ClickHouse/tests/queries/0_stateless/01322_student_ttest.sql

DROP TABLE IF EXISTS student_ttest;

/*Check t-stat and p-value and compare it with scipy.stat implementation
  First: a=1, sigma (not sigma^2)=5, size=500
  Second: a=1, sigma = 5, size = 500 */
CREATE TABLE student_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO student_ttest VALUES (0.88854,-2.90702), (-5.76966,3.61651), (6.76618,4.27458), (3.55546,4.82133), (-9.76948,9.59483), (4.92323,1.00424), (-0.36352,2.04147), (0.97018,-3.58214), (4.61656,6.59543), (-6.78292,-1.00532), (4.02008,-3.59794), (12.41838,-2.82434), (5.14417,-3.13194), (3.86836,9.90977), (-1.26199,0.523), (12.44106,4.62779), (3.28349,-2.56872), (1.77261,2.25807), (-8.94748,1.04044), (-1.01449,-2.35744), (-1.26377,10.81531), (6.79682,-9.68469), (6.32333,3.80885), (-8.21214,12.70435), (-1.68565,-6.01112), (9.7557,1.89065), (3.66694,5.08892), (1.39967,3.45254), (-5.52035,11.58151), (-10.95601,0.85035), (0.93877,8.38397), (1.45933,1.17169), (-5.40551,4.74621), (-0.83857,-1.66614), (8.50794,4.2414), (-6.68686,1.68765), (5.03099,1.85223), (1.56251,9.10111), (4.17381,-2.38085), (-2.92644,-14.79595), (5.11068,-3.8938), (2.09617,-3.41864), (11.7787,-3.15282), (6.50336,-0.56684), (0.62098,12.87997), (-7.97121,6.89115), (3.81902,12.921), (0.33151,-7.94908), (10.68584,2.45687), (0.56007,2.14957), (-7.38621,7.55081), (5.05882,-3.71534), (2.34616,-2.41064), (11.3806,-0.80734), (5.95276,-4.75651), (-3.01429,2.05241), (5.98169,-5.44523), (0.96985,-2.75054), (-1.15932,-13.00131), (2.11547,-2.74451), (2.49668,-1.39004), (-12.49569,-3.02854), (-4.94667,7.65112), (-3.64215,1.1245), (-8.35595,6.74117), (3.211,-0.75777), (2.33805,8.93451), (2.38608,-8.85559), (-3.2862,-0.36405), (-0.80454,4.02742), (-0.53483,6.88718), (10.66445,-1.05124), (-0.37619,3.04085), (0.48246,3.32368), (7.41919,1.147), (0.42414,3.41554), (-2.32335,-3.47851), (-0.70223,-0.47684), (-5.9332,-0.55605), (-1.20561,-0.17006), (3.39865,2.26218), (9.61739,12.45494), (-0.78651,-1.84097), (-4.00256,1.64934), (-7.99646,-7.07496), (8.72923,-9.99462), (0.71859,6.09954), (-1.62726,-1.05319), (5.11234,3.04757), (-0.95625,0.93899), (-3.75573,-4.63243), (1.03141,-7.43322), (-3.33588,-7.298), (1.51804,-6.59016), (-3.30935,-6.11649), (-1.97507,0.56682), (4.06456,2.00661), (3.27195,-2.79814), (-7.81761,2.84482), (-3.81785,3.65348), (-4.18311,-4.22807), (-11.33313,-4.54336), (-0.25221,-3.63343), (7.2514,2.96878), (5.30301,6.11661), (2.46762,-1.70919), (4.22716,-4.71133), (0.33916,6.09652), (9.7638,-6.83454), (-7.58684,0.18006), (-4.09888,1.51676), (4.26617,-5.31646), (-0.56744,-3.21215), (4.65125,-5.07599), (-1.30301,-2.36591), (4.53771,3.55724), (9.96929,4.8904), (3.72939,-3.22586), (-2.29818,-1.74928), (3.09417,5.73458), (0.82251,1.41188), (5.29975,2.86255), (2.8685,2.90179), (-5.73321,-2.19949), (-1.85651,1.72727), (-1.07984,1.76939), (9.78342,-0.12848), (-13.49652,-0.52), (3.68791,3.48333), (1.9998,7.8262), (1.11674,0.09099), (9.43869,7.77017), (4.07029,9.