisfied, the test statistic distribution should
// match the claimed null distribution.
TestResult test = statistics.KolmogorovSmirnovTest(distribution);
Assert.IsTrue(test.Probability > 0.05);
}
private static ContingencyTable CreateExperiment(double p, double q0, double q1, int N)
{
ContingencyTable e = new ContingencyTable(2, 2);
Random rng = new Random(1);
for (int i = 0; i < N; i++)
{
int r, c;
if (rng.NextDouble() < p)
{
r = 0;
if (rng.NextDouble() < q0)
{
c = 0;
}
else
{
c = 1;
}
}
else
{
r = 1;
if (rng.NextDouble() < q1)
{
c = 0;
}
else
{
c = 1;
}
}
e[r, c] += 1;
}
return(e);
}
public void ContingencyTableProbabilities()
{
// Construct data where (i) there are both reference-nulls and nullable-struct-nulls,
// (ii) all values of one column are equally, (iii) values of other column depend on value of first column
List <string> groups = new List <string>()
{
"A", "B", "C", null
};
FrameTable data = new FrameTable();
data.AddColumn <string>("Group");
data.AddColumn <bool?>("Outcome");
int n = 512;
double pOutcomeNull = 0.05;
Func <int, double> pOutcome = groupIndex => 0.8 - 0.2 * groupIndex;
Random rng = new Random(10101010);
for (int i = 0; i < n; i++)
{
int groupIndex = rng.Next(0, groups.Count);
string group = groups[groupIndex];
bool? outcome = (rng.NextDouble() < pOutcome(groupIndex));
if (rng.NextDouble() < pOutcomeNull)
{
outcome = null;
}
data.AddRow(group, outcome);
}
// Form a contingency table.
ContingencyTable <string, bool?> table = Bivariate.Crosstabs(data["Group"].As <string>(), data["Outcome"].As <bool?>());
// Total counts should match
Assert.IsTrue(table.Total == n);
// All values should be represented
foreach (string row in table.Rows)
{
Assert.IsTrue(groups.Contains(row));
}
// Counts in each cell and marginal totals should match
foreach (string group in table.Rows)
{
int rowTotal = 0;
foreach (bool?outcome in table.Columns)
{
FrameView view = data.Where(r => ((string)r["Group"] == group) && ((bool?)r["Outcome"] == outcome));
Assert.IsTrue(table[group, outcome] == view.Rows.Count);
rowTotal += view.Rows.Count;
}
Assert.IsTrue(rowTotal == table.RowTotal(group));
}
// Inferred probabilities should agree with model
Assert.IsTrue(table.ProbabilityOfColumn(null).ConfidenceInterval(0.99).ClosedContains(pOutcomeNull));
for (int groupIndex = 0; groupIndex < groups.Count; groupIndex++)
{
string group = groups[groupIndex];
Assert.IsTrue(table.ProbabilityOfRow(group).ConfidenceInterval(0.99).ClosedContains(0.25));
Assert.IsTrue(table.ProbabilityOfColumnConditionalOnRow(true, group).ConfidenceInterval(0.99).ClosedContains(pOutcome(groupIndex) * (1.0 - pOutcomeNull)));
}
Assert.IsTrue(table.ProbabilityOfColumn(null).ConfidenceInterval(0.99).ClosedContains(pOutcomeNull));
// Pearson test should catch that rows and columns are corrleated
Assert.IsTrue(table.PearsonChiSquaredTest().Probability < 0.05);
}
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}");
}
public void BinaryContingencyInvalidConstructionTest()
{
int[,] M = new int[2, 3];
ContingencyTable table = new ContingencyTable(2, 3);
BinaryContingencyTableOperations binary = table.Binary;
}
