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}.");
}
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}");
}