49484), (5.32715,1.42825), (7.16504,1.99624), (6.66096,4.00419), (-5.7111,1.07925), (-0.38575,-0.09987), (4.49165,-5.48733), (-3.36489,-1.83517), (7.71814,2.38059), (-1.58966,1.42075), (-1.61063,-1.11968), (-0.91602,-6.46035), (0.73459,7.66576), (-3.24463,4.6307), (6.3947,5.55989), (-2.77845,3.16684), (4.45899,5.07671), (-8.84186,-10.20566), (2.62276,-4.73386), (1.774,1.28353), (4.3692,6.75679), (0.05942,12.09895), (-1.44042,7.0049), (-2.53594,7.16156), (-2.24752,-0.64311), (4.98874,-0.66747), (4.05434,3.99996), (-2.56483,9.07298), (-6.79286,-4.60971), (-2.06165,0.70744), (-0.26056,2.56774), (1.89567,9.32424), (-3.15145,3.95087), (-7.31321,7.11372), (0.28936,-0.89284), (-0.63111,8.6155), (0.22611,-0.14141), (-9.3377,-4.86319), (-5.76638,-6.95801), (3.87306,4.44883), (6.7011,4.6156), (9.03915,-2.3579), (-1.21835,-5.1186), (0.82892,8.12819), (2.80656,2.78392), (-1.34746,-4.30221), (-1.99912,-1.47506), (0.6036,6.8598), (-3.46117,0.47636), (5.23732,0.95383), (-1.86702,7.79779), (-5.86115,-2.61767), (6.48523,-10.5087), (-7.40158,-2.74299), (-1.38913,3.87369), (4.94613,-1.07093), (-2.07818,4.98864), (2.39808,-7.50772), (4.89238,6.41316), (4.39481,1.39061), (5.20425,-3.1747), (13.62598,-2.13621), (-2.86293,-0.02203), (-3.62396,0.89025), (-4.28695,-5.87746), (4.66425,3.60026), (2.20871,-0.23178), (1.60382,-2.1897), (-9.87024,-5.85101), (-7.37302,-1.6053), (-4.17814,3.6184), (2.5148,-8.53795), (3.21708,-0.35987), (-11.48089,2.15301), (1.19821,-6.60692), (-0.07436,9.54341), (-1.10652,1.11511), (4.03395,2.94025), (-4.35883,12.05657), (2.04013,3.75156), (0.52264,7.95597), (8.14004,-0.99449), (-8.86949,0.90597), (-0.35807,-7.90627), (-10.71113,3.50863), (-2.13755,-1.47493), (0.50715,4.11671), (6.30826,10.06325), (2.37527,-1.06059), (0.20872,-1.37737), (-5.85729,-0.42542), (-4.97217,-3.90267), (-9.78434,9.35037), (-1.53277,-7.91219), (0.14827,-4.69945), (-1.053,3.63776), (1.74558,3.46492), (11.17194,2.84518), (9.35487,-3.04301), (-9.17209,8.82764), (10.41814,7.80134), (7.41206,7.87755), (3.71775,7.01035), (-2.04674,2.43271), (6.18037,11.36418), (5.6383,-6.92659), (-0.90058,5.95541), (-1.27073,3.59436), (-2.3473,5.18429), (-8.44271,4.20225), (2.75551,0.5029), (-1.15521,4.03074), (4.08722,5.23152), (-1.70399,10.65409), (7.24114,-0.69845), (-8.43976,11.70096), (-1.53052,5.80692), (-0.00526,-8.1819), (-4.04813,4.31485), (-2.84299,5.7227), (-5.201,5.67398), (7.75774,-1.75826), (-2.85791,7.54164), (-3.86071,-1.79026), (-1.80029,-1.7395), (-5.26015,5.65042), (-3.158,0.38765), (7.71014,-4.64719), (-4.84866,-10.22048), (-8.38785,-2.05447), (7.67021,-2.43441), (4.96521,-5.38551), (-0.40919,5.47764), (-3.25711,8.26637), (3.07685,-3.6421), (2.89376,-11.66269), (-10.47331,3.972), (-3.48942,5.46642), (1.13906,-3.72304), (-8.57454,5.75251), (-3.38963,5.12841), (-2.3195,0.59067), (-1.60694,5.21138), (-5.57406,-4.58702), (-0.93075,-8.737), (-11.76579,-2.12737), (10.68283,0.22888), (8.74324,-1.46448), (7.66409,2.40311), (4.76715,-5.21814), (0.44539,13.94749), (-1.35941,-2.77448), (4.18849,-3.7867), (-6.17097,3.4954), (0.27977,3.12586), (-1.45006,-7.01485), (-4.81694,-3.20727), (-3.0297,6.31415), (0.02145,2.37521), (2.46883,8.13787), (9.60317,2.15956), (-9.93898,-0.40842), (1.05549,-7.27283), (5.55366,4.27575), (-3.80722,-2.89126), (-4.18851,6.84344), (1.00351,7.0869), (3.11385,-5.18837), (-5.17623,2.67648), (-3.18396,-6.57021), (-6.65302,0.60429), (-0.50832,-1.04921), (-4.04375,7.12873), (4.52707,1.68973), (6.63124,-2.58404), (-3.72082,-3.83114), (5.79825,-7.26546), (-2.0158,-5.07153), (-2.78369,-0.80395), (-1.91821,2.09455), (6.31714,4.33374), (-1.80869,8.54335), (8.55586,0.80566), (2.40826,-8.38085), (-8.46361,7.54812), (5.04452,8.78007), (-0.84665,1.5857), (2.30903,8.43855), (-3.71837,-1.90846), (-0.69419,-1.2434), (3.6733,7.16172), (-1.96098,-3.44129), (2.36747,-6.37542), (-12.03622,-4.99486), (4.38481,4.99033), (2.93955,-1.83734), (2.16804,-2.83289), (-0.08218,-4.13997), (-3.97934,1.40163), (-7.43985,8.57867), (0.91666,-1.87639), (7.23432,3.41667), (-6.13303,6.31762), (-10.23217,1.58473), (-6.21681,1.63625), (-0.80934,-6.93618), (0.17914,3.58046), (2.13338,-6.8097), (6.97656,4.69978), (6.90455,-1.72912), (6.25943,5.29491), (-6.04019,-1.63062), (-7.30909,5.83818), (1.4589,17.0769), (12.00208,4.54301), (2.22457,-1.33801), (-2.45912,5.64339), (-6.92213,1.26913), (4.05547,-1.01553), (0.04709,4.8316), (-7.70952,3.08635), (-1.47883,-2.27738), (1.3701,-1.13761), (-4.92928,10.08698), (-2.75872,5.33827), (-0.09178,2.84345), (2.62642,-1.51132), (-1.14623,13.46078), (2.76609,8.58965), (4.94404,-2.36683), (-7.01764,-1.8217), (-10.91568,1.96981), (-2.49738,2.31718), (0.73576,3.66493), (2.25436,1.93104), (-1.72956,5.20332), (2.41054,3.20519), (5.72149,3.34631), (-6.41371,7.0087), (3.38217,-7.96126), (1.24133,-0.62182), (10.03634,-4.65227), (-2.37303,10.6572), (-1.35543,4.50891), (-1.4387,9.74298), (-4.0976,3.85707), (-0.82501,6.41144), (-1.93498,1.48649), (5.59955,2.28076), (5.46656,2.75342), (2.43568,-5.40401), (-0.23926,7.11389), (-4.9945,5.74368), (-4.96655,6.78345), (-0.59258,3.83773), (2.02497,0.70959), (0.67583,0.57434), (3.16522,1.5888), (-1.9673,3.94889), (-6.75319,5.8234), (-6.69723,7.78366), (0.81148,9.08354), (4.44531,-7.99182), (-4.43522,-2.77033), (-5.28602,-10.29342), (-3.58829,1.76251), (-7.97395,2.09266), (-2.84891,4.20614), (-3.95112,-3.63064), (3.54945,-2.17794), (12.12376,-2.66225), (-3.12347,-2.74707), (3.65209,-1.93431), (9.34031,1.38629), (-0.26348,4.12816), (-5.23968,-1.58902), (2.22336,-5.08864), (-10.70405,-2.30491), (-4.41319,2.64605), (-5.94912,1.16158), (1.8147,2.63534), (7.69287,1.4956), (9.46125,-4.60768), (4.72497,0.60771), (-0.57565,3.29549), (-1.12303,-1.42592), (2.90272,0.8883), (-4.4584,-1.10612), (4.28819,-2.57296), (11.64512,5.88085), (-1.80395,7.40745), (2.51605,13.48116), (-3.18439,5.53539), (-0.70213,-1.46014), (-7.68383,3.73304), (-8.32268,3.5435), (-8.71115,-3.89151), (9.96933,4.16265), (0.95675,2.32663), (3.35114,5.31735), (-2.66008,6.33485), (7.75