statistics-0.14.0.0: tests/Tests/NonParametric.hs
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ViewPatterns #-}
-- Tests for Statistics.Test.NonParametric
module Tests.NonParametric (tests) where
import Statistics.Distribution.Normal (standard)
import Statistics.Test.KolmogorovSmirnov
import Statistics.Test.MannWhitneyU
import Statistics.Test.KruskalWallis
import Statistics.Test.WilcoxonT
import Statistics.Types (PValue,pValue,cl95,mkPValue)
import Test.Framework (testGroup)
import Test.Framework.Providers.HUnit
import qualified Test.Framework as Tst
import Test.HUnit (assertEqual)
import Tests.ApproxEq (eq)
import Tests.Helpers (testAssertion, testEquality)
import Tests.NonParametric.Table (tableKSD, tableKS2D)
import qualified Data.Vector.Unboxed as U
tests :: Tst.Test
tests = testGroup "Nonparametric tests"
$ concat [ mannWhitneyTests
, wilcoxonSumTests
, wilcoxonPairTests
, kruskalWallisRankTests
, kruskalWallisTests
, kolmogorovSmirnovDTest
]
----------------------------------------------------------------
mannWhitneyTests :: [Tst.Test]
mannWhitneyTests = zipWith test [(0::Int)..] testData ++
[ testEquality "Mann-Whitney U Critical Values, m=1"
(replicate (20*3) Nothing)
[mannWhitneyUCriticalValue (1,x) (mkPValue p) | x <- [1..20], p <- [0.005,0.01,0.025]]
, testEquality "Mann-Whitney U Critical Values, m=2, p=0.025"
(replicate 7 Nothing ++ map Just [0,0,0,0,1,1,1,1,1,2,2,2,2])
[mannWhitneyUCriticalValue (2,x) (mkPValue 0.025) | x <- [1..20]]
, testEquality "Mann-Whitney U Critical Values, m=6, p=0.05"
(replicate 1 Nothing ++ map Just [0, 2,3,5,7,8,10,12,14,16,17,19,21,23,25,26,28,30,32])
[mannWhitneyUCriticalValue (6,x) (mkPValue 0.05) | x <- [1..20]]
, testEquality "Mann-Whitney U Critical Values, m=20, p=0.025"
(replicate 1 Nothing ++ map Just [2,8,14,20,27,34,41,48,55,62,69,76,83,90,98,105,112,119,127])
[mannWhitneyUCriticalValue (20,x) (mkPValue 0.025) | x <- [1..20]]
]
where
test n (a, b, c, d)
= testCase "Mann-Whitney" $ do
assertEqual ("Mann-Whitney U " ++ show n) c us
assertEqual ("Mann-Whitney U Sig " ++ show n) d ss
where
us = mannWhitneyU (U.fromList a) (U.fromList b)
ss = mannWhitneyUSignificant SamplesDiffer (length a, length b) p005 us
-- List of (Sample A, Sample B, (Positive Rank, Negative Rank))
testData :: [([Double], [Double], (Double, Double), Maybe TestResult)]
testData = [ ( [3,4,2,6,2,5]
, [9,7,5,10,6,8]
, (2, 34)
, Just Significant
)
, ( [540,480,600,590,605]
, [760,890,1105,595,940]
, (2, 23)
, Just Significant
)
, ( [19,22,16,29,24]
, [20,11,17,12]
, (17, 3)
, Just NotSignificant
)
, ( [126,148,85,61, 179,93, 45,189,85,93]
, [194,128,69,135,171,149,89,248,79,137]
, (35,65)
, Just NotSignificant
)
, ( [1..30]
, [1..30]
, (450,450)
, Just NotSignificant
)
, ( [1 .. 30]
, [11.5 .. 40 ]
, (190.0,710.0)
, Just Significant
)
]
wilcoxonSumTests :: [Tst.Test]
wilcoxonSumTests = zipWith test [(0::Int)..] testData
where
test n (a, b, c) = testCase "Wilcoxon Sum"
$ assertEqual ("Wilcoxon Sum " ++ show n) c (wilcoxonRankSums (U.fromList a) (U.fromList b))
-- List of (Sample A, Sample B, (Positive Rank, Negative Rank))
testData :: [([Double], [Double], (Double, Double))]
