DROP TABLE IF EXISTS welch_ttest;
CREATE TABLE welch_ttest (left Float64, right UInt8) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (27.5, 0), (21.0, 0), (19.0, 0), (23.6, 0), (17.0, 0), (17.9, 0), (16.9, 0), (20.1, 0), (21.9, 0), (22.6, 0), (23.1, 0), (19.6, 0), (19.0, 0), (21.7, 0), (21.4, 0), (27.1, 1), (22.0, 1), (20.8, 1), (23.4, 1), (23.4, 1), (23.5, 1), (25.8, 1), (22.0, 1), (24.8, 1), (20.2, 1), (21.9, 1), (22.1, 1), (22.9, 1), (20.5, 1), (24.4, 1);

SELECT '0.021378001462867';
SELECT roundBankers(welchTTest(left, right).2, 6) from welch_ttest;
DROP TABLE IF EXISTS welch_ttest;


CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (30.02, 0), (29.99, 0), (30.11, 0), (29.97, 0), (30.01, 0), (29.99, 0), (29.89, 1), (29.93, 1), (29.72, 1), (29.98, 1), (30.02, 1), (29.98, 1);
SELECT '0.090773324285671';
SELECT roundBankers(welchTTest(left, right).2, 6) from welch_ttest;
DROP TABLE IF EXISTS welch_ttest;

CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (0.010268, 0), (0.000167, 0), (0.000167, 0), (0.159258, 1), (0.136278, 1), (0.122389, 1);
SELECT '0.00339907162713746';
SELECT roundBankers(welchTTest(left, right).2, 6) from welch_ttest;
DROP TABLE IF EXISTS welch_ttest;

CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (14.72789, 0), (9.61661, 0), (13.57615, 0), (3.98392, 0), (11.98889, 0), (10.99422, 0), (5.44792, 0), (20.29346, 0), (7.05926, 0), (9.22732, 0), (12.06847, 0), (13.52612, 0), (8.24597, 0), (9.35245, 0), (10.12297, 0), (15.80624, 0), (13.68613, 0), (10.72729, 0), (5.62078, 0), (6.12229, 0), (6.03801, 0), (8.95585, 0), (24.04613, 0), (9.04757, 0), (2.68263, 0), (15.43935, 0), (2.89423, 0), (4.01423, 0), (4.30568, 0), (11.99948, 0), (8.40574, 0), (10.86642, 0), (9.4266, 0), (-8.12752, 0), (7.91634, 0), (7.3967, 0), (2.26431, 0), (14.20118, 0), (6.68233, 0), (15.46221, 0), (7.88467, 0), (11.20011, 0), (8.92027, 0), (10.27926, 0), (5.14395, 0), (5.62178, 0), (12.84383, 0), (9.98009, 0), (-0.69789, 0), (11.41386, 0), (7.76863, 0), (7.21743, 0), (1.81176, 0), (9.43762, 0), (19.22117, 0), (2.97128, 0), (14.32851, 0), (7.54959, 0), (3.81545, 0), (10.1281, 0), (2.48596, 0), (10.0461, 0), (3.59714, 0), (9.73522, 0), (18.8077, 0), (3.15148, 0), (12.26062, 0), (5.66707, 0), (6.58623, 0), (17.30902, 0), (9.91391, 0), (5.36946, 0), (15.73637, 0), (16.96281, 0), (11.54063, 0), (18.37358, 0), (11.38255, 0), (10.53256, 0), (8.08833, 0), (16.27556, 0), (2.42969, 0), (9.56127, 0), (7.32998, 0), (9.19511, 0), (9.66903, 0), (4.15029, 0), (8.83511, 0), (14.60617, 0), (14.06143, 0), (5.39556, 0), (10.11871, 0), (10.56619, 0), (14.4462, 0), (10.42106, 0), (7.75551, 0), (11.00418, 0), (4.47226, 0), (16.35461, 0), (18.55174, 0), (11.82044, 0), (7.39454, 0), (11.27767, 0), (6.83827, 0), (7.76858, 0), (15.97614, 0), (14.53781, 0), (12.99546, 0), (16.91151, 0), (9.65012, 0), (14.25487, 0), (14.03618, 0), (2.57382, 0), (2.50779, 0), (14.24787, 0), (13.34666, 0), (7.31102, 0), (10.22981, 0), (17.4435, 0), (21.2074, 0), (6.64191, 0), (18.7086, 0), (14.78686, 0), (9.85287, 0), (4.48263, 0), (14.17469, 0), (14.4342, 0), (19.2481, 0), (3.47165, 0), (8.28712, 0), (8.81657, 0), (0.92319, 0), (20.41106, 0), (6.76127, 0), (22.00242, 0), (8.66129, 0), (10.9929, 0), (17.95494, 0), (17.20996, 0), (12.18888, 0), (12.14257, 0), (15.81243, 0), (4.43362, 0), (1.17567, 0), (15.60881, 0), (9.34833, 0), (6.33513, 0), (-0.83095, 0), (12.43268, 0), (6.63207, 0), (11.96877, 0), (14.81029, 0), (21.84876, 0), (3.75896, 0), (6.91307, 0), (13.73015, 0), (8.63753, 0), (15.71679, 0), (1.74565, 0), (9.16895, 0), (5.70685, 0), (5.00117, 0), (13.06888, 0), (7.51204, 0), (15.34885, 0), (5.20264, 0), (8.59043, 0), (6.45619, 0), (14.61979, 0), (11.7075, 0), (14.04901, 0), (4.20525, 0), (15.1733, 0), (3.12934, 0), (8.08049, 0), (15.41273, 0), (16.90751, 0), (5.86893, 0), (7.1086, 0), (4.418, 0), (12.0614, 0), (7.07887, 0), (3.61585, 0), (11.73001, 0), (10.80449, 0), (8.40311, 0), (9.91276, 0), (16.4164, 0), (5.25034, 0), (15.20283, 0), (10.42909, 0), (9.53888, 0), (14.68939, 0), (6.60007, 0), (18.31058, 0), (7.01885, 0), (18.71631, 0), (10.50002, 0), (10.7517, 0), (4.23224, 0), (2.28924, 0), (8.56059, 0), (8.25095, 0), (9.15673, 0), (13.28409, 0), (8.4513, 0), (2.83911, 0), (2.79676, 0), (9.11055, 0), (7.18529, 0), (-4.1258, 0), (5.28306, 0), (6.82757, 0), (10.89035, 0), (5.24822, 0), (11.935, 0), (6.45675, 0), (10.18088, 0), (4.9932, 0), (18.09939, 0), (8.11738, 0), (5.37883, 0), (10.50339, 0), (16.64093, 0), (14.77263, 0), (13.71385, 0), (6.98746, 0), (10.74635, 0), (5.49432, 0), (13.46078, 0), (10.67565, 0), (9.0291, 0), (11.51417, 0), (13.07118, 0), (9.5049, 0), (8.50611, 0), (6.47606, 0), (13.06526, 0), (19.08658, 0), (9.49741, 0), (10.60865, 0), (2.28996, 0), (8.12846, 0), (5.62241, 0), (4.07712, 0), (17.98526, 0), (9.466, 0), (11.38904, 0), (5.91826, 0), (1.52059, 0), (18.79161, 0), (18.20669, 0), (-1.67829, 0), (18.01586, 0), (16.31577, 0), (7.88281, 0), (8.46179, 0), (10.31113, 0), (14.88377, 0), (1.31835, 0), (2.53176, 0), (9.48625, 0), (3.97936, 0), (11.52319, 0), (13.24178, 0), (7.58739, 0), (10.00959, 0), (9.73361, 0), (8.35716, 0), (1.65491, 0), (11.11521, 0), (6.08355, 0), (10.04582, 0), (11.58237, 0), (16.40249, 0), (1.9691, 0), (13.22776, 0), (2.67059, 0), (9.83651, 0), (2.12539, 0), (9.27114, 0), (9.0699, 0), (2.78179, 0), (12.49311, 0), (12.97662, 0), (15.06359, 0), (16.91565, 0), (5.92011, 0), (5.81304, 0), (8.46425, 0), (9.48705, 0), (4.68191, 0), (5.70028, 0), (-0.78798, 