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Eric Coissac
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- Update obioptions.Version from "Release 4.4.29" to "/v/ Release v5" - Update version.txt from 4.29 → .30 (automated by Makefile)
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1.7 KiB
obistats Package: Mann-Whitney U-test Implementation
The obistats package provides a non-parametric statistical test for comparing two independent samples: the Mann–Whitney U-test, also known as the Wilcoxon rank-sum test.
Core Functionality
-
MannWhitneyUTest(x1, x2 []float64, alt LocationHypothesis)
Performs the test between two samplesx1andx2, under a user-specified alternative hypothesis (LocationLess,LocationDiffers, orLocationGreater). -
Returns a structured result:
- Sample sizes (
N1,N2) - U statistic (with tie handling: ties contribute 0.5)
- Alternative hypothesis used (
AltHypothesis) - Achieved p-value (
P)
- Sample sizes (
Key Features
- Non-parametric: No assumption of normality — suitable for ordinal data or non-Gaussian distributions.
- Exact vs Approximate:
- Uses exact U distribution for small samples (≤50 without ties, ≤25 with ties).
- Falls back to normal approximation for larger samples (with tie and continuity corrections).
- Tie Handling:
- Ranks averaged for tied values.
- Tie correction applied in variance estimation.
- Error Handling: Returns
ErrSampleSize(empty input) orErrSamplesEqual(all values identical).
Implementation Notes
- Uses labeled merge to interleave sorted samples while preserving origin labels.
- Computes U via rank sums:
U1 = R1 − n₁(n₁+1)/2. - Supports one-tailed and two-tailed tests.
- Includes helper functions:
labeledMerge,tieCorrection.
References
Mann & Whitney (1947); Klotz (1966).
Efficiency slightly lower than t-test on normal data, but more robust to outliers and distributional assumptions.