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38 lines
22 KiB
SQL
38 lines
22 KiB
SQL
/*Check only p-value first*/
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (27.5,27.1), (21.0,22.0), (19.0,20.8), (23.6,23.4), (17.0,23.4), (17.9,23.5), (16.9,25.8), (20.1,22.0), (21.9,24.8), (22.6,20.2), (23.1,21.9), (19.6,22.1), (19.0,22.9), (21.7,20.5), (21.4,24.4);
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SELECT '0.021378001462867';
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SELECT roundBankers(WelchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (30.02,29.89), (29.99,29.93), (30.11,29.72), (29.97,29.98), (30.01,30.02), (29.99,29.98);
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SELECT '0.090773324285671';
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SELECT roundBankers(WelchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (0.010268,0.159258), (0.000167,0.136278), (0.000167,0.122389);
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SELECT '0.00339907162713746';
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SELECT roundBankers(WelchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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/*Check t-stat and p-value and compare it with scipy.stat implementation
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First: a=10, sigma (not sigma^2)=5, size=500
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Second: a=10, sigma = 10, size = 500 */
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (14.72789,-8.65656), (9.61661,22.98234), (13.57615,23.80821), (3.98392,13.33939), (11.98889,-4.05537), (10.99422,23.5155), (5.44792,-6.45272), (20.29346,17.7903), (7.05926,11.463), (9.22732,5.28021), (12.06847,8.39157), (13.52612,6.02464), (8.24597,14.43732), (9.35245,15.76584), (10.12297,1.54391), (15.80624,1.24897), (13.68613,27.1507), (10.72729,7.71091), (5.62078,15.71846), (6.12229,32.97808), (6.03801,-1.79334), (8.95585,-9.23439), (24.04613,11.27838), (9.04757,0.72703), (2.68263,18.51557), (15.43935,9.16619), (2.89423,17.29624), (4.01423,-1.30208), (4.30568,-3.48018), (11.99948,10.12082), (8.40574,-8.01318), (10.86642,-14.22264), (9.4266,16.58174), (-8.12752,-0.55975), (7.91634,5.61449), (7.3967,1.44626), (2.26431,7.89158), (14.20118,1.13369), (6.68233,-0.82609), (15.46221,12.23365), (7.88467,12.45443), (11.20011,14.46915), (8.92027,13.72627), (10.27926,18.41459), (5.14395,29.66702), (5.62178,1.51619), (12.84383,10.40078), (9.98009,3.33266), (-0.69789,6.12036), (11.41386,11.86553), (7.76863,6.59422), (7.21743,22.0948), (1.81176,1.79623), (9.43762,14.29513), (19.22117,19.69162), (2.97128,-7.98033), (14.32851,5.48433), (7.54959,-2.28474), (3.81545,9.91876), (10.1281,10.64097), (2.48596,0.22523), (10.0461,17.01773), (3.59714,22.37388), (9.73522,14.04215), (18.8077,23.1244), (3.15148,18.96958), (12.26062,8.42663), (5.66707,3.7165), (6.58623,14.29366), (17.30902,23.50886), (9.91391,26.33722), (5.36946,26.72396), (15.73637,13.26287), (16.96281,12.97607), (11.54063,17.41838), (18.37358,8.63875), (11.38255,17.08943), (10.53256,23.15356), (8.08833,-4.4965), (16.27556,7.58895), (2.42969,26.04074), (9.56127,6.84245), (7.32998,20.56287), (9.19511,3.84735), (9.66903,-2.76304), (4.15029,13.1615), (8.83511,8.21954), (14.60617,-3.49943), (14.06143,22.12419), (5.39556,7.08323), (10.11871,16.12937), (10.56619,-0.32672), (14.4462,16.5942), (10.42106,7.68977), (7.75551,11.39484), (11.00418,-5.11987), (4.47226,20.87404), (16.35461,8.01007), (18.55174,3.26497), (11.82044,5.61253), (7.39454,20.69182), (11.27767,0.0296), (6.83827,21.904), (7.76858,22.46572), (15.97614,3.63685), (14.53781,-5.10846), (12.99546,14.86389), (16.91151,5.47188), (9.65012,18.44095