0), (10.03442, 0), (15.45433, 0), (9.43845, 0), (3.05825, 0), (6.92126, 0), (14.05905, 0), (19.71579, 0), (15.0131, 0), (4.50386, 0), (1.31061, 0), (10.81197, 0), (14.32942, 0), (9.26469, 0), (7.27679, 0), (22.69295, 0), (12.03763, 0), (7.34876, 0), (16.60689, 0), (7.48786, 0), (15.78602, 0), (17.21048, 0), (13.93482, 0), (9.69911, 0), (12.24315, 0), (10.58131, 0), (19.57006, 0), (9.8856, 0), (11.70302, 0), (7.89864, 0), (12.24831, 0), (16.93707, 0), (9.65467, 0), (4.221, 0), (15.45229, 0), (12.83088, 0), (7.58313, 0), (12.895, 0), (10.02471, 0), (13.36059, 0), (5.07864, 0), (9.72017, 0), (11.05809, 0), (15.28528, 0), (13.99834, 0), (19.26989, 0), (9.41846, 0), (11.65425, 0), (8.49638, 0), (6.38592, 0), (-4.69837, 0), (12.22061, 0), (9.41331, 0), (13.2075, 0), (12.97005, 0), (11.44352, 0), (9.79805, 0), (6.93116, 0), (10.07691, 0), (22.05892, 0), (7.80353, 0), (-2.17276, 0), (0.61509, 0), (8.35842, 0), (17.77108, 0), (14.70841, 0), (1.27992, 0), (15.62699, 0), (9.32914, 0), (15.41866, 0), (10.82009, 0), (3.29902, 0), (9.21998, 0), (7.93845, 0), (10.33344, 0), (12.06399, 0), (5.5308, 0), (8.38727, 0), (18.11104, 0), (8.86565, 0), (19.41825, 0), (9.52376, 0), (3.94552, 0), (9.37587, 0), (15.44954, 0), (15.90527, 0), (13.18927, 0), (7.01646, 0), (9.06005, 0), (9.06431, 0), (5.76006, 0), (9.18705, 0), (-3.48446, 0), (15.89817, 0), (12.94719, 0), (23.69426, 0), (17.47755, 0), (15.61528, 0), (0.54832, 0), (14.32916, 0), (9.55305, 0), (13.79891, 0), (0.82544, 0), (13.34875, 0), (9.07614, 0), (5.19621, 0), (2.1451, 0), (9.87726, 0), (8.45439, 0), (-1.41842, 0), (7.93598, 0), (11.23151, 0), (17.84458, 0), (7.02237, 0), (10.7842, 0), (4.42832, 0), (4.45044, 0), (1.50938, 0), (21.21651, 0), (6.2097, 0), (6.84354, 0), (18.53804, 0), (12.01072, 0), (4.8345, 0), (20.41587, 0), (14.48353, 0), (8.71116, 0), (12.42818, 0), (14.89244, 0), (8.03033, 0), (5.25917, 0), (2.30092, 0), (10.22504, 0), (15.37573, 0), (7.13666, 0), (4.45018, 0), (10.18405, 0), (3.91025, 0), (14.52304, 0), (13.14771, 0), (11.99219, 0), (9.21345, 0), (8.85106, 0), (12.91887, 0), (15.62308, 0), (11.88034, 0), (15.12097, 0), (11.58168, 0), (16.83051, 0), (5.25405, 0), (2.19976, 0), (4.56716, 0), (16.46053, 0), (5.61995, 0), (8.67704, 0), (5.62789, 0), (9.84815, 0), (13.05834, 0), (11.74205, 0), (3.88393, 0), (16.15321, 0), (4.83925, 0), (13.00334, 0), (4.4028, 0), (4.35794, 0), (4.47478, 0), (2.38713, 0), (4.25235, 0), (10.87509, 0), (9.82411, 0), (13.61518, 0), (10.25507, 0), (4.0335, 0), (10.69881, 0), (5.70321, 0), (6.96244, 0), (9.35874, 0), (6.28076, 0), (8.29015, 0), (6.88653, 0), (7.70687, 0), (8.2001, 0), (6.73415, 0), (3.82052, 0), (3.94469, 0), (15.82384, 0), (2.54004, 0), (10.74876, 0), (12.60517, 0), (17.7024, 0), (4.6722, 0), (13.67341, 0), (6.4565, 0), (12.95699, 0), (4.56912, 0), (5.58464, 0), (4.0638, 0), (13.05559, 0), (5.38269, 0), (0.16354, 0), (7.23962, 0), (7.38577, 0), (8.50951, 0), (13.72574, 0), (17.80421, 0), (3.01135, 0), (8.02608, 0), (14.23847, 0), (-8.65656, 1), (22.98234, 1), (23.80821, 1), (13.33939, 1), (-4.05537, 1), (23.5155, 1), (-6.45272, 1), (17.7903, 1), (11.463, 1), (5.28021, 1), (8.39157, 1), (6.02464, 1), (14.43732, 1), (15.76584, 1), (1.54391, 1), (1.24897, 1), (27.1507, 1), (7.71091, 1), (15.71846, 1), (32.97808, 1), (-1.79334, 1), (-9.23439, 1), (11.27838, 1), (0.72703, 1), (18.51557, 1), (9.16619, 1), (17.29624, 1), (-1.30208, 1), (-3.48018, 1), (10.12082, 1), (-8.01318, 1), (-14.22264, 1), (16.58174, 1), (-0.55975, 1), (5.61449, 1), (1.44626, 1), (7.89158, 1), (1.13369, 1), (-0.82609, 1), (12.23365, 1), (12.45443, 1), (14.46915, 1), (13.72627, 1), (18.41459, 1), (29.66702, 1), (1.51619, 1), (10.40078, 1), (3.33266, 1), (6.12036, 1), (11.86553, 1), (6.59422, 1), (22.0948, 1), (1.79623, 1), (14.29513, 1), (19.69162, 1), (-7.98033, 1), (5.48433, 1), (-2.28474, 1), (9.91876, 1), (10.64097, 1), (0.22523, 1), (17.01773, 1), (22.37388, 1), (14.04215, 1), (23.1244, 1), (18.96958, 1), (8.42663, 1), (3.7165, 1), (14.29366, 1), (23.50886, 1), (26.33722, 1), (26.72396, 1), (13.26287, 1), (12.97607, 1), (17.41838, 1), (8.63875, 1), (17.08943, 1), (23.15356, 1), (-4.4965, 1), (7.58895, 1), (26.04074, 1), (6.84245, 1), (20.56287, 1), (3.84735, 1), (-2.76304, 1), (13.1615, 1), (8.21954, 1), (-3.49943, 1), (22.12419, 1), (7.08323, 1), (16.12937, 1), (-0.32672, 1), (16.5942, 1), (7.68977, 1), (11.39484, 1), (-5.11987, 1), (20.87404, 1), (8.01007, 1), (3.26497, 1), (5.61253, 1), (20.69182, 1), (0.0296, 1), (21.904, 1), (22.46572, 1), (3.63685, 1), (-5.10846, 1), (14.86389, 1), (5.47188, 1), (18.44095, 1), (16.71368, 1), (6.36704, 1), (8.82663, 1), (14.6727, 1), (7.98383, 1), (2.65568, 1), (21.45827, 1), (11.77948, 1), (4.71979, 1), (3.17951, 1), (13.90226, 1), (15.50578, 1), (10.8026, 1), (16.91369, 1), (9.90552, 1), (13.87322, 1), (4.12366, 1), (-3.78985, 1), (1.7599, 1), (3.43715, 1), (-3.45246, 1), (23.64571, 1), (-4.96877, 1), (3.93514, 1), (1.49914, 1), (12.71519, 1), (5.11521, 1), (4.79872, 1), (20.89391, 1), (5.363, 1), (8.02765, 1), (14.30804, 1), (11.49002, 1), (14.25281, 1), (7.6573, 1), (15.49686, 1), (3.29327, 1), (2.27236, 1), (12.58104, 1), (19.19128, 1), (15.25901, 1), (6.5221, 1), (10.10965, 1), (12.75249, 1), (16.50977, 1), (-8.6697, 1), (8.28553, 1), (1.44315, 1), (4.65869, 1), (0.98149, 1), (0.16623, 1), (17.66332, 1), (4.35346, 1), (6.52742, 1), (-1.06631, 1), (-5.28454, 1), (14.25583, 1), (8.74058, 1), (1.89553, 1), (-0.92959, 1), (10.30289, 1), (-6.3744, 