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-- Tests for Statistics.Test.NonParametric
module Tests.NonparametricTest (
nonparametricTests
) where
import qualified Data.Vector.Unboxed as U
import Test.HUnit (assertEqual)
import Test.Framework
import Test.Framework.Providers.HUnit
import Statistics.Test.MannWhitneyU
import Statistics.Test.WilcoxonT
import Tests.Helpers
import Tests.NonparametricTest.Table
import Statistics.Test.KolmogorovSmirnov
import Statistics.Distribution.Normal (standard)
nonparametricTests :: Test
nonparametricTests = testGroup "Nonparametric tests"
$ concat [ mannWhitneyTests
, wilcoxonSumTests
, wilcoxonPairTests
, kolmogorovSmirnovDTest
]
----------------------------------------------------------------
mannWhitneyTests :: [Test]
mannWhitneyTests = zipWith test [(0::Int)..] testData ++
[ testEquality "Mann-Whitney U Critical Values, m=1"
(replicate (20*3) Nothing)
[mannWhitneyUCriticalValue (1,x) 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) 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) 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) 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 TwoTailed (length a, length b) 0.05 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 :: [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 :: [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 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 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 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 0.005 | x <- [1..27]]
]
where
test n (a, b, c) = testEquality ("Wilcoxon Paired " ++ show n) c res
where res = (wilcoxonMatchedPairSignedRank (U.fromList a) (U.fromList b))
-- List of (Sample A, Sample B, (Positive Rank, Negative Rank))
testData :: [([Double], [Double], (Double, Double))]
testData = [ ([1..10], [1..10], (0, 0 ))
, ([1..5], [6..10], (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]
, ( 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]
, (18, -3)
)
, ( [130,170,125,170,130,130,145,160]
, [120,163,120,135,143,136,144,120]
, (27, -9)
)
, ( [540,580,600,680,430,740,600,690,605,520]
, [760,710,1105,880,500,990,1050,640,595,520]
, (3, -42)
)
]
to4dp tgt x = x >= tgt - 0.00005 && x < tgt + 0.00005
----------------------------------------------------------------
-- K-S test
----------------------------------------------------------------
kolmogorovSmirnovDTest :: [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 )
]
|