456,2.1339), (0.73568,0.82708), (0.3483,-2.95155), (-1.09203,-6.76019), (-7.76963,-4.20179), (5.81902,8.78354), (-3.41424,1.41863), (-0.39209,7.65689), (4.67608,-6.52601), (0.68753,-4.4426), (5.17179,-4.49483), (4.98983,-3.91479), (-0.12659,-2.84562), (3.25267,2.58974), (1.50184,2.24424), (2.94507,-4.65846), (-0.42333,8.4062), (-3.66227,8.20262), (8.90812,-8.63752), (4.74411,4.97966), (2.22018,-0.35563), (-2.07976,-4.72116), (4.8711,-2.95997), (0.5023,2.73959), (6.31569,-0.23956), (-4.36903,10.13915), (3.82146,11.83775), (-6.99477,-2.50332), (3.61225,-0.58181), (14.69335,-7.62836), (0.58368,2.26478), (4.65341,-3.50179), (-3.14272,-2.08023), (2.67048,4.07256), (4.64963,-1.40826), (-2.70828,-2.33644), (1.42923,3.00197), (5.84498,4.23668), (-4.76568,-2.24647), (0.19907,1.0445), (1.67486,-0.31901), (5.32145,8.62657), (-8.03477,3.92817), (3.46776,0.08462), (4.66374,10.15884), (-5.37394,0.4113), (5.39045,4.45847), (-1.44756,5.82941), (-1.64419,6.59202), (3.39699,-3.73441), (-2.94659,-5.86969), (-2.38437,-4.56543), (-0.23958,-1.32636), (6.88389,-0.17884), (-2.7172,-3.56181), (-1.53419,-0.66932), (7.38841,6.87538), (-5.44178,0.73527), (-0.89287,-0.24177), (2.93546,-0.8657), (-0.26901,-0.22977), (-4.70044,1.02095), (2.25846,6.16311), (-9.28813,-5.68027), (6.04268,-3.7619), (4.41693,4.22959), (1.75714,-1.5249);
SELECT '-2.610898982580138', '0.00916587538237954';
SELECT roundBankers(StudentTTest(left, right).1, 16) as t_stat, roundBankers(StudentTTest(left, right).2, 16) as p_value from student_ttest;
DROP TABLE IF EXISTS student_ttest;

/*Check t-stat and p-value and compare it with scipy.stat implementation
  First: a=1, sigma (not sigma^2)=5, size=500
  Second: a=1, sigma = 5, size = 500 */
CREATE TABLE student_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO student_ttest VALUES (4.52546,8.69444), (3.73628,3.81414), (-0.39478,12.38442), (5.15633,8.9738), (0.50539,9.19594), (-5.34036,7.21009), (0.19336,4.97743), (8.35729,4.94756), (6.95818,19.80911), (-2.93812,13.75358), (8.30807,16.56373), (-3.3517,9.72882), (4.16279,4.64509), (-3.17231,17.76854), (1.93545,4.80693), (11.06606,8.79505), (-4.22678,10.88868), (-1.99975,6.21932), (-4.51178,15.11614), (-4.50711,13.24703), (1.89786,14.76476), (-6.19638,-0.6117), (-3.70188,17.48993), (5.01334,12.11847), (1.79036,4.87439), (2.14435,18.56479), (3.0282,1.23712), (2.35528,5.41596), (-12.18535,4.54994), (5.59709,11.37668), (-12.92336,9.5982), (-0.04281,6.59822), (-0.16923,1.16703), (0.88924,8.88418), (-4.68414,10.95047), (8.01099,5.52787), (2.61686,-1.11647), (-2.76895,14.49946), (3.32165,3.27585), (-0.85135,-0.42025), (1.21368,6.37906), (4.38673,2.5242), (6.20964,8.1405), (-1.23172,6.46732), (4.65516,9.89332), (-1.87143,10.4374), (0.86429,-1.06465), (2.51184,6.84902), (-1.88822,10.96576), (-1.61802,7.83319), (1.93653,14.39823), (-3.66631,7.02594), (-1.05294,13.46629), (-10.74718,10.39531), (16.49295,11.27348), (-7.65494,9.32187), (-3.39303,12.32667), (-4.89418,8.98905), (3.2521,9.54757), (