1), (-8.1706, 1), (10.95369, 1), (4.94384, 1), (28.40568, 1), (3.7004, 1), (2.52363, 1), (4.07997, 1), (7.8849, 1), (17.95409, 1), (16.67021, 1), (11.34377, 1), (-0.07446, 1), (22.00223, 1), (3.31778, 1), (18.50719, 1), (-3.58655, 1), (6.5394, 1), (12.40459, 1), (16.59866, 1), (7.54176, 1), (-1.51044, 1), (12.69758, 1), (2.9842, 1), (2.49187, 1), (2.04113, 1), (-2.46544, 1), (15.18368, 1), (-0.04058, 1), (-0.4127, 1), (10.5526, 1), (12.03982, 1), (12.10923, 1), (11.54954, 1), (-1.18613, 1), (11.30984, 1), (23.54105, 1), (10.67321, 1), (24.09196, 1), (7.5008, 1), (12.52233, 1), (4.30673, 1), (9.35793, 1), (4.44472, 1), (-7.00679, 1), (8.56241, 1), (23.73891, 1), (15.62708, 1), (16.09205, 1), (12.52074, 1), (14.58927, 1), (-4.80187, 1), (8.47964, 1), (7.75477, 1), (12.6893, 1), (7.14147, 1), (12.12654, 1), (12.32334, 1), (7.98909, 1), (3.26652, 1), (20.53684, 1), (32.3369, 1), (19.74911, 1), (-4.62897, 1), (8.26483, 1), (20.88451, 1), (-2.12982, 1), (25.61459, 1), (5.32091, 1), (-4.1196, 1), (7.57937, 1), (21.15847, 1), (6.46355, 1), (7.74846, 1), (19.62636, 1), (28.34629, 1), (26.73919, 1), (20.40427, 1), (3.03378, 1), (10.2537, 1), (7.47745, 1), (10.79184, 1), (3.91962, 1), (19.97973, 1), (18.87711, 1), (12.56157, 1), (11.46033, 1), (3.78661, 1), (-9.45748, 1), (12.06033, 1), (-0.74615, 1), (13.2815, 1), (24.78052, 1), (5.83337, 1), (17.4111, 1), (19.70331, 1), (11.78446, 1), (-1.366, 1), (1.37458, 1), (16.31483, 1), (32.63464, 1), (-3.79736, 1), (19.17984, 1), (-0.27705, 1), (-3.69456, 1), (28.38058, 1), (-1.36876, 1), (-25.63301, 1), (3.58644, 1), (-6.85667, 1), (13.42225, 1), (12.04671, 1), (28.99468, 1), (7.87662, 1), (2.61119, 1), (-3.56022, 1), (1.50022, 1), (14.55836, 1), (9.35831, 1), (16.9366, 1), (29.23126, 1), (15.31386, 1), (13.46112, 1), (7.39667, 1), (11.15599, 1), (9.80499, 1), (22.64923, 1), (8.67693, 1), (18.67335, 1), (-3.19127, 1), (22.94716, 1), (17.86834, 1), (16.98267, 1), (15.91653, 1), (11.79718, 1), (18.50208, 1), (8.90755, 1), (10.44843, 1), (4.67433, 1), (6.82287, 1), (10.82228, 1), (-4.18631, 1), (20.3872, 1), (11.84735, 1), (21.25376, 1), (10.55032, 1), (12.19023, 1), (0.63369, 1), (7.92381, 1), (17.90933, 1), (15.30781, 1), (10.01877, 1), (0.88744, 1), (22.20967, 1), (-4.23117, 1), (21.50819, 1), (11.27421, 1), (-16.23179, 1), (33.43085, 1), (5.15093, 1), (1.34505, 1), (6.027, 1), (-10.43035, 1), (27.45998, 1), (19.24886, 1), (-4.44761, 1), (5.453, 1), (12.73758, 1), (11.2897, 1), (31.032, 1), (7.39168, 1), (11.95245, 1), (26.279, 1), (-1.0255, 1), (10.36675, 1), (11.58439, 1), (27.8405, 1), (13.1707, 1), (31.39133, 1), (27.08301, 1), (-2.14368, 1), (4.08476, 1), (21.5573, 1), (16.69822, 1), (7.69955, 1), (8.32793, 1), (6.49235, 1), (-7.3284, 1), (10.58264, 1), (-6.17006, 1), (34.55782, 1), (10.93221, 1), (44.24299, 1), (14.6224, 1), (-7.42798, 1), (15.52351, 1), (11.33982, 1), (10.46716, 1), (13.0986, 1), (-4.25988, 1), (9.55316, 1), (0.75489, 1), (25.99212, 1), (-0.81401, 1), (3.49551, 1), (22.99402, 1), (10.99628, 1), (23.70223, 1), (2.71482, 1), (22.82309, 1), (31.25686, 1), (4.86318, 1), (-1.06476, 1), (15.10298, 1), (-0.61015, 1), (17.81246, 1), (-1.55788, 1), (18.09709, 1), (9.11271, 1), (9.94682, 1), (-7.33194, 1), (-4.67293, 1), (21.81717, 1), (7.16318, 1), (13.25649, 1), (13.88776, 1), (4.95793, 1), (17.65303, 1), (14.47382, 1), (13.19373, 1), (31.86093, 1), (5.73161, 1), (10.96492, 1), (6.97951, 1), (1.75136, 1), (10.96144, 1), (15.08137, 1), (9.95311, 1), (7.07729, 1), (3.08148, 1), (22.37954, 1), (8.51951, 1), (2.88746, 1), (26.73509, 1), (-2.88939, 1), (-2.82367, 1), (-0.35783, 1), (14.22076, 1), (11.50295, 1), (7.10171, 1), (8.28488, 1), (0.54178, 1), (13.8022, 1), (15.62157, 1), (10.79173, 1), (28.18946, 1), (30.43524, 1), (2.54914, 1), (9.89421, 1), (13.08631, 1), (4.68761, 1), (5.61516, 1), (22.88072, 1), (7.4735, 1), (11.27382, 1), (2.39559, 1), (-3.31889, 1), (9.61957, 1), (23.01381, 1), (-1.23467, 1), (9.07691, 1), (15.78056, 1), (12.28421, 1), (9.44888, 1), (13.16928, 1), (4.33357, 1), (2.21737, 1), (33.17833, 1), (13.25407, 1), (-2.47961, 1), (6.41401, 1), (18.8439, 1), (-4.63375, 1), (-8.2909, 1), (12.18221, 1), (-2.95356, 1), (19.61659, 1), (12.45056, 1), (-4.17198, 1), (21.9641, 1), (11.96416, 1), (12.74573, 1), (10.47873, 1), (12.73295, 1), (11.31373, 1), (9.9827, 1), (5.87138, 1), (4.24372, 1), (-23.72256, 1), (28.41337, 1), (4.88103, 1), (3.61902, 1), (8.93586, 1), (16.40759, 1), (27.84494, 1), (5.6001, 1), (14.51379, 1), (13.5576, 1), (12.92213, 1), (3.90686, 1), (17.07104, 1), (15.84268, 1), (17.38777, 1), (16.54766, 1), (5.94487, 1), (17.02804, 1), (7.66386, 1), (10.43088, 1), (6.16059, 1), (20.46178, 1), (20.02888, 1), (20.95949, 1), (6.50808, 1), (7.22366, 1), (8.06659, 1), (16.08241, 1), (13.83514, 1), (-0.33454, 1), (12.98848, 1), (12.99024, 1);
SELECT '-0.5028215369186904', '0.6152361677168877';
SELECT roundBankers(welchTTest(left, right).1, 6) as t_stat, roundBankers(welchTTest(left, right).2, 6) as p_value from welch_ttest;
DROP TABLE IF EXISTS welch_ttest;


CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (4.82025, 0), (6.13896, 0), (15.20277, 0), (14.15351, 0), (7.21338, 0), (8.55506, 0), (13.80816, 0), (11.28411, 0), (7.4612, 0), (7.43759, 0), (12.9832, 0), (-5.74783, 0), (12.47114, 0), (15.14223, 0), (3.40603, 0), (9.27323, 0), (7.88547, 0), (8.56456, 0), (4.59731, 0), (7.91213, 0), (7.33894, 0), (21.74811, 0), (11.92111, 0), (0.18828, 0), (10.47314, 0), (20.37396, 0), (11.04991, 0), (13.30083, 0), (14.28065, 0), (2.86942, 0), (24.96072, 0), (14.20164, 0), (18.28769, 0), (10.50949, 0), (9.22273, 0), (11.77608, 0), (8.56872, 0), (13.74535, 0), (11.65209, 0), (12.51894, 0), (17.76256, 0), (13.52122, 0), (8.70796, 0), (6.04749, 0), (16.33064, 0), (8.35636, 0), (14.03496, 0), (11.05834, 0), (14.49261, 0), (2.59383, 0), (8.01022, 0), (4.05458, 0), (13.26384, 0), (14.62058, 0), (10.52489, 0), (8.46357, 0), (6.4147, 0), (9.70071, 0), (12.47581, 0), (4.38333, 0), (17.54172, 0), (10.12109, 0), (7.73186, 0), (14.0279, 0), (11.6621, 0), (17.47045, 0), (15.50223, 0), (15.46034, 0), (13.39964, 0), (14.98025, 0), (15.87912, 0), (17.67374, 0), (9.64073, 0), (12.84904, 0), (7.70278, 0), (13.03156, 0), (9.04512, 0), (15.97014, 0), (8.96389, 0), (11.48009, 0), (9.71153, 0), (13.00084, 0), (12.39803, 0), (13.08188, 0), (5.82244, 0), (10.81871, 0), (8.2539, 0), (7.52114, 0), (9.11488, 0), (8.37482, 0), (14.48652, 0), (11.42152, 0), (16.03111, 0), (13.14057, 0), (-2.26351, 0), (15.50394, 0), (14.88603, 0), (13.37257, 0), (11.84026, 0), (7.66558, 0), (6.24584, 0), (3.6312, 0), (2.7018, 0), (5.63656, 0), (5.82643, 0), (10.06745, 0), (-0.5831, 0), (14.84202, 0), (9.5524, 0), (19.71713, 0), (14.23109, 0), (8.69105, 0), (5.33742, 0), (7.30372, 0), (7.93342, 0), (15.20884, 0), (7.53839, 0), (13.45311, 0), (11.04473, 0), (10.76673, 0), (15.44145, 0), (14.06596, 0), (9.14873, 0), (12.88372, 0), (8.74994, 0), (10.53263, 0), (16.16694, 0), (8.37197, 0), (3.43739, 0), (4.72799, 0), (9.08802, 0), (11.2531, 0), (5.16115, 0), (10.20895, 0), (18.70884, 0), (15.88924, 0), (3.38758, 0), (6.46449, 0), (10.21088, 0), (14.08458, 0), (15.74508, 0), (19.31896, 0), (13.19641, 0), (11.95409, 0), (10.70718, 0), (1.05245, 0), (10.04772, 0), (17.01369, 0), (10.2286, 0), (19.58323, 0), (7.02892, 0), (4.16866, 0), (8.94326, 0), (4.99854, 0), (8.88352, 0), (18.65422, 0), (17.32328, 0), (9.33492, 0), (14.94788, 0), (8.05863, 0), (14.6737, 0), (10.93801, 0), (0.54036, 0), (-0.34242, 0), (5.89076, 0), (3.15189, 0), (1.94421, 0), (6.38698, 0), (10.50654, 0), (8.95362, 0), (6.23711, 0), (11.75359, 0), (12.42155, 0), (-1.55472, 0), (4.6688, 0), (10.48087, 0), (11.74615, 0), (9.26822, 0), (7.55517, 0), (12.76005, 0), (16.47102, 0), (11.31297, 0), (14.37437, 0), (2.38799, 0), (6.44577, 0), (5.07471, 0), (11.55123, 0), (7.76795, 0), (10.60116, 0), (14.40885, 0), (11.58158, 0), (8.81648, 0), (12.92299, 0), (11.26939, 0), (17.95014, 0), (2.95002, 0), (17.41959, 0), (11.12455, 0), (8.78541, 0), (14.36413, 0), (12.98554, 0), (12.58505, 0), (15.49789, 0), (11.70999, 0), (0.65596, 0), (11.08202, 0), (14.75752, 0), (6.84385, 0), (9.27245, 0), (13.78243, 0), (17.4863, 0), (4.01777, 0), (11.82861, 0), (13.86551, 0), (6.16591, 0), (8.71589, 0), (16.77195, 0), (17.23243, 0), (-2.12941, 0), (5.66629, 0), (12.45153, 0), (1.63971, 0), (13.84031, 0), (4.6144, 0), (5.26169, 0), (9.27769, 0), (9.14288, 0), (9.71953, 0), (9.38446, 0), (1.64788, 0), (11.72922, 0), (13.68926, 0), (9.42952, 0), (12.05574, 0), (9.09148, 0), (5.32273, 0), (20.25258, 0), (10.14599, 0), (10.82156, 0), (5.75736, 0), (7.13567, 0), (9.29746, 0), (5.1618, 0), (10.076, 0), (21.65669, 0), (13.35486, 0), (6.79957, 0), (8.76243, 0), (14.59294, 0), (16.90609, 0), (10.50337, 0), (-0.07923, 0), (13.51648, 0), (12.0676, 0), (0.86482, 0), (9.03563, 0), (5.38751, 0), (17.16866, 0), (2.78702, 0), (11.15548, 0), (12.30843, 0), (8.04897, 0), (9.95814, 0), (11.29308, 0), (14.13032, 0), (21.05877, 0), (3.57386, 0), (7.96631, 0), (3.30484, 0), (18.61856, 0), (16.35184, 0), (7.65236, 0), (18.02895, 0), (9.79458, 0), (16.7274, 0), (8.84453, 0), (13.05709, 0), (10.91447, 0), (8.40171, 0), (16.95211, 0), (11.82194, 0), (19.87978, 0), (12.88455, 0), (-0.00947, 0), (12.28109, 0), (6.96462, 0), (13.75282, 0), (14.39141, 0), (11.07193, 0), (12.88039, 0), (11.38253, 0), (21.02707, 0), (7.51955, 0), (6.31984, 0), (15.6543, 0), (14.80315, 0), (8.38024, 0), (21.7516, 0), (14.31336, 0), (15.04703, 0), (5.73787, 0), (13.16911, 0), (12.40695, 0), (9.88968, 0), (8.46703, 0), (8.70637, 0), (8.03551, 0), (5.9757, 0), (12.22951, 0), (3.14736, 0), (10.51266, 0), (18.593, 0), (10.82213, 0), (7.14216, 0), (6.81154, 0), (-0.6486, 0), (20.56136, 0), (11.35367, 0), (11.38205, 0), (17.14, 0), (14.91215, 0), (15.50207, 0), (5.93162, 0), (3.74869, 0), (14.11532, 0), (7.38954, 0), (5.45764, 0), (18.33733, 0), (9.91923, 0), (2.38991, 0), (14.16756, 0), (2.39791, 0), (6.92586, 0), (5.32474, 0), (2.28812, 0), (5.71718, 0), (5.84197, 0), (2.76206, 0), (19.05928, 0), (11.51788, 0), (6.56648, 0), (3.35735, 0), (7.55948, 0), (19.99908, 0), (13.00634, 0), (18.36886, 0), (11.14675, 0), (16.72931, 0), (12.50106, 0), (6.00605, 0), (23.06653, 0), (5.39694, 0), (9.53167, 0), (12.76944, 0), (7.20604, 0), (13.25391, 0), (13.7341, 0), (10.85292, 0), (-7.75835, 0), (10.29728, 0), (13.70099, 0), (10.17959, 0), (9.98399, 0), (12.69389, 0), (-0.28848, 0), (-2.18319, 0), (13.36378, 0), (10.09232, 0), (5.49489, 0), (5.46156, 0), (0.94225, 0), (12.79205, 0), (10.09593, 0), (6.06218, 0), (0.89463, 0), (11.88986, 0), (10.79733, 0), (1.51371, 0), (2.20967, 0), (15.45732, 0), (16.5262, 0), (5.99724, 0), (8.3613, 0), (15.68183, 0), (15.32117, 0), (14.15674, 0), (6.64553, 0), (4.20777, 0), (-0.10521, 0), (-0.88169, 0), (1.85913, 0), (9.73673, 0), (0.30926, 0), (6.17559, 0), (11.76602, 0), (5.68385, 0), (14.57088, 0), (12.81509, 0), (9.85682, 0), (12.06376, 0), (6.08874, 0), (11.63921, 0), (14.86722, 0), (10.41035, 0), (2.93794, 