), (14.25487,16.71368), (14.03618,6.36704), (2.57382,8.82663), (2.50779,14.6727), (14.24787,7.98383), (13.34666,2.65568), (7.31102,21.45827), (10.22981,11.77948), (17.4435,4.71979), (21.2074,3.17951), (6.64191,13.90226), (18.7086,15.50578), (14.78686,10.8026), (9.85287,16.91369), (4.48263,9.90552), (14.17469,13.87322), (14.4342,4.12366), (19.2481,-3.78985), (3.47165,1.7599), (8.28712,3.43715), (8.81657,-3.45246), (0.92319,23.64571), (20.41106,-4.96877), (6.76127,3.93514), (22.00242,1.49914), (8.66129,12.71519), (10.9929,5.11521), (17.95494,4.79872), (17.20996,20.89391), (12.18888,5.363), (12.14257,8.02765), (15.81243,14.30804), (4.43362,11.49002), (1.17567,14.25281), (15.60881,7.6573), (9.34833,15.49686), (6.33513,3.29327), (-0.83095,2.27236), (12.43268,12.58104), (6.63207,19.19128), (11.96877,15.25901), (14.81029,6.5221), (21.84876,10.10965), (3.75896,12.75249), (6.91307,16.50977), (13.73015,-8.6697), (8.63753,8.28553), (15.71679,1.44315), (1.74565,4.65869), (9.16895,0.98149), (5.70685,0.16623), (5.00117,17.66332), (13.06888,4.35346), (7.51204,6.52742), (15.34885,-1.06631), (5.20264,-5.28454), (8.59043,14.25583), (6.45619,8.74058), (14.61979,1.89553), (11.7075,-0.92959), (14.04901,10.30289), (4.20525,-6.3744), (15.1733,-8.1706), (3.12934,10.95369), (8.08049,4.94384), (15.41273,28.40568), (16.90751,3.7004), (5.86893,2.52363), (7.1086,4.07997), (4.418,7.8849), (12.0614,17.95409), (7.07887,16.67021), (3.61585,11.34377), (11.73001,-0.07446), (10.80449,22.00223), (8.40311,3.31778), (9.91276,18.50719), (16.4164,-3.58655), (5.25034,6.5394), (15.20283,12.40459), (10.42909,16.59866), (9.53888,7.54176), (14.68939,-1.51044), (6.60007,12.69758), (18.31058,2.9842), (7.01885,2.49187), (18.71631,2.04113), (10.50002,-2.46544), (10.7517,15.18368), (4.23224,-0.04058), (2.28924,-0.4127), (8.56059,10.5526), (8.25095,12.03982), (9.15673,12.10923), (13.28409,11.54954), (8.4513,-1.18613), (2.83911,11.30984), (2.79676,23.54105), (9.11055,10.67321), (7.18529,24.09196), (-4.1258,7.5008), (5.28306,12.52233), (6.82757,4.30673), (10.89035,9.35793), (5.24822,4.44472), (11.935,-7.00679), (6.45675,8.56241), (10.18088,23.73891), (4.9932,15.62708), (18.09939,16.09205), (8.11738,12.52074), (5.37883,14.58927), (10.50339,-4.80187), (16.64093,8.47964), (14.77263,7.75477), (13.71385,12.6893), (6.98746,7.14147), (10.74635,12.12654), (5.49432,12.32334), (13.46078,7.98909), (10.67565,3.26652), (9.0291,20.53684), (11.51417,32.3369), (13.07118,19.74911), (9.5049,-4.62897), (8.50611,8.26483), (6.47606,20.88451), (13.06526,-2.12982), (19.08658,25.61459), (9.49741,5.32091), (10.60865,-4.1196), (2.28996,7.57937), (8.12846,21.15847), (5.62241,6.46355), (4.07712,7.74846), (17.98526,19.62636), (9.466,28.34629), (11.38904,26.73919), (5.91826,20.40427), (1.52059,3.03378), (18.79161,10.2537), (18.20669,7.47745), (-1.67829,10.79184), (18.01586,3.91962), (16.31577,19.97973), (7.88281,18.87711), (8.46179,12.56157), (10.31113,11.46033), (14.88377,3.78661), (1.31835,-9.45748), (2.53176,12.06033), (9.48625,-0.74615), (3.97936,13.2815), (11.52319,24.78052), (13.24178,5.83337), (7.58739,17.4111), (10.00959,19.70331), (9.73361,11.78446), (8.35716,-1.366), (1.65491,1.37458), (11.11521,16.31483), (6.08355,32.63464), (10.04582,-3.79736), (11.58237,19.17984), (16.40249,-0.27705), (1.9691,-3.69456), (13.22776,28.38058), (2.67059,-1.36876), (9.83651,-25.63301), (2.12539,3.58644), (9.27114,-6.85667), (9.0699,13.42225), (2.78179,12.04671), (12.49311,28.99468), (12.97662,7.87662), (15.06359,2.61119), (16.91565,-3.56022), (5.92011,1.50022), (5.81304,14.55836), (8.46425,9.35831), (9.48705,16.9366), (4.68191,29.23126), (5.70028,15.31386), (-0.78798,13.46112), (10.03442,7.39667), (15.45433,11.15599), (9.43845