0.05831,5.98325), (-3.00409,3.47248), (5.76702,9.26966), (2.67674,5.77816), (10.52623,6.32966), (-0.54501,9.49313), (-4.89835,6.21337), (3.52457,10.00242), (-0.0451,6.25167), (-6.61226,15.64671), (9.02391,2.78968), (5.52571,6.55442), (4.54352,3.68819), (-3.8394,9.55934), (-7.75295,4.166), (5.91167,12.32471), (1.38897,7.10969), (6.24166,16.31723), (5.58536,12.99482), (4.7591,10.11585), (-2.58336,10.29455), (-1.91263,18.27524), (3.31575,12.84435), (5.3507,13.11954), (-15.22081,12.84147), (-0.84775,15.55658), (-4.538,11.45329), (6.71177,7.50912), (0.52882,8.56226), (2.0242,8.63104), (5.69146,15.68026), (4.63328,21.6361), (0.22984,6.23925), (-2.84052,8.65714), (7.91867,9.9423), (1.11001,12.28213), (-0.11251,3.11279), (-0.20905,13.58128), (0.03287,16.51407), (-1.59397,16.60476), (-5.39405,12.02022), (-7.1233,12.11035), (4.51517,9.47832), (-0.70967,6.40742), (5.67299,8.87252), (-0.33835,15.14265), (-1.83047,2.23572), (-0.62877,11.57144), (-7.23148,18.87737), (0.1802,12.1833), (11.73325,11.17519), (2.17603,16.80422), (-0.11683,6.81423), (-1.29102,12.12546), (-0.23201,8.06153), (-6.8643,10.97228), (-6.85153,7.30596), (-4.77163,15.44026), (6.11721,8.00993), (5.96406,12.60196), (3.59135,13.96832), (-0.60095,14.03207), (3.11163,4.53758), (-0.18831,8.08297), (0.67657,4.90451), (-3.16117,8.14253), (0.26957,19.88605), (2.18653,13.85254), (-5.94611,23.01839), (-4.39352,6.02084), (-3.71525,9.60319), (5.11103,1.90511), (1.33998,10.35237), (1.01629,16.27082), (-3.36917,12.52379), (-3.99661,11.37435), (8.19336,13.61823), (2.89168,15.77622), (-11.10373,15.17254), (11.68005,6.711), (3.08282,4.74205), (-6.81506,10.09812), (-2.34587,6.61722), (-2.68725,10.34164), (0.3577,8.96602), (-3.05682,12.32157), (9.08062,11.75711), (-0.77913,13.49499), (10.35215,8.57713), (6.82565,11.50313), (-1.24674,1.13097), (5.18822,7.83205), (-3.70743,5.77957), (1.40319,15.5519), (5.89432,10.82676), (1.43152,11.51218), (6.70638,9.29779), (9.76613,9.77021), (4.27604,9.94114), (-2.63141,15.54513), (-7.8133,19.10736), (-0.06668,15.04205), (1.05391,9.03114), (4.41797,24.0104), (0.09337,9.94205), (6.16075,2.5925), (7.49413,8.82726), (-3.52872,10.0209), (-2.17126,8.1635), (-3.87605,4.24074), (3.26607,7.67291), (-3.28045,5.21642), (2.1429,11.2808), (1.53386,6.88172), (0.21169,5.98743), (-0.63674,17.97249), (5.84893,6.46323), (-0.63498,15.37416), (8.29526,2.89957), (-1.08358,17.13044), (-2.306,11.06355), (2.86991,3.09625), (-0.76074,-2.33019), (5.49191,7.42675), (1.82883,15.06792), (-3.70497,8.81116), (-0.53232,19.17446), (-11.49722,18.77181), (3.44877,14.06443), (-1.8596,12.81241), (-10.34851,2.72299), (1.13093,18.67739), (-10.93389,11.63275), (-3.39703,2.23891), (0.19749,13.01195), (-3.68389,7.43402), (-4.67863,8.14599), (10.78916,16.65328), (0.37675,1.362), (3.98094,3.87957), (-3.64775,11.16134), (-4.8443,6.25357), (1.102,4.21945), (8.72112,12.50047), (-1.47361,6.45486), (6.24183,18.99924), (6.83569,18.09508), (-3.11684,13.59528), (4.91306,3.39681), (-0.03628,13.33157), (5.1282