0), (12.21841, 0), (0.23804, 0), (3.14845, 0), (7.29748, 0), (3.06134, 0), (13.77684, 0), (16.21992, 0), (5.33511, 0), (9.68959, 0), (9.44169, 0), (18.08012, 0), (4.04224, 0), (8.77918, 0), (10.18324, 0), (9.38914, 0), (11.76995, 0), (14.19963, 0), (6.88817, 0), (16.56123, 0), (15.39885, 0), (5.21241, 0), (4.44408, 0), (17.87587, 0), (12.53337, 0), (13.60916, 0), (6.60104, 0), (7.35453, 0), (18.61572, 0), (6.10437, 0), (13.08682, 0), (12.15404, 0), (4.90789, 0), (2.13353, 0), (12.49593, 0), (11.93056, 0), (13.29408, 0), (5.70038, 0), (8.40271, 0), (5.19456, 0), (-5.51028, 0), (14.0329, 0), (10.38365, 0), (6.56812, 0), (4.21129, 0), (9.7157, 0), (9.88553, 0), (13.45346, 0), (4.97752, 0), (12.77595, 0), (8.56465, 0), (4.27703, 0), (18.12502, 0), (12.45735, 0), (12.42912, 0), (12.08125, 0), (10.85779, 0), (4.36013, 0), (11.85062, 0), (8.47776, 0), (9.60822, 0), (11.3069, 0), (14.25525, 0), (1.55168, 0), (14.57782, 0), (7.84786, 0), (9.87774, 0), (14.75575, 0), (3.68774, 0), (9.37667, 0), (20.28676, 0), (12.10027, 0), (8.01819, 0), (18.78158, 0), (20.85402, 0), (18.98069, 0), (16.1429, 0), (9.24047, 0), (14.12487, 0), (10.18841, 0), (-3.04478, 0), (5.7552, 0), (9.30376, 0), (11.42837, 0), (6.02364, 0), (8.86984, 0), (10.91177, 0), (10.04418, 0), (18.10774, 0), (7.49384, 0), (9.11556, 0), (9.7051, 0), (5.23268, 0), (9.04647, 0), (8.81547, 0), (2.65098, 0), (-2.69857, 1), (15.80943, 1), (7.31555, 1), (3.96517, 1), (4.77809, 1), (9.6472, 1), (-26.41717, 1), (-10.85635, 1), (-1.4376, 1), (-0.96308, 1), (2.84315, 1), (5.79467, 1), (-3.06091, 1), (-14.62902, 1), (22.08022, 1), (-2.11982, 1), (-4.84824, 1), (-10.50447, 1), (2.4891, 1), (9.90324, 1), (-22.66866, 1), (-0.97103, 1), (-16.57608, 1), (-3.78749, 1), (25.84511, 1), (5.30797, 1), (-18.19466, 1), (11.72708, 1), (0.2891, 1), (-9.83474, 1), (6.69942, 1), (18.09604, 1), (18.52651, 1), (1.38201, 1), (7.64615, 1), (17.66598, 1), (-2.44141, 1), (-9.01598, 1), (27.69142, 1), (4.06946, 1), (-15.0077, 1), (-10.49648, 1), (-4.88322, 1), (-25.09805, 1), (-4.64024, 1), (20.94434, 1), (24.12126, 1), (-14.10962, 1), (10.6512, 1), (14.50687, 1), (-19.88081, 1), (-11.55271, 1), (13.16921, 1), (16.63864, 1), (-24.08114, 1), (-9.09949, 1), (-10.54702, 1), (0.20813, 1), (8.19066, 1), (-2.70523, 1), (-0.23954, 1), (7.19398, 1), (-7.1618, 1), (-7.44322, 1), (-17.92031, 1), (-1.58146, 1), (9.18338, 1), (3.25838, 1), (-14.30234, 1), (1.84695, 1), (31.13794, 1), (-0.85067, 1), (19.02787, 1), (-3.09594, 1), (13.45584, 1), (-5.48104, 1), (-22.74928, 1), (-8.03697, 1), (17.31143, 1), (-16.65231, 1), (-18.58713, 1), (-16.52641, 1), (14.95261, 1), (12.56762, 1), (15.00188, 1), (1.85858, 1), (2.1926, 1), (-2.4095, 1), (21.56873, 1), (3.35509, 1), (-4.98672, 1), (35.08603, 1), (-10.01602, 1), (-3.85153, 1), (-6.81974, 1), (19.56525, 1), (-9.35488, 1), (0.24268, 1), (-3.51488, 1), (-0.37066, 1), (24.20888, 1), (-11.73537, 1), (0.01282, 1), (0.03963, 1), (-9.65589, 1), (-0.37429, 1), (5.61255, 1), (0.49984, 1), (-10.15066, 1), (-14.54314, 1), (16.56889, 1), (-7.73873, 1), (-3.76422, 1), (1.40722, 1), (2.28818, 1), (-13.12643, 1), (5.17082, 1), (4.79089, 1), (-17.42643, 1), (8.72548, 1), (-3.70285, 1), (16.77893, 1), (13.382, 1), (19.98418, 1), (0.00483, 1), (-4.75951, 1), (2.35391, 1), (21.65809, 1), (-9.2714, 1), (-18.38253, 1), (7.23097, 1), (14.97927, 1), (-4.02197, 1), (-29.8189, 1), (-12.8554, 1), (-7.60124, 1), (-14.90158, 1), (-3.31486, 1), (31.38144, 1), (-8.61288, 1), (15.31895, 1), (-10.19488, 1), (13.796, 1), (-0.32912, 1), (-0.0684, 1), (-30.06834, 1), (24.93912, 1), (-3.26506, 1), (-8.29751, 1), (-5.39189, 1), (-25.08603, 1), (-1.45318, 1), (16.72724, 1), (-3.38467, 1), (-26.00478, 1), (7.28369, 1), (16.96226, 1), (16.5858, 1), (10.46583, 1), (3.84345, 1), (-2.99382, 1), (1.42078, 1), (-11.0123, 1), (2.09909, 1), (1.21064, 1), (15.36079, 1), (-21.61349, 1), (22.7726, 1), (10.50512, 1), (-6.95825, 1), (9.20036, 1), (15.66902, 1), (3.28098, 1), (-9.05692, 1), (0.32882, 1), (-1.64934, 1), (-4.81406, 1), (-5.06006, 1), (19.97493, 1), (2.88646, 1), (-0.34552, 1), (7.55186, 1), (-22.96115, 1), (31.29166, 1), (6.18798, 1), (-2.52715, 1), (-11.58799, 1), (14.13596, 1), (13.45069, 1), (12.15179, 1), (3.44491, 1), (-8.78006, 1), (18.32087, 1), (11.91757, 1), (-2.00179, 1), (10.88411, 1), (9.09327, 1), (6.62484, 1), (8.87178, 1), (11.52254, 1), (-14.15988, 1), (-17.19515, 1), (14.03089, 1), (-2.4095, 1), (-16.83575, 1), (2.71469, 1), (4.84351, 1), (-1.17651, 1), (-3.37529, 1), (-19.92137, 1), (4.48952, 1), (-12.4906, 1), (-5.65277, 1), (8.50819, 1), (-19.61261, 1), (12.54156, 1), (11.06784, 1), (-12.59285, 1), (3.43683, 1), (-3.00325, 1), (12.49082, 1), (7.20955, 1), (17.6547, 1), (15.8619, 1), (24.3048, 1), (-8.05434, 1), (-6.06901, 1), (-15.69515, 1), (-11.13917, 1), (-3.90757, 1), (-2.57038, 1), (5.14065, 1), (17.8497, 1), (-8.64665, 1), (-18.68331, 1), (5.8567, 1), (-20.93884, 1), (4.40583, 1), (14.35985, 1), (4.18134, 1), (4.3635, 1), (9.35428, 1), (2.8908, 1), (16.01017, 1), (-1.48499, 1), (-9.97949, 1), (1.03055, 1), (-2.79697, 1), (6.85977, 1), (4.73213, 1), (2.7815, 1), (-2.46866, 1), (18.39425, 1), (-0.80378, 1), (-0.22982, 1), (-16.11608, 1), (3.0862, 1), (3.20779, 1), (10.50146, 1), (-0.21305, 1), (11.21012, 1), (-0.99825, 1), (18.39633, 1), (-3.39003, 1), (-0.64411, 1), (-1.39932, 1), (15.45319, 1), (-0.66044, 1), (-15.2223, 1), (-34.39907, 1), (-3.57836, 1), (16.82828, 1), (1.66624, 1), (15.43475, 1), (8.17776, 1), (5.50486, 