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Eric Coissac
8c7017a99d
- Update obioptions.Version from "Release 4.4.29" to "/v/ Release v5" - Update version.txt from 4.29 → .30 (automated by Makefile)
38 lines
1.7 KiB
Markdown
38 lines
1.7 KiB
Markdown
# `obistats` Package: Mann-Whitney U-test Implementation
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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.
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## Core Functionality
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- **`MannWhitneyUTest(x1, x2 []float64, alt LocationHypothesis)`**
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Performs the test between two samples `x1` and `x2`, under a user-specified alternative hypothesis (`LocationLess`, `LocationDiffers`, or `LocationGreater`).
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- Returns a structured result:
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- Sample sizes (`N1`, `N2`)
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- U statistic (with tie handling: ties contribute 0.5)
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- Alternative hypothesis used (`AltHypothesis`)
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- Achieved *p*-value (`P`)
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## Key Features
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- **Non-parametric**: No assumption of normality — suitable for ordinal data or non-Gaussian distributions.
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- **Exact vs Approximate**:
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- Uses *exact U distribution* for small samples (≤50 without ties, ≤25 with ties).
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- Falls back to *normal approximation* for larger samples (with tie and continuity corrections).
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- **Tie Handling**:
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- Ranks averaged for tied values.
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- Tie correction applied in variance estimation.
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- **Error Handling**: Returns `ErrSampleSize` (empty input) or `ErrSamplesEqual` (all values identical).
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## Implementation Notes
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- Uses labeled merge to interleave sorted samples while preserving origin labels.
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- Computes U via rank sums: `U1 = R1 − n₁(n₁+1)/2`.
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- Supports one-tailed and two-tailed tests.
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- Includes helper functions: `labeledMerge`, `tieCorrection`.
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## References
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Mann & Whitney (1947); Klotz (1966).
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Efficiency slightly lower than *t*-test on normal data, but more robust to outliers and distributional assumptions.
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