[Repo Assist] feat: add Mann-Whitney U test (Wilcoxon rank-sum) for two independent samples

[github-actions]

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Summary

Adds MannWhitneyTest.create — the Mann-Whitney U test (also known as the Wilcoxon rank-sum test) for comparing two independent samples. This complements the existing WilcoxonTest which handles paired (signed-rank) samples.

This addresses requests in issues #117 and #213 for a two-sample nonparametric test.

What's new

New file: src/FSharp.Stats/Testing/MannWhitney.fs

open FSharp.Stats.Testing

let sample1 = [| 6.; 7.; 8.; 9.; 10. |]
let sample2 = [| 1.; 2.; 3.; 4.; 5.  |]

let result = MannWhitneyTest.create sample1 sample2 true
// result.U1          = 25.0   (sample1 dominates all 25 pairs)
// result.U2          = 0.0
// result.Statistic   = z-score (normal approximation)
// result.PValueRight ≈ 0.006  (H1: sample1 > sample2)
// result.PValue      ≈ 0.012  (two-sided)

MannWhitneyTestStatistics record:

Field	Description
U1	Times a value from sample 1 precedes a value from sample 2 (ties count as 0.5)
U2	Times a value from sample 2 precedes a value from sample 1; U1 + U2 = n1×n2
Statistic	Z-score from normal approximation
PValueLeft	P(sample 1 stochastically < sample 2)
PValueRight	P(sample 1 stochastically > sample 2)
PValue	Two-sided p-value

Implementation details

• Ranks the combined sample using Rank.RankAverage() (average ranks for ties)
• U1 = R1 − n1(n1+1)/2, where R1 is the rank sum of sample 1
• Normal approximation: μ = n1n2/2, σ2 = (n1n2/(N(N−1))) × ((N3−N−Σtk(tk2−1))/12)
• Optional continuity correction (±0.5) — recommended for small samples; matches R's correct=TRUE
• Result values cross-checked against R's wilcox.test(..., exact=FALSE)

Test Status

✅ All 1201 tests pass (8 new tests added in Testing.fs):

Test	Description
U statistics - clear separation	U1=25, U2=0 for completely separated samples
U1 + U2 = n1*n2	Invariant holds for all three test cases
p-values - clear separation, no cc	PValueRight < 0.01
p-values - clear separation, with cc	PValue ≈ 0.0122 (matches R)
U statistics - moderate overlap	U1=15, U2=10
p-value not significant - moderate overlap	p > 0.05
U statistics with ties	U1=4, U2=12 (tie correction applied)
p-values with ties	PValueLeft ≈ 0.121, PValue ≈ 0.243

Trade-offs / limitations

• Uses normal approximation only; exact p-values for small samples (N < 20) are not yet implemented. The function works but results may be less accurate for very small samples.
• Does not currently expose n1 and n2 in the result record (can be inferred from input lengths).

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Codecov Report

❌ Patch coverage is 87.50000% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 47.92%. Comparing base (3533493) to head (5169712).
⚠️ Report is 204 commits behind head on developer.

Files with missing lines	Patch %	Lines
src/FSharp.Stats/Testing/MannWhitney.fs	75.86%	2 Missing and 5 partials ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##           developer     #376      +/-   ##
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+ Coverage      47.61%   47.92%   +0.30%     
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  Files            152      136      -16     
  Lines          16765    12967    -3798     
  Branches        2253     1717     -536     
=============================================
- Hits            7983     6214    -1769     
+ Misses          8097     6231    -1866     
+ Partials         685      522     -163     

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[annacwe]

I had a quick clarifying question regarding this PR. As far as I understand, there was a previous attempt to implement the Mann-Whitney U test (#182), and the discussion at the time seemed to conclude that for n+m<100 the exact Wilcoxon distribution should be used instead (see also #213 and #293).

One reason I hadn't merged this yet is that, unless I'm missing something, the exact distribution does not appear to be implemented here. Instead, the implementation currently uses a normal approximation for sample sizes ≥ 20, while smaller sample sizes are not yet supported.

Is the plan going forward to implement the Wilcoxon distribution separately and then extend this test to support smaller sample sizes?

[bvenn]

Yes, I think the documentation makes it clear enough, that for small sample sizes the test is not robust. As you pointed out in the future a exact distribution can be implemented. I had a deep dive some while ago and it is difficult to implement that exact distribution. Maybe repo-assist is a game-changer here. We definitely should plan to incorporate the exact calculation.