1), (10.43082, 1), (-6.63332, 1), (2.28008, 1), (16.37203, 1), (5.16313, 1), (-8.85281, 1), (13.26692, 1), (-7.46842, 1), (8.43091, 1), (-13.18172, 1), (-0.72401, 1), (22.3881, 1), (10.65448, 1), (2.81289, 1), (10.92405, 1), (-8.95358, 1), (19.80653, 1), (-12.86527, 1), (5.38826, 1), (-6.83501, 1), (-15.7647, 1), (-27.67412, 1), (8.6499, 1), (-4.89542, 1), (16.76167, 1), (12.84284, 1), (-17.27324, 1), (-4.18726, 1), (-14.62366, 1), (-5.49863, 1), (-16.22846, 1), (10.60329, 1), (6.46781, 1), (1.70458, 1), (10.77448, 1), (0.8463, 1), (13.0482, 1), (-4.36264, 1), (3.22647, 1), (2.38828, 1), (6.7946, 1), (-0.25254, 1), (1.2497, 1), (1.6544, 1), (4.1019, 1), (11.27839, 1), (-5.04127, 1), (18.11674, 1), (0.51231, 1), (-0.51029, 1), (13.52556, 1), (16.10171, 1), (5.68197, 1), (-2.85904, 1), (-8.89167, 1), (6.24489, 1), (10.85319, 1), (-0.39816, 1), (3.87079, 1), (-3.1867, 1), (1.55322, 1), (16.86779, 1), (-14.60321, 1), (-1.81952, 1), (-3.11624, 1), (1.24193, 1), (10.18179, 1), (4.69796, 1), (0.69032, 1), (11.7723, 1), (7.62896, 1), (9.89741, 1), (9.11484, 1), (-3.84676, 1), (-0.4777, 1), (0.95958, 1), (-7.95056, 1), (-10.97474, 1), (-6.54861, 1), (34.74933, 1), (27.39463, 1), (4.18299, 1), (6.02476, 1), (-1.99397, 1), (1.26478, 1), (23.37106, 1), (10.49682, 1), (-11.04354, 1), (-12.22284, 1), (-9.87635, 1), (28.90511, 1), (6.77613, 1), (0.55352, 1), (0.37031, 1), (7.1418, 1), (3.24897, 1), (-1.60918, 1), (3.1675, 1), (-17.97072, 1), (-5.61743, 1), (14.1422, 1), (14.87695, 1), (-4.65961, 1), (-0.99174, 1), (-2.96623, 1), (-9.02263, 1), (-17.2088, 1), (2.78608, 1), (6.74239, 1), (4.8524, 1), (7.46731, 1), (1.04894, 1), (-12.8023, 1), (-17.18188, 1), (-5.08801, 1), (22.13942, 1), (-0.36384, 1), (17.80564, 1), (7.67504, 1), (1.59779, 1), (4.10942, 1), (0.61074, 1), (-14.40767, 1), (10.59906, 1), (16.57017, 1), (-15.17526, 1), (-6.98549, 1), (-0.64548, 1), (3.23756, 1), (14.65504, 1), (4.583, 1), (12.72378, 1), (5.26547, 1), (0.81781, 1), (9.38273, 1), (10.37636, 1), (10.70325, 1), (-0.83043, 1), (-7.53149, 1), (-9.09147, 1), (-19.51381, 1), (-28.44508, 1), (6.44392, 1), (11.10201, 1), (-2.86184, 1), (8.30673, 1), (8.8797, 1), (10.68053, 1), (15.62919, 1), (8.00579, 1), (6.4651, 1), (-4.50029, 1), (18.04514, 1), (11.12996, 1), (-5.14007, 1), (9.43857, 1), (3.13476, 1), (4.9772, 1), (-17.45782, 1), (0.05552, 1), (-1.90283, 1), (2.67908, 1), (-2.62243, 1), (-3.22767, 1), (-8.70222, 1), (-23.11605, 1), (21.6757, 1), (12.70076, 1), (4.4322, 1), (11.69344, 1), (9.18052, 1), (-2.2549, 1), (-2.15615, 1), (20.29765, 1), (-0.29536, 1), (15.50109, 1), (8.79187, 1), (5.11533, 1), (-20.44436, 1), (-3.00909, 1), (-4.48291, 1), (21.84462, 1), (1.94225, 1), (-2.81908, 1), (17.19418, 1), (-9.33528, 1), (-0.17346, 1), (0.03958, 1), (-35.17786, 1), (8.36887, 1), (-9.02292, 1), (-10.98804, 1), (0.29335, 1), (4.29634, 1), (3.87718, 1), (-9.08532, 1), (7.13922, 1), (-7.62463, 1), (-10.5666, 1), (4.68165, 1), (-3.30172, 1), (13.04852, 1), (13.45616, 1), (2.41043, 1), (-0.36501, 1), (-15.67383, 1), (17.92217, 1), (8.42106, 1), (3.22063, 1), (-7.31753, 1), (21.99596, 1), (-36.8273, 1), (-20.46391, 1), (5.74179, 1), (-15.83178, 1), (14.90454, 1), (-8.84645, 1), (3.72036, 1), (4.6877, 1), (16.35418, 1), (3.15441, 1), (2.39907, 1), (-17.58664, 1), (-13.18269, 1);
SELECT '14.971190998235835', '5.898143508382202e-44';
SELECT roundBankers(welchTTest(left, right).1, 6) as t_stat, roundBankers(welchTTest(left, right).2, 6) as p_value from welch_ttest;
SELECT roundBankers(welchTTest(0.95)(left, right).3, 6) as t_stat, roundBankers(welchTTest(0.95)(left, right).4, 6) as p_value from welch_ttest;
DROP TABLE IF EXISTS welch_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 (0.88854, 0), (-5.76966, 0), (6.76618, 0), (3.55546, 0), (-9.76948, 0), (4.92323, 0), (-0.36352, 0), (0.97018, 0), (4.61656, 0), (-6.78292, 0), (4.02008, 0), (12.41838, 0), (5.14417, 0), (3.86836, 0), (-1.26199, 0), (12.44106, 0), (3.28349, 0), (1.77261, 0), (-8.94748, 0), (-1.01449, 0), (-1.26377, 0), (6.79682, 0), (6.32333, 0), (-8.21214, 0), (-1.68565, 0), (9.7557, 0), (3.66694, 0), (1.39967, 0), (-5.52035, 0), (-10.95601, 0), (0.93877, 0), (1.45933, 0), (-5.40551, 0), (-0.83857, 0), (8.50794, 0), (-6.68686, 0), (5.03099, 0), (1.56251, 0), (4.17381, 0), (-2.92644, 0), (5.11068, 0), (2.09617, 0), (11.7787, 0), (6.50336, 0), (0.62098, 0), (-7.97121, 0), (3.81902, 0), (0.33151, 0), (10.68584, 0), (0.56007, 0), (-7.38621, 0), (5.05882, 0), (2.34616, 0), (11.3806, 0), (5.95276, 0), (-3.01429, 0), (5.98169, 0), (0.96985, 0), (-1.15932, 0), (2.11547, 0), (2.49668, 0), (-12.49569, 0), (-4.94667, 0), (-3.64215, 0), (-8.35595, 0), (3.211, 0), (2.33805, 0), (2.38608, 0), (-3.2862, 0), (-0.80454, 0), (-0.53483, 0), (10.66445, 0), (-0.37619, 0), (0.48246, 0), (7.41919, 0), (0.42414, 0), (-2.32335, 0), (-0.70223, 0), (-5.9332, 0), (-1.20561, 0), (3.39865, 0), (9.61739, 0), (-0.78651, 0), (-4.00256, 0), (-7.99646, 0), (8.72923, 0), (0.71859, 0), (-1.62726, 0), (5.11234, 0), (-0.95625, 0), (-3.75573, 0), (1.03141, 0), (-3.33588, 0), (1.51804, 0), (-3.30935, 0), (-1.97507, 0), (4.06456, 0), (3.27195, 0), (-7.81761, 0), (-3.81785, 0), (-4.18311, 0), (-11.33313, 0), (-0.25221, 0), (7.2514, 0), (5.30301, 0), (2.46762, 0), (4.22716, 0), (0.33916, 0), (9.7638, 0), (-7.58684, 0), (-4.09888, 0), (4.26617, 0), (-0.56744, 0), (4.65125, 0), (-1.30301, 0), (4.53771, 0), (9.96929, 0), (3.72939, 0), (-2.29818, 0), (3.09417, 0), (0.82251, 0), (5.29975, 0), (2.8685, 