,5.8945), (-2.38558,5.61212), (2.33351,8.41149), (-0.97191,13.78608), (-0.05588,6.08609), (-4.70019,12.76962), (-5.12371,3.26206), (0.65606,0.25528), (-0.11574,11.9083), (4.4238,4.35071), (6.93399,11.19855), (3.68712,13.87404), (-0.01187,6.87986), (1.8332,8.32566), (5.81322,22.51334), (-4.04709,2.5226), (-8.26397,16.84498), (-2.11273,6.26108), (5.28396,13.84824), (0.73054,6.03262), (6.43559,14.12668), (4.35565,16.01939), (-1.05545,8.19237), (5.00087,18.01595), (-2.72239,9.45609), (7.32313,6.90459), (2.11548,12.83115), (-3.40953,10.603), (6.97051,13.70439), (-0.45567,6.1633), (1.31699,4.1151), (-1.49871,8.20499), (7.14772,11.67903), (0.79277,7.30851), (6.9698,6.50941), (2.08733,7.3949), (-3.55962,12.80075), (0.75601,5.62043), (1.21,18.2542), (-2.17877,17.9393), (1.83206,16.4569), (5.72463,8.78811), (7.42257,4.85949), (0.97829,-3.36394), (7.54238,5.38683), (9.91081,12.26083), (-4.61743,10.27907), (-4.40799,11.5144), (9.99854,11.57335), (8.53725,1.94203), (3.2905,7.78228), (0.38634,11.79385), (-2.53374,10.18415), (4.94758,14.67613), (4.79624,4.70301), (5.57664,12.72151), (-6.44871,-3.35508), (3.34431,17.63775), (0.14209,2.53883), (10.88431,14.01483), (0.31846,12.4387), (-0.54703,11.15408), (-4.67791,7.74882), (-5.68011,13.60956), (-4.93362,7.81991), (1.2271,10.90969), (5.27512,8.19828), (-3.84611,-1.18523), (6.81706,0.5916), (10.33033,0.35805), (5.13979,12.98364), (3.66534,11.38628), (-2.07219,13.94644), (10.65442,2.03781), (-3.31751,10.74447), (-1.82011,12.35656), (-0.39886,7.08701), (1.77052,2.69871), (1.29049,19.66653), (7.92344,7.88636), (-2.92595,10.36916), (-2.67107,1.632), (5.64708,11.86081), (0.34639,13.47602), (-3.04356,6.60204), (3.98828,7.01303), (-1.36695,20.19992), (-8.48462,18.88249), (-4.04669,11.34367), (9.84561,12.97305), (-6.1537,9.5776), (0.82433,17.91364), (1.92449,18.3247), (2.51288,9.9211), (0.40965,7.14257), (2.89183,6.59133), (3.84347,12.35274), (0.66829,10.57523), (-3.45094,12.12859), (1.3544,9.47177), (-9.85456,0.60659), (5.25689,4.72996), (-5.26018,4.51121), (-6.16912,13.28893), (-1.77163,8.09014), (3.96687,8.02511), (0.70893,13.85406), (-5.45342,1.75412), (-3.89706,6.00641), (3.11868,6.35554), (4.41714,7.11293), (7.64841,8.30442), (0.00489,12.63024), (3.2263,12.38966), (-5.33042,7.6801), (2.52189,11.33744), (-7.40308,4.67713), (0.67891,7.62276), (2.49343,2.14478), (5.43133,15.32988), (-0.67541,1.52299), (-0.60299,17.00017), (-6.32903,8.29701), (-3.44336,10.92961), (-0.23963,6.78449), (6.94686,7.02698), (6.59442,11.51719), (-4.18532,9.97926), (-1.8228,7.44251), (-0.29443,7.58541), (2.99821,4.76058), (2.51942,12.88959), (-3.49176,9.974), (-0.57979,17.03689), (8.69471,11.14554), (-1.19427,11.7392), (-3.17119,11.50029), (-2.99566,19.41759), (-3.34493,9.65127), (-2.33826,9.87673), (-5.04164,14.13485), (-0.48214,9.78034), (7.45097,1.57826), (3.04787,3.72091), (2.92632,9.4054), (1.39694,23.22816), (4.38686,-0.12571), (3.25753,6.97343), (7.14218,10.09049), (-4.04341,11.78393), (-9.19352,3.01909), (2.78473,16.09