,9.80499), (3.05825,22.64923), (6.92126,8.67693), (14.05905,18.67335), (19.71579,-3.19127), (15.0131,22.94716), (4.50386,17.86834), (1.31061,16.98267), (10.81197,15.91653), (14.32942,11.79718), (9.26469,18.50208), (7.27679,8.90755), (22.69295,10.44843), (12.03763,4.67433), (7.34876,6.82287), (16.60689,10.82228), (7.48786,-4.18631), (15.78602,20.3872), (17.21048,11.84735), (13.93482,21.25376), (9.69911,10.55032), (12.24315,12.19023), (10.58131,0.63369), (19.57006,7.92381), (9.8856,17.90933), (11.70302,15.30781), (7.89864,10.01877), (12.24831,0.88744), (16.93707,22.20967), (9.65467,-4.23117), (4.221,21.50819), (15.45229,11.27421), (12.83088,-16.23179), (7.58313,33.43085), (12.895,5.15093), (10.02471,1.34505), (13.36059,6.027), (5.07864,-10.43035), (9.72017,27.45998), (11.05809,19.24886), (15.28528,-4.44761), (13.99834,5.453), (19.26989,12.73758), (9.41846,11.2897), (11.65425,31.032), (8.49638,7.39168), (6.38592,11.95245), (-4.69837,26.279), (12.22061,-1.0255), (9.41331,10.36675), (13.2075,11.58439), (12.97005,27.8405), (11.44352,13.1707), (9.79805,31.39133), (6.93116,27.08301), (10.07691,-2.14368), (22.05892,4.08476), (7.80353,21.5573), (-2.17276,16.69822), (0.61509,7.69955), (8.35842,8.32793), (17.77108,6.49235), (14.70841,-7.3284), (1.27992,10.58264), (15.62699,-6.17006), (9.32914,34.55782), (15.41866,10.93221), (10.82009,44.24299), (3.29902,14.6224), (9.21998,-7.42798), (7.93845,15.52351), (10.33344,11.33982), (12.06399,10.46716), (5.5308,13.0986), (8.38727,-4.25988), (18.11104,9.55316), (8.86565,0.75489), (19.41825,25.99212), (9.52376,-0.81401), (3.94552,3.49551), (9.37587,22.99402), (15.44954,10.99628), (15.90527,23.70223), (13.18927,2.71482), (7.01646,22.82309), (9.06005,31.25686), (9.06431,4.86318), (5.76006,-1.06476), (9.18705,15.10298), (-3.48446,-0.61015), (15.89817,17.81246), (12.94719,-1.55788), (23.69426,18.09709), (17.47755,9.11271), (15.61528,9.94682), (0.54832,-7.33194), (14.32916,-4.67293), (9.55305,21.81717), (13.79891,7.16318), (0.82544,13.25649), (13.34875,13.88776), (9.07614,4.95793), (5.19621,17.65303), (2.1451,14.47382), (9.87726,13.19373), (8.45439,31.86093), (-1.41842,5.73161), (7.93598,10.96492), (11.23151,6.97951), (17.84458,1.75136), (7.02237,10.96144), (10.7842,15.08137), (4.42832,9.95311), (4.45044,7.07729), (1.50938,3.08148), (21.21651,22.37954), (6.2097,8.51951), (6.84354,2.88746), (18.53804,26.73509), (12.01072,-2.88939), (4.8345,-2.82367), (20.41587,-0.35783), (14.48353,14.22076), (8.71116,11.50295), (12.42818,7.10171), (14.89244,8.28488), (8.03033,0.54178), (5.25917,13.8022), (2.30092,15.62157), (10.22504,10.79173), (15.37573,28.18946), (7.13666,30.43524), (4.45018,2.54914), (10.18405,9.89421), (3.91025,13.08631), (14.52304,4.68761), (13.14771,5.61516), (11.99219,22.88072), (9.21345,7.4735), (8.85106,11.27382), (12.91887,2.39559), (15.62308,-3.31889), (11.88034,9.61957), (15.12097,23.01381), (11.58168,-1.23467), (16.83051,9.07691), (5.25405,15.78056), (2.19976,12.28421), (4.56716,9.44888), (16.46053,13.16928), (5.61995,4.33357), (8.67704,2.21737), (5.62789,33.17833), (9.84815,13.25407), (13.05834,-2.47961), (11.74205,6.41401), (3.88393,18.8439), (16.15321,-4.63375), (4.83925,-8.2909), (13.00334,12.18221), (4.4028,-2.95356), (4.35794,19.61659), (4.47478,12.45056), (2.38713,-4.17198), (4.25235,21.9641), (10.87509,11.96416), (9.82411,12.74573), (13.61518,10.47873), (10.25507,12.73295), (4.0335,11.31373), (10.69881,9.9827), (5.70321,5.87138), (6.96244,4.24372), (9.35874,-23.72256), (6.28076,28.41337), (8.29015,4.88103), (6.88653,3.61902), (7.70687,8.93586), (8.2001,16.40759), (6.73415,27.84494), (3.82052,5.6001), (3.94469,14.51379), (15.82384,13.5576), (2.54004,12.92213), (10.74876,3.90686), (12.60517,17.07104), (17.7024,15.84268), (4.6722,17.38777), (13.67341,16.54766), (6.4565,5.94487), (12.95699,17.02804), (4.56912,7.66386), (5.58464,10.43088), (4.0638,6.16059), (13.05559,20.46178), (5.38269,20.02888), (0.16354,20.95949), (7.23962,6.50808), (7.38577,7.22366), (8.50951,8.06659), (13.72574,16.08241), (17.80421,13.83514), (3.01135,-0.33454), (8.02608,12.98848), (14.23847,12.99024);