testData = [ ( [8.50,9.48,8.65,8.16,8.83,7.76,8.63]
, [8.27,8.20,8.25,8.14,9.00,8.10,7.20,8.32,7.70]
, (75, 61)
)
, ( [0.45,0.50,0.61,0.63,0.75,0.85,0.93]
, [0.44,0.45,0.52,0.53,0.56,0.58,0.58,0.65,0.79]
, (71.5, 64.5)
)
]
wilcoxonPairTests :: [Tst.Test]
wilcoxonPairTests = zipWith test [(0::Int)..] testData ++
-- Taken from the Mitic paper:
[ testAssertion "Sig 16, 35" (to4dp 0.0467 $ wilcoxonMatchedPairSignificance 16 35)
, testAssertion "Sig 16, 36" (to4dp 0.0523 $ wilcoxonMatchedPairSignificance 16 36)
, testEquality "Wilcoxon critical values, p=0.05"
(replicate 4 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,30,35,41,47,53,60,67,75,83,91,100,110,119])
[wilcoxonMatchedPairCriticalValue x (mkPValue 0.05) | x <- [1..27]]
, testEquality "Wilcoxon critical values, p=0.025"
(replicate 5 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,29,34,40,46,52,58,65,73,81,89,98,107])
[wilcoxonMatchedPairCriticalValue x (mkPValue 0.025) | x <- [1..27]]
, testEquality "Wilcoxon critical values, p=0.01"
(replicate 6 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,43,49,55,62,69,76,84,92])
[wilcoxonMatchedPairCriticalValue x (mkPValue 0.01) | x <- [1..27]]
, testEquality "Wilcoxon critical values, p=0.005"
(replicate 7 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,42,48,54,61,68,75,83])
[wilcoxonMatchedPairCriticalValue x (mkPValue 0.005) | x <- [1..27]]
]
where
test n (a, b, c) = testEquality ("Wilcoxon Paired " ++ show n) c res
where res = wilcoxonMatchedPairSignedRank (U.zip (U.fromList a) (U.fromList b))
-- List of (Sample A, Sample B, (Positive Rank, Negative Rank))
testData :: [([Double], [Double], (Int,Double, Double))]
testData = [ ([1..10], [1..10], (0, 0, 0 ))
, ([1..5], [6..10], (5, 0, 5*(-3)))
-- Worked example from the Internet:
, ( [125,115,130,140,140,115,140,125,140,135]
, [110,122,125,120,140,124,123,137,135,145]
, ( 9
, sum $ filter (> 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]
, sum $ filter (< 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]
)
)
-- Worked examples from books/papers:
, ( [2.4,1.9,2.3,1.9,2.4,2.5]
, [2.0,2.1,2.0,2.0,1.8,2.0]
, (6, 18, -3)
)
, ( [130,170,125,170,130,130,145,160]
, [120,163,120,135,143,136,144,120]
, (8, 27, -9)
)
, ( [540,580,600,680,430,740,600,690,605,520]
, [760,710,1105,880,500,990,1050,640,595,520]
, (9, 3, -42)
)
]
to4dp tgt (pValue -> x) = x >= tgt - 0.00005 && x < tgt + 0.00005
----------------------------------------------------------------
kruskalWallisRankTests :: [Tst.Test]
kruskalWallisRankTests = zipWith test [(0::Int)..] testData
where
test n (a, b) = testCase "Kruskal-Wallis Ranking"
$ assertEqual ("Kruskal-Wallis " ++ show n) (map U.fromList b) (kruskalWallisRank $ map U.fromList a)
testData :: [([[Int]],[[Double]])]
testData = [ ( [ [68,93,123,83,108,122]
, [119,116,101,103,113,84]
, [70,68,54,73,81,68]
, [61,54,59,67,59,70]
]
, [ [8.0,14.0,16.0,19.0,23.0,24.0]
, [15.0,17.0,18.0,20.0,21.0,22.0]
, [1.5,8.0,8.0,10.5,12.0,13.0]
, [1.5,3.5,3.5,5.0,6.0,10.5]
]
)
]
kruskalWallisTests :: [Tst.Test]
kruskalWallisTests = zipWith test [(0::Int)..] testData
where
test n (a, b, c) = testCase "Kruskal-Wallis" $ do
