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));
TestResult p = e1.PearsonChiSquaredTest();
Assert.IsTrue(p.Probability < 0.05);
TestResult f = e1.Binary.FisherExactTest();
Assert.IsTrue(f.Probability < 0.05);
}
public void ContingencyTableOperations()
{
ContingencyTable t = new ContingencyTable(4, 3);
Assert.IsTrue(t.Rows.Count == 4);
Assert.IsTrue(t.Columns.Count == 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[1, 1] == 2);
Assert.IsTrue(t.RowTotal(2) == 0);
Assert.IsTrue(t.ColumnTotal(1) == 2);
Assert.IsTrue(t.Total == 2);
t.Increment(2, 1);
Assert.IsTrue(t[2, 1] == 1);
Assert.IsTrue(t.RowTotal(2) == 1);
Assert.IsTrue(t.ColumnTotal(1) == 3);
Assert.IsTrue(t.Total == 3);
t.Decrement(1, 1);
Assert.IsTrue(t[1, 1] == 1);
Assert.IsTrue(t.RowTotal(2) == 1);
Assert.IsTrue(t.ColumnTotal(1) == 2);
Assert.IsTrue(t.Total == 2);
}
public void BinaryContingencyNullTest()
{
// Create a table with no significant association and test for it.
ContingencyTable e0 = CreateExperiment(0.25, 0.33, 0.33, 128);
Assert.IsTrue(e0.Total == 128);
Assert.IsTrue(e0.RowTotal(0) + e0.RowTotal(1) == e0.Total);
Assert.IsTrue(e0.ColumnTotal(0) + e0.ColumnTotal(1) == e0.Total);
UncertainValue lnr = e0.Binary.LogOddsRatio;
Assert.IsTrue(lnr.ConfidenceInterval(0.95).ClosedContains(0.0));
UncertainValue r = e0.Binary.OddsRatio;
Assert.IsTrue(r.ConfidenceInterval(0.95).ClosedContains(1.0));
TestResult p = e0.PearsonChiSquaredTest();
Assert.IsTrue(p.Probability > 0.05);
TestResult f = e0.Binary.FisherExactTest();
Assert.IsTrue(f.Probability > 0.05);
}
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 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 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 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);
}