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SELECT '-0.5028215369186904', '0.6152361677168877';
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SELECT roundBankers(WelchTTest(left, right).1, 16) as t_stat, roundBankers(WelchTTest(left, right).2, 16) as p_value from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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/*Check t-stat and p-value and compare it with scipy.stat implementation
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First: a=10, sigma (not sigma^2)=5, size=500
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Second: a=1, sigma = 12, size = 500 */
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (4.82025,-2.69857), (6.13896,15.80943), (15.20277,7.31555), (14.15351,3.96517), (7.21338,4.77809), (8.55506,9.6472), (13.80816,-26.41717), (11.28411,-10.85635), (7.4612,-1.4376), (7.43759,-0.96308), (12.9832,2.84315), (-5.74783,5.79467), (12.47114,-3.06091), (15.14223,-14.62902), (3.40603,22.08022), (9.27323,-2.11982), (7.88547,-4.84824), (8.56456,-10.50447), (4.59731,2.4891), (7.91213,9.90324), (7.33894,-22.66866), (21.74811,-0.97103), (11.92111,-16.57608), (0.18828,-3.78749), (10.47314,25.84511), (20.37396,5.30797), (11.04991,-18.19466), (13.30083,11.72708), (14.28065,0.2891), (2.86942,-9.83474), (24.96072,6.69942), (14.20164,18.09604), (18.28769,18.52651), (10.50949,1.38201), (9.22273,7.64615), (11.77608,17.66598), (8.56872,-2.44141), (13.74535,-9.01598), (11.65209,27.69142), (12.51894,4.06946), (17.76256,-15.0077), (13.52122,-10.49648), (8.70796,-4.88322), (6.04749,-25.09805), (16.33064,-4.64024), (8.35636,20.94434), (14.03496,24.12126), (11.05834,-14.10962), (14.49261,10.6512), (2.59383,14.50687), (8.01022,-19.88081), (4.05458,-11.55271), (13.26384,13.16921), (14.62058,16.63864), (10.52489,-24.08114), (8.46357,-9.09949), (6.4147,-10.54702), (9.70071,0.20813), (12.47581,8.19066), (4.38333,-2.70523), (17.54172,-0.23954), (10.12109,7.19398), (7.73186,-7.1618), (14.0279,-7.44322), (11.6621,-17.92031), (17.47045,-1.58146), (15.50223,9.18338), (15.46034,3.25838), (13.39964,-14.30234), (14.98025,1.84695), (15.87912,31.13794), (17.67374,-0.85067), (9.64073,19.02787), (12.84904,-3.09594), (7.70278,13.45584), (13.03156,-5.48104), (9.04512,-22.74928), (15.97014,-8.03697), (8.96389,17.31143), (11.48009,-16.65231), (9.71153,-18.58713), (13.00084,-16.52641), (12.39803,14.95261), (13.08188,12.56762), (5.82244,15.00188), (10.81871,1.85858), (8.2539,2.1926), (7.52114,-2.4095), (9.11488,21.56873), (8.37482,3.35509), (14.48652,-4.98672), (11.42152,35.08603), (16.03111,-10.01602), (13.14057,-3.85153), (-2.26351,-6.81974), 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(6.02364,-20.46391), (8.86984,5.74179), (10.91177,-15.83178), (10.04418,14.90454), (18.10774,-8.84645), (7.49384,3.72036), (9.11556,4.6877), (9.7051,16.35418), (5.23268,3.15441), (9.04647,2.39907), (8.81547,-17.58664), (2.65098,-13.18269);
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SELECT '14.971190998235835', '5.898143508382202e-44';
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SELECT roundBankers(WelchTTest(left, right).1, 16) as t_stat, roundBankers(WelchTTest(left, right).2, 16) as p_value from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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