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Added Spearman p value #125

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Added Spearman p value #125

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02a23af
Added standardize normalization technique.
Jul 17, 2017
d04a271
Added p-value to the Spearman correlation.
Jul 17, 2017
74ba3c8
Revert "Added standardize normalization technique."
Jul 17, 2017
612efa8
Moved p-value to pearson.
Aug 11, 2017
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19 changes: 14 additions & 5 deletions Statistics/Correlation.hs
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Original file line number Diff line number Diff line change
Expand Up @@ -14,9 +14,12 @@ module Statistics.Correlation

import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as U
import Statistics.Distribution
import Statistics.Distribution.StudentT
import Statistics.Matrix
import Statistics.Sample
import Statistics.Test.Internal (rankUnsorted)
import Statistics.Types (mkPValue, PValue)


----------------------------------------------------------------
Expand All @@ -26,15 +29,20 @@ import Statistics.Test.Internal (rankUnsorted)
-- | Pearson correlation for sample of pairs. Exactly same as
-- 'Statistics.Sample.correlation'
pearson :: (G.Vector v (Double, Double), G.Vector v Double)
=> v (Double, Double) -> Double
pearson = correlation
=> v (Double, Double) -> (Double, PValue Double)
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you should probably document the return value? that's not clear to an amateur like me at least.

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Yes it's absolutely necessary to document meaning of p-value and what hypothesis is being tested.

pearson xy = (coeff, p)
where
coeff = correlation xy
n = fromIntegral . G.length $ xy
stat = coeff * ((sqrt (n - 2)) / (1 - (coeff ** 2)))
p = mkPValue $ 2 * (complCumulative (studentT (n - 2)) . abs $ stat)
{-# INLINE pearson #-}

-- | Compute pairwise pearson correlation between rows of a matrix
pearsonMatByRow :: Matrix -> Matrix
pearsonMatByRow m
= generateSym (rows m)
(\i j -> pearson $ row m i `U.zip` row m j)
(\i j -> fst . pearson $ row m i `U.zip` row m j)
{-# INLINE pearsonMatByRow #-}


Expand All @@ -43,7 +51,8 @@ pearsonMatByRow m
-- Spearman
----------------------------------------------------------------

-- | compute spearman correlation between two samples
-- | Compute spearman correlation between two samples with p value. P value is
-- calculated using Student's /t/ distribution with /n - 2/ degrees of freedom
spearman :: ( Ord a
, Ord b
, G.Vector v a
Expand All @@ -56,7 +65,7 @@ spearman :: ( Ord a
, G.Vector v (Int, b)
)
=> v (a, b)
-> Double
-> (Double, PValue Double)
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It's especially important for Spearman correlation. What is meaning of p-value here? Is it described anywhere? I'm not sure that student's distribution will arise for ranks

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Wikipedia sources the following for this test:

Press; Vettering; Teukolsky; Flannery (1992). Numerical Recipes in C: The Art of Scientific Computing (2nd ed.). p. 640.

The equation is 14.6.2. Whether this approximation is optimal, I do not know, but I'm sure there are better methods out there for p-values for Spearman's correlation coefficient, but I used the Student's t distribution as a simple solution.

spearman xy
= pearson
$ G.zip (rankUnsorted x) (rankUnsorted y)
Expand Down