0), (-5.73321, 0), (-1.85651, 0), (-1.07984, 0), (9.78342, 0), (-13.49652, 0), (3.68791, 0), (1.9998, 0), (1.11674, 0), (9.43869, 0), (4.07029, 0), (5.32715, 0), (7.16504, 0), (6.66096, 0), (-5.7111, 0), (-0.38575, 0), (4.49165, 0), (-3.36489, 0), (7.71814, 0), (-1.58966, 0), (-1.61063, 0), (-0.91602, 0), (0.73459, 0), (-3.24463, 0), (6.3947, 0), (-2.77845, 0), (4.45899, 0), (-8.84186, 0), (2.62276, 0), (1.774, 0), (4.3692, 0), (0.05942, 0), (-1.44042, 0), (-2.53594, 0), (-2.24752, 0), (4.98874, 0), (4.05434, 0), (-2.56483, 0), (-6.79286, 0), (-2.06165, 0), (-0.26056, 0), (1.89567, 0), (-3.15145, 0), (-7.31321, 0), (0.28936, 0), (-0.63111, 0), (0.22611, 0), (-9.3377, 0), (-5.76638, 0), (3.87306, 0), (6.7011, 0), (9.03915, 0), (-1.21835, 0), (0.82892, 0), (2.80656, 0), (-1.34746, 0), (-1.99912, 0), (0.6036, 0), (-3.46117, 0), (5.23732, 0), (-1.86702, 0), (-5.86115, 0), (6.48523, 0), (-7.40158, 0), (-1.38913, 0), (4.94613, 0), (-2.07818, 0), (2.39808, 0), (4.89238, 0), (4.39481, 0), (5.20425, 0), (13.62598, 0), (-2.86293, 0), (-3.62396, 0), (-4.28695, 0), (4.66425, 0), (2.20871, 0), (1.60382, 0), (-9.87024, 0), (-7.37302, 0), (-4.17814, 0), (2.5148, 0), (3.21708, 0), (-11.48089, 0), (1.19821, 0), (-0.07436, 0), (-1.10652, 0), (4.03395, 0), (-4.35883, 0), (2.04013, 0), (0.52264, 0), (8.14004, 0), (-8.86949, 0), (-0.35807, 0), (-10.71113, 0), (-2.13755, 0), (0.50715, 0), (6.30826, 0), (2.37527, 0), (0.20872, 0), (-5.85729, 0), (-4.97217, 0), (-9.78434, 0), (-1.53277, 0), (0.14827, 0), (-1.053, 0), (1.74558, 0), (11.17194, 0), (9.35487, 0), (-9.17209, 0), (10.41814, 0), (7.41206, 0), (3.71775, 0), (-2.04674, 0), (6.18037, 0), (5.6383, 0), (-0.90058, 0), (-1.27073, 0), (-2.3473, 0), (-8.44271, 0), (2.75551, 0), (-1.15521, 0), (4.08722, 0), (-1.70399, 0), (7.24114, 0), (-8.43976, 0), (-1.53052, 0), (-0.00526, 0), (-4.04813, 0), (-2.84299, 0), (-5.201, 0), (7.75774, 0), (-2.85791, 0), (-3.86071, 0), (-1.80029, 0), (-5.26015, 0), (-3.158, 0), (7.71014, 0), (-4.84866, 0), (-8.38785, 0), (7.67021, 0), (4.96521, 0), (-0.40919, 0), (-3.25711, 0), (3.07685, 0), (2.89376, 0), (-10.47331, 0), (-3.48942, 0), (1.13906, 0), (-8.57454, 0), (-3.38963, 0), (-2.3195, 0), (-1.60694, 0), (-5.57406, 0), (-0.93075, 0), (-11.76579, 0), (10.68283, 0), (8.74324, 0), (7.66409, 0), (4.76715, 0), (0.44539, 0), (-1.35941, 0), (4.18849, 0), (-6.17097, 0), (0.27977, 0), (-1.45006, 0), (-4.81694, 0), (-3.0297, 0), (0.02145, 0), (2.46883, 0), (9.60317, 0), (-9.93898, 0), (1.05549, 0), (5.55366, 0), (-3.80722, 0), (-4.18851, 0), (1.00351, 0), (3.11385, 0), (-5.17623, 0), (-3.18396, 0), (-6.65302, 0), (-0.50832, 0), (-4.04375, 0), (4.52707, 0), (6.63124, 0), (-3.72082, 0), (5.79825, 0), (-2.0158, 0), (-2.78369, 0), (-1.91821, 0), (6.31714, 0), (-1.80869, 0), (8.55586, 0), (2.40826, 0), (-8.46361, 0), (5.04452, 0), (-0.84665, 0), (2.30903, 0), (-3.71837, 0), (-0.69419, 0), (3.6733, 0), (-1.96098, 0), (2.36747, 0), (-12.03622, 0), (4.38481, 0), (2.93955, 0), (2.16804, 0), (-0.08218, 0), (-3.97934, 0), (-7.43985, 0), (0.91666, 0), (7.23432, 0), (-6.13303, 0), (-10.23217, 0), (-6.21681, 0), (-0.80934, 0), (0.17914, 0), (2.13338, 0), (6.97656, 0), (6.90455, 0), (6.25943, 0), (-6.04019, 0), (-7.30909, 0), (1.4589, 0), (12.00208, 0), (2.22457, 0), (-2.45912, 0), (-6.92213, 0), (4.05547, 0), (0.04709, 0), (-7.70952, 0), (-1.47883, 0), (1.3701, 0), (-4.92928, 0), (-2.75872, 0), (-0.09178, 0), (2.62642, 0), (-1.14623, 0), (2.76609, 0), (4.94404, 0), (-7.01764, 0), (-10.91568, 0), (-2.49738, 0), (0.73576, 0), (2.25436, 0), (-1.72956, 0), (2.41054, 0), (5.72149, 0), (-6.41371, 0), (3.38217, 0), (1.24133, 0), (10.03634, 0), (-2.37303, 0), (-1.35543, 0), (-1.4387, 0), (-4.0976, 0), (-0.82501, 0), (-1.93498, 0), (5.59955, 0), (5.46656, 0), (2.43568, 0), (-0.23926, 0), (-4.9945, 0), (-4.96655, 0), (-0.59258, 0), (2.02497, 0), (0.67583, 0), (3.16522, 0), (-1.9673, 0), (-6.75319, 0), (-6.69723, 0), (0.81148, 0), (4.44531, 0), (-4.43522, 0), (-5.28602, 0), (-3.58829, 0), (-7.97395, 0), (-2.84891, 0), (-3.95112, 0), (3.54945, 0), (12.12376, 0), (-3.12347, 0), (3.65209, 0), (9.34031, 0), (-0.26348, 0), (-5.23968, 0), (2.22336, 0), (-10.70405, 0), (-4.41319, 0), (-5.94912, 0), (1.8147, 0), (7.69287, 0), (9.46125, 0), (4.72497, 0), (-0.57565, 0), (-1.12303, 0), (2.90272, 0), (-4.4584, 0), (4.28819, 0), (11.64512, 0), (-1.80395, 0), (2.51605, 0), (-3.18439, 0), (-0.70213, 0), (-7.68383, 0), (-8.32268, 0), (-8.71115, 0), (9.96933, 0), (0.95675, 0), (3.35114, 0), (-2.66008, 0), (7.75456, 0), (0.73568, 0), (0.3483, 0), (-1.09203, 0), (-7.76963, 0), (5.81902, 0), (-3.41424, 0), (-0.39209, 0), (4.67608, 0), (0.68753, 0), (5.17179, 0), (4.98983, 0), (-0.12659, 0), (3.25267, 0), (1.50184, 0), (2.94507, 0), (-0.42333, 0), (-3.66227, 0), (8.90812, 0), (4.74411, 0), (2.22018, 0), (-2.07976, 0), (4.8711, 0), (0.5023, 0), (6.31569, 0), (-4.36903, 0), (3.82146, 0), (-6.99477, 0), (3.61225, 0), (14.69335, 0), (0.58368, 0), (4.65341, 0), (-3.14272, 0), (2.67048, 0), (4.64963, 0), (-2.70828, 0), (1.42923, 0), (5.84498, 0), (-4.76568, 0), (0.19907, 0), (1.67486, 0), (5.32145, 0), (-8.03477, 0), (3.46776, 0), (4.66374, 0), (-5.37394, 0), (5.39045, 0), (-1.44756, 0), (-1.64419, 0), (3.39699, 0), (-2.94659, 0), (-2.38437, 0), (-0.23958, 0), (6.88389, 0), (-2.7172, 0), (-1.53419, 0), (7.38841, 0), (-5.44178, 0), (-0.89287, 0), (2.93546, 0), (-0.26901, 0), (-4.70044, 0), (2.25846, 0), (-9.28813, 0), (6.04268, 0), (4.41693, 0), (1.75714, 