448), (0.33331,6.25485), (9.89238,7.13164), (6.00566,7.75879), (-1.7511,9.56834), (4.77815,6.14824), (5.07457,13.53454), (2.56132,8.26364), (2.38317,8.7095), (-1.63486,10.61607), (-1.46871,10.64418), (-5.8681,23.9106), (-2.96227,11.38978), (-1.90638,11.4383), (-13.3052,18.41498), (-2.14705,3.70959), (-9.62069,19.95918), (2.29313,9.53847), (0.22162,14.04957), (-1.83956,13.70151), (4.1853,5.45046), (6.05965,10.95061), (-0.23737,9.55156), (6.07452,17.92345), (4.34629,6.23976), (4.02922,8.71029), (3.62622,13.58736), (-3.95825,8.78527), (-1.63412,11.14213), (-1.25727,12.23717), (5.06323,16.44557), (-0.66176,0.47144), (2.36606,9.7198), (-5.77792,13.50981), (4.535,14.27806), (1.02031,13.50793), (4.49345,7.47381), (-4.99791,11.07844), (2.46716,9.89844), (3.65471,21.48548), (11.2283,6.92085), (6.69743,4.44074), (-5.60375,19.98074), (0.28683,7.92826), (-0.85737,16.6313), (4.26726,17.17618), (-3.4322,13.80807), (-2.07039,5.37083), (-2.26798,9.73962), (-0.99818,10.66273), (0.41335,8.90639), (5.18124,12.24596), (-5.01858,16.89203), (2.05561,12.69184), (-0.12117,15.59077), (0.99471,6.94287), (6.89979,-0.1801), (-4.18527,3.25318), (-6.35104,8.08804), (3.89734,13.78384), (-1.979,0.46434), (3.15404,7.78224), (3.52672,9.10987), (2.48372,-0.89391), (-6.13089,14.3696), (2.2968,3.01763), (-2.74324,8.03559), (-0.12876,7.24609), (-1.51135,11.86271), (-3.92434,6.28196), (-1.71254,8.9725), (-1.25878,14.46114), (2.03021,9.50216), (4.31726,16.30413), (-3.02908,1.02795), (9.7093,1.88717), (-3.36284,9.80106), (6.70938,4.53487), (0.42762,16.34543), (5.04726,7.71098), (2.78386,2.74639), (6.83022,6.51875), (-3.02109,10.42308), (-0.65382,13.57901), (-15.58675,0.52784), (5.89746,4.4708), (-4.11598,6.39619), (-1.37208,14.57666), (10.08082,2.71602), (5.35686,12.53905), (1.93331,11.4292), (10.47444,12.44641), (-2.36872,14.50894), (6.50752,17.64374), (2.54603,11.03218), (-0.4332,9.82789), (5.26572,10.11104), (2.09016,2.16137), (1.15513,10.24054), (14.95941,12.86909), (-3.85505,15.22845), (-2.36239,5.05411), (1.64338,10.84836), (-4.25074,11.15717), (7.29744,0.91782), (-1.18964,13.29961), (5.60612,15.11314), (-3.77011,11.54004), (6.67642,-0.94238), (-0.06862,19.32581), (5.60514,10.20744), (3.7341,6.54857), (9.59001,8.69108), (3.30093,8.2296), (-2.75658,8.4474), (4.71994,6.81178), (0.74699,5.99415), (2.91095,13.99336), (-7.36829,8.7469), (-5.29487,8.62349), (3.31079,1.84212), (1.06974,4.4762), (-1.18424,9.25421), (-7.415,10.44229), (3.40595,12.21649), (-7.63085,10.45968), (1.13336,15.34722), (-0.0096,5.50868), (0.8928,10.93609), (-0.5943,2.78631), (7.48306,11.86145), (10.11943,18.67385), (5.60459,10.64051), (4.00189,12.75565), (2.35823,6.63666), (0.33475,12.19343), (3.47072,9.08636), (-6.68867,11.67256), (3.31031,20.31392), (2.17159,11.66443);
SELECT -28.740781574102936, 7.667329672103986e-133;
SELECT roundBankers(StudentTTest(left, right).1, 16) as t_stat, roundBankers(StudentTTest(left, right).2, 16) as p_value from student_ttest;
DROP TABLE IF EXISTS student_ttest;