-- 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 Test.Framework (Test, testGroup) import Test.Framework.Providers.HUnit 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 :: Test tests = testGroup "Nonparametric tests" \$ concat [ mannWhitneyTests , wilcoxonSumTests , wilcoxonPairTests , kruskalWallisRankTests , kruskalWallisTests , 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 ---------------------------------------------------------------- kruskalWallisRankTests :: [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 = [ ( [ [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 :: [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 = kruskalWallisTest 0.05 \$ map U.fromList a round100 :: Double -> Integer round100 = round . (*100) 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 :: [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 ) ]