public void ContingencyTableProbabilitiesAndUncertainties()
{
// start with an underlying population
double[,] pp = new double[, ]
{
{ 1.0 / 45.0, 2.0 / 45.0, 3.0 / 45.0 },
{ 4.0 / 45.0, 5.0 / 45.0, 6.0 / 45.0 },
{ 7.0 / 45.0, 8.0 / 45.0, 9.0 / 45.0 }
};
// form 50 contingency tables, each with N = 50
Random rng = new Random(314159);
BivariateSample p22s = new BivariateSample();
BivariateSample pr0s = new BivariateSample();
BivariateSample pc1s = new BivariateSample();
BivariateSample pr2c0s = new BivariateSample();
BivariateSample pc1r2s = new BivariateSample();
for (int i = 0; i < 50; i++)
{
ContingencyTable T = new ContingencyTable(3, 3);
for (int j = 0; j < 50; j++)
{
int r, c;
ChooseRandomCell(pp, rng.NextDouble(), out r, out c);
T.Increment(r, c);
}
Assert.IsTrue(T.Total == 50);
// for each contingency table, compute estimates of various population quantities
UncertainValue p22 = T.ProbabilityOf(2, 2);
UncertainValue pr0 = T.ProbabilityOfRow(0);
UncertainValue pc1 = T.ProbabilityOfColumn(1);
UncertainValue pr2c0 = T.ProbabilityOfRowConditionalOnColumn(2, 0);
UncertainValue pc1r2 = T.ProbabilityOfColumnConditionalOnRow(1, 2);
p22s.Add(p22.Value, p22.Uncertainty);
pr0s.Add(pr0.Value, pr0.Uncertainty);
pc1s.Add(pc1.Value, pc1.Uncertainty);
pr2c0s.Add(pr2c0.Value, pr2c0.Uncertainty);
pc1r2s.Add(pc1r2.Value, pc1r2.Uncertainty);
}
// the estimated population mean of each probability should include the correct probability in the underlyting distribution
Assert.IsTrue(p22s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(9.0 / 45.0));
Assert.IsTrue(pr0s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(6.0 / 45.0));
Assert.IsTrue(pc1s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(15.0 / 45.0));
Assert.IsTrue(pr2c0s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(7.0 / 12.0));
Assert.IsTrue(pc1r2s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(8.0 / 24.0));
// the estimated uncertainty for each population parameter should be the standard deviation across independent measurements
// since the reported uncertainly changes each time, we use the mean value for comparison
Assert.IsTrue(p22s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(p22s.Y.Mean));
Assert.IsTrue(pr0s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pr0s.Y.Mean));
Assert.IsTrue(pc1s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pc1s.Y.Mean));
Assert.IsTrue(pr2c0s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pr2c0s.Y.Mean));
Assert.IsTrue(pc1r2s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pc1r2s.Y.Mean));
}
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}.");
}
