Stats spearman matrix

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Spearman.Matrix

Spearman's rho between every pair of variables, scipy.stats.spearmanr on a 2-D array.

public static CorrelationMatrix Matrix(ReadOnlySpan<double> data, int variableCount, Alternative alternative = Alternative.TwoSided, NanPolicy nanPolicy = NanPolicy.Propagate)

Parameters — data is the observations, row-major: one row per observation, variableCount values each. variableCount is at least two. alternative is which tail each p-value covers. nanPolicy is scipy's nan_policy.

Returns — a CorrelationMatrix: the correlations and their p-values, each variableCount × variableCount and row-major.

Exceptions — ArgumentOutOfRangeException when variableCount is below two. ArgumentException when data is not a whole number of rows, or holds a NaN under NanPolicy.Raise.

Example — three variables, the second rising with the first and the third falling.

using Lodestar.Stats;

// Six observations of three variables, row by row.
double[] data =
[
    1.2, 3.4, 10.0,
    2.3, 3.1, 8.0,
    3.1, 4.8, 9.5,
    4.0, 4.2, 6.1,
    5.5, 6.9, 4.0,
    6.1, 6.0, 3.3,
];

CorrelationMatrix matrix = Spearman.Matrix(data, variableCount: 3);

double rising = Math.Round(matrix.Statistics[1], 6);    // => 0.828571
double falling = Math.Round(matrix.Statistics[2], 6);   // => -0.942857
double p = Math.Round(matrix.PValues[2], 6);            // => 0.004805

Remarks — each off-diagonal entry is Spearman.Test on its two columns. Under NanPolicy.Omit rows are dropped pair by pair, so each pair keeps every row complete for its two variables, as scipy's does; under NanPolicy.Propagate a variable holding a NaN has NaN in its row and column and every other entry is computed. The diagonal follows scipy's two paths: under omit, where the data hold a NaN, it is (1, 0) whatever the alternative; otherwise it is computed as numpy.corrcoef computes it, which can round one ulp below 1. scipy returns a scalar for two variables; this returns the matrix.

Applies to — net10.0, netstandard2.0.

See also — Spearman.Test, CorrelationMatrix.