assertEqual ("Kruskal-Wallis " ++ show n) (round100 b) (round100 kw)
assertEqual ("Kruskal-Wallis Sig " ++ show n) c kwt
where
kw = kruskalWallis $ map U.fromList a
kwt = isSignificant p005 `fmap` kruskalWallisTest (map U.fromList a)
round100 :: Double -> Integer
round100 = round . (*100)
testData :: [([[Double]], Double, Maybe TestResult)]
testData = [ ( [ [68,93,123,83,108,122]
, [119,116,101,103,113,84]
, [70,68,54,73,81,68]
, [61,54,59,67,59,70]
]
, 16.03
, Just Significant
)
, ( [ [5,5,3,5,5,5,5]
, [5,5,5,5,7,5,5]
, [5,5,6,5,5,5,5]
, [4,5,5,5,6,5,5]
]
, 2.24
, Just NotSignificant
)
, ( [ [36,48,5,67,53]
, [49,33,60,2,55]
, [71,31,140,59,42]
]
, 1.22
, Just NotSignificant
)
, ( [ [6,38,3,17,11,30,15,16,25,5]
, [34,28,42,13,40,31,9,32,39,27]
, [13,35,19,4,29,0,7,33,18,24]
]
, 6.10
, Just Significant
)
]
----------------------------------------------------------------
-- K-S test
----------------------------------------------------------------
kolmogorovSmirnovDTest :: [Tst.Test]
kolmogorovSmirnovDTest =
[ testAssertion "K-S D statistics" $
and [ eq 1e-6 (kolmogorovSmirnovD standard (toU sample)) reference
| (reference,sample) <- tableKSD
]
, testAssertion "K-S 2-sample statistics" $
and [ eq 1e-6 (kolmogorovSmirnov2D (toU xs) (toU ys)) reference
| (reference,xs,ys) <- tableKS2D
]
, testAssertion "K-S probability" $
and [ eq 1e-14 (kolmogorovSmirnovProbability n d) p
| (d,n,p) <- testData
]
]
where
toU = U.fromList
-- Test data for the calculation of cumulative probability
-- P(D[n] < d).
--
-- Test data is:
-- (D[n], n, p)
-- Table is generated using sample program from paper
testData :: [(Double,Int,Double)]
testData =
[ (0.09 , 3, 0 )
, (0.2 , 3, 0.00177777777777778 )
, (0.301 , 3, 0.116357025777778 )
, (0.392 , 3, 0.383127210666667 )
, (0.5003 , 3, 0.667366306558667 )
, (0.604 , 3, 0.861569877333333 )
, (0.699 , 3, 0.945458198 )
, (0.802 , 3, 0.984475216 )
, (0.9 , 3, 0.998 )
, (0.09 , 5, 0 )
, (0.2 , 5, 0.0384 )
, (0.301 , 5, 0.33993786080016 )
, (0.392 , 5, 0.66931908083712 )
, (0.5003 , 5, 0.888397260183794 )
, (0.604 , 5, 0.971609957879808 )
, (0.699 , 5, 0.994331075994008 )
, (0.802 , 5, 0.999391366368064 )
, (0.9 , 5, 0.99998 )
, (0.09 , 8, 3.37615237575e-06 )
, (0.2 , 8, 0.151622071801758 )
, (0.301 , 8, 0.613891042670582 )
, (0.392 , 8, 0.871491561427005 )
, (0.5003 , 8, 0.977534089199071 )
, (0.604 , 8, 0.997473116268255 )
, (0.699 , 8, 0.999806082005123 )
, (0.802 , 8, 0.999995133786947 )
, (0.9 , 8, 0.99999998 )
, (0.09 , 10, 3.89639433093119e-05)
, (0.2 , 10, 0.25128096 )
, (0.301 , 10, 0.732913126355935 )
, (0.392 , 10, 0.932185254518767 )
, (0.5003 , 10, 0.992276179340446 )
, (0.604 , 10, 0.999495533516769 )
, (0.699 , 10, 0.999979691783985 )
, (0.802 , 10, 0.999999801409237 )
, (0.09 , 20, 0.00794502217168886 )
, (0.2 , 20, 0.647279826376584 )
, (0.301 , 20, 0.958017466965765 )
, (0.392 , 20, 0.997206424843499 )
, (0.5003 , 20, 0.999962641414228 )
, (0.09 , 30, 0.0498147538075168 )
, (0.2 , 30, 0.842030838984526 )
, (0.301 , 30, 0.993403560017612 )
, (0.392 , 30, 0.99988478803318 )
, (0.09 , 100, 0.629367974413669 )
]
p005 :: PValue Double
p005 = mkPValue 0.05