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);
}
