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TTestResult.ConfidenceInterval

The confidence interval for the difference this test measured.

public (double Low, double High) ConfidenceInterval(double level = 0.95)

Parameters — level is the confidence level, strictly between 0 and 1.

Returns — (double Low, double High): the interval around the mean, or the difference of means, the test compared. A one-sided test's interval is half-open — narrower in only one direction, since the test spent its whole error budget on one side — so the far bound is double.PositiveInfinity or double.NegativeInfinity rather than merely a larger number.

Exceptions — ArgumentOutOfRangeException when level is NaN or outside (0, 1).

Example — a two-sided interval, and a one-sided one on the same test.

using Lodestar.Stats;

double[] sample = [12.1, 9.4, 15.0, 11.2, 8.8, 13.9, 10.5];
TTestResult result = TTest.OneSample(sample, populationMean: 10.0);

(double low, double high) = result.ConfidenceInterval(0.95);
double roundedLow = Math.Round(low, 4);     // => 9.4503
double roundedHigh = Math.Round(high, 4);   // => 13.664

TTestResult oneSided = TTest.OneSample(sample, populationMean: 10.0, Alternative.Greater);
(double oneLow, double oneHigh) = oneSided.ConfidenceInterval(0.95);
double roundedOneLow = Math.Round(oneLow, 4);   // => 9.884
bool isInfinite = double.IsPositiveInfinity(oneHigh);   // => True

Remarks — the interval brackets the population mean itself for TTest.OneSample, and the difference of means for TTest.Independent and TTest.Paired — never the statistic's own scale. Alternative.TwoSided spends level's error budget on both tails, so its interval is narrower on each side than the one-sided interval's single open side is on its own; Alternative.Greater and Alternative.Less each spend the whole budget on one side and leave the other unbounded, which is why oneHigh above is infinite rather than merely larger than high.

This mirrors scipy's own TtestResult.confidence_interval, which returns the equivalent of a named tuple rather than a type of its own — a (double, double) here for the same reason.

Applies to — net10.0, netstandard2.0.

See also — TTestResult, TTest.OneSample, TTest.Independent, TTest.Paired, the Python equivalence table.