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Chi2ContingencyResult

A contingency-table chi-square result.

public sealed record Chi2ContingencyResult(double Statistic, double PValue, int Dof, double[][] ExpectedFrequencies)

Properties — Statistic is the chi-square statistic. PValue is the upper-tail p-value. Dof is the degrees of freedom, (rows - 1) * (columns - 1). ExpectedFrequencies is the table expected under independence, row-major, the same shape as the input table.

Example — the table ChiSquare.Contingency tests for independence.

using Lodestar.Stats;

double[][] table =
[
    [30.0, 20.0],
    [15.0, 35.0],
];

Chi2ContingencyResult result = ChiSquare.Contingency(table);

int dof = result.Dof;                                  // => 1
double expected01 = result.ExpectedFrequencies[0][1];   // => 27.5

Remarks — ExpectedFrequencies is what the table would look like if the two factors were independent, each cell rowTotal * columnTotal / grandTotal; comparing it against table cell by cell is what the statistic itself does. It shares table's exact shape rather than a flattened form, so result.ExpectedFrequencies[i][j] lines up directly with table[i][j].

Being a record, and double[][] comparing by reference rather than by value, two Chi2ContingencyResults are equal only when they share the very same expected-frequencies array — a detail that matters for a unit test comparing two results, and not otherwise.

Applies to — net10.0, netstandard2.0.

See also — ChiSquare.Contingency, TestResult, the Python equivalence table.