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.Probability(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));
}
