FR: Mann-Whitney-U test #182
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| open FSharp.Stats | ||
| open FSharp.Stats.Testing | ||
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| // TO DO: Bergmann et al. (2000) showed that there are different implementations of this test that lead to different results. |
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Please check if your computations are correct before PR can be merged. Additionally, check your results against established packages in R, SPSS or puplications rather than volatile wikipedia chapters.
| // let abundance = // method for equal ranks instead of mean ranks when identical values occur. | ||
| // sortedMerge | ||
| // |> Array.map ( | ||
| // fun v -> Array.filter (fun v2 -> v2 = v) sortedMerge | ||
| // >> Array.length | ||
| // ) | ||
| // let myMap = sortedMerge |> Array.mapi (fun i x -> x, i + 2 - Array.item i abundance) |> Map // wrong: must return mean of ranksums with equal ranks, not always the same rank! | ||
| // let rankedMerge = sortedMerge |> Array.map (fun (v,group) -> float myMap.[(v,group)],v,group) |
| let uTestTests = | ||
| // taken from https://de.wikipedia.org/wiki/Wilcoxon-Mann-Whitney-Test#Beispiel | ||
| let testList1 = | ||
| ([0;400;500;550;600;650;750;800;900;950;1000;1100;1200;1500;1600;1800;1900;2000;2200;3500 ],["M";"W";"M";"W";"M";"W";"M";"M";"W";"W";"M";"M";"W";"M";"W";"M";"M";"M";"M";"M"]) |
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add duplicates to check ranking procedure
| let u1 = seq1Length * seq2Length + (seq1Length * (seq1Length + 1.) / 2.) - rankSumSeq1 | ||
| let u2 = seq1Length * seq2Length + (seq2Length * (seq2Length + 1.) / 2.) - rankSumSeq2 |
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temporary results should not be calculated twice
| |> Array.filter (fun (rank,v,group') -> group' = group) | ||
| |> Array.fold (fun state (rank,v,group') -> state + rank) 0. |
| |> Array.filter (fun (rank,v,group') -> group' = group) | ||
| |> Array.fold (fun state (rank,v,group') -> state + rank) 0. |
| let sortedMerge = | ||
| (seq1 |> Seq.map (fun v -> float v, 0), seq2 |> Seq.map (fun v -> float v, 1)) // 0 = first group; 1 = second group | ||
| ||> Seq.append | ||
| |> Seq.sortByDescending (fun (v,groupIndex) -> v) |
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Is it necessary that the sequences are sorted? The ranking is order-independent and as I can see there is no need for sorting.
| } | ||
| let createUTest statistic : UTestTestStatistics = | ||
| let cdf = Distributions.Continuous.Normal.CDF 0. 1. statistic |
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The approximation via the z-Distribution is only valid for large samples.
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Since the distribution is discrete, I cannot find any other (continuous) approximation than the one via normal distribution.
https://stats.stackexchange.com/a/251734
So, what do you suggest? Delete the whole test because of normal approximation might be too inaccurate at low sample sizes?
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We should aim to implement the exact distribution for n+m<100 and the approximation for larger values
see #213 (comment)
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I have been dealing with some issues in a different MannWhitney implementation and I fear that version isn't maintained. Is there anything I can do to help get this across the finish line? Might still be helpful to compare results with that implementation, since it has been otherwise fairly robust. Happy to help with testing and potentially any missing implementation details. |
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@daz10000 Yeah, I didn't work on this for a long time. I am also not really happy about the implementation since there are major issues with it: d25e88a#r908169551 and d25e88a#r795088327. Links seem to not work properly (at least on my machine), therefore screenshots:
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I suspect half the work is in the last 10% for these things. Getting a basic version working vs getting something robust. I consider the R versions the gold standard for better or worse. I've come to the conclusion too that I might be abusing the test itself with the data sets I'm using which is probably for better or worse severely stressing implementations. |
Please reference the issue(s) this PR is related to
Tackles #117
Please list the changes introduced in this PR
Description
Mann-Whitney-U test added to the Testing portfolio. Corresponding unit test as well.