0), (-2.90702, 1), (3.61651, 1), (4.27458, 1), (4.82133, 1), (9.59483, 1), (1.00424, 1), (2.04147, 1), (-3.58214, 1), (6.59543, 1), (-1.00532, 1), (-3.59794, 1), (-2.82434, 1), (-3.13194, 1), (9.90977, 1), (0.523, 1), (4.62779, 1), (-2.56872, 1), (2.25807, 1), (1.04044, 1), (-2.35744, 1), (10.81531, 1), (-9.68469, 1), (3.80885, 1), (12.70435, 1), (-6.01112, 1), (1.89065, 1), (5.08892, 1), (3.45254, 1), (11.58151, 1), (0.85035, 1), (8.38397, 1), (1.17169, 1), (4.74621, 1), (-1.66614, 1), (4.2414, 1), (1.68765, 1), (1.85223, 1), (9.10111, 1), (-2.38085, 1), (-14.79595, 1), (-3.8938, 1), (-3.41864, 1), (-3.15282, 1), (-0.56684, 1), (12.87997, 1), (6.89115, 1), (12.921, 1), (-7.94908, 1), (2.45687, 1), (2.14957, 1), (7.55081, 1), (-3.71534, 1), (-2.41064, 1), (-0.80734, 1), (-4.75651, 1), (2.05241, 1), (-5.44523, 1), (-2.75054, 1), (-13.00131, 1), (-2.74451, 1), (-1.39004, 1), (-3.02854, 1), (7.65112, 1), (1.1245, 1), (6.74117, 1), (-0.75777, 1), (8.93451, 1), (-8.85559, 1), (-0.36405, 1), (4.02742, 1), (6.88718, 1), (-1.05124, 1), (3.04085, 1), (3.32368, 1), (1.147, 1), (3.41554, 1), (-3.47851, 1), (-0.47684, 1), (-0.55605, 1), (-0.17006, 1), (2.26218, 1), (12.45494, 1), (-1.84097, 1), (1.64934, 1), (-7.07496, 1), (-9.99462, 1), (6.09954, 1), (-1.05319, 1), (3.04757, 1), (0.93899, 1), (-4.63243, 1), (-7.43322, 1), (-7.298, 1), (-6.59016, 1), (-6.11649, 1), (0.56682, 1), (2.00661, 1), (-2.79814, 1), (2.84482, 1), (3.65348, 1), (-4.22807, 1), (-4.54336, 1), (-3.63343, 1), (2.96878, 1), (6.11661, 1), (-1.70919, 1), (-4.71133, 1), (6.09652, 1), (-6.83454, 1), (0.18006, 1), (1.51676, 1), (-5.31646, 1), (-3.21215, 1), (-5.07599, 1), (-2.36591, 1), (3.55724, 1), (4.8904, 1), (-3.22586, 1), (-1.74928, 1), (5.73458, 1), (1.41188, 1), (2.86255, 1), (2.90179, 1), (-2.19949, 1), (1.72727, 1), (1.76939, 1), (-0.12848, 1), (-0.52, 1), (3.48333, 1), (7.8262, 1), (0.09099, 1), (7.77017, 1), (9.49484, 1), (1.42825, 1), (1.99624, 1), (4.00419, 1), (1.07925, 1), (-0.09987, 1), (-5.48733, 1), (-1.83517, 1), (2.38059, 1), (1.42075, 1), (-1.11968, 1), (-6.46035, 1), (7.66576, 1), (4.6307, 1), (5.55989, 1), (3.16684, 1), (5.07671, 1), (-10.20566, 1), (-4.73386, 1), (1.28353, 1), (6.75679, 1), (12.09895, 1), (7.0049, 1), (7.16156, 1), (-0.64311, 1), (-0.66747, 1), (3.99996, 1), (9.07298, 1), (-4.60971, 1), (0.70744, 1), (2.56774, 1), (9.32424, 1), (3.95087, 1), (7.11372, 1), (-0.89284, 1), (8.6155, 1), (-0.14141, 1), (-4.86319, 1), (-6.95801, 1), (4.44883, 1), (4.6156, 1), (-2.3579, 1), (-5.1186, 1), (8.12819, 1), (2.78392, 1), (-4.30221, 1), (-1.47506, 1), (6.8598, 1), (0.47636, 1), (0.95383, 1), (7.79779, 1), (-2.61767, 1), (-10.5087, 1), (-2.74299, 1), (3.87369, 1), (-1.07093, 1), (4.98864, 1), (-7.50772, 1), (6.41316, 1), (1.39061, 1), (-3.1747, 1), (-2.13621, 1), (-0.02203, 1), (0.89025, 1), (-5.87746, 1), (3.60026, 1), (-0.23178, 1), (-2.1897, 1), (-5.85101, 1), (-1.6053, 1), (3.6184, 1), (-8.53795, 1), (-0.35987, 1), (2.15301, 1), (-6.60692, 1), (9.54341, 1), (1.11511, 1), (2.94025, 1), (12.05657, 1), (3.75156, 1), (7.95597, 1), (-0.99449, 1), (0.90597, 1), (-7.90627, 1), (3.50863, 1), (-1.47493, 1), (4.11671, 1), (10.06325, 1), (-1.06059, 1), (-1.37737, 1), (-0.42542, 1), (-3.90267, 1), (9.35037, 1), (-7.91219, 1), (-4.69945, 1), (3.63776, 1), (3.46492, 1), (2.84518, 1), (-3.04301, 1), (8.82764, 1), (7.80134, 1), (7.87755, 1), (7.01035, 1), (2.43271, 1), (11.36418, 1), (-6.92659, 1), (5.95541, 1), (3.59436, 1), (5.18429, 1), (4.20225, 1), (0.5029, 1), (4.03074, 1), (5.23152, 1), (10.65409, 1), (-0.69845, 1), (11.70096, 1), (5.80692, 1), (-8.1819, 1), (4.31485, 1), (5.7227, 1), (5.67398, 1), (-1.75826, 1), (7.54164, 1), (-1.79026, 1), (-1.7395, 1), (5.65042, 1), (0.38765, 1), (-4.64719, 1), (-10.22048, 1), (-2.05447, 1), (-2.43441, 1), (-5.38551, 1), (5.47764, 1), (8.26637, 1), (-3.6421, 1), (-11.66269, 1), (3.972, 1), (5.46642, 1), (-3.72304, 1), (5.75251, 1), (5.12841, 1), (0.59067, 1), (5.21138, 1), (-4.58702, 1), (-8.737, 1), (-2.12737, 1), (0.22888, 1), (-1.46448, 1), (2.40311, 1), (-5.21814, 1), (13.94749, 1), (-2.77448, 1), (-3.7867, 1), (3.4954, 1), (3.12586, 1), (-7.01485, 1), (-3.20727, 1), (6.31415, 1), (2.37521, 1), (8.13787, 1), (2.15956, 1), (-0.40842, 1), (-7.27283, 1), (4.27575, 1), (-2.89126, 1), (6.84344, 1), (7.0869, 1), (-5.18837, 1), (2.67648, 1), (-6.57021, 1), (0.60429, 1), (-1.04921, 1), (7.12873, 1), (1.68973, 1), (-2.58404, 1), (-3.83114, 1), (-7.26546, 1), (-5.07153, 1), (-0.80395, 1), (2.09455, 1), (4.33374, 1), (8.54335, 1), (0.80566, 1), (-8.38085, 1), (7.54812, 1), (8.78007, 1), (1.5857, 1), (8.43855, 1), (-1.90846, 1), (-1.2434, 1), (7.16172, 1), (-3.44129, 1), (-6.37542, 1), (-4.99486, 1), (4.99033, 1), (-1.83734, 1), (-2.83289, 1), (-4.13997, 1), (1.40163, 1), (8.57867, 1), (-1.87639, 1), (3.41667, 1), (6.31762, 1), (1.58473, 1), (1.63625, 1), (-6.93618, 1), (3.58046, 1), (-6.8097, 1), (4.69978, 1), (-1.72912, 1), (5.29491, 1), (-1.63062, 1), (5.83818, 1), (17.0769, 1), (4.54301, 1), (-1.33801, 1), (5.64339, 1), (1.26913, 1), (-1.01553, 1), (4.8316, 1), (3.08635, 1), (-2.27738, 1), (-1.13761, 1), (10.08698, 1), (5.33827, 1), (2.84345, 1), (-1.51132, 1), (13.46078, 1), (8.58965, 1), (-2.36683, 1), (-1.8217, 1), (1.96981, 1), (2.31718, 1), (3.66493, 1), (1.93104, 1), (5.20332, 1), (3.20519, 1), (3.34631, 1), (7.0087, 1), (-7.96126, 1), (-0.62182, 1), (-4.65227, 1), (10.6572, 1), (4.50891, 1), (9.74298, 1), (3.85707, 1), (6.41144, 1), (1.48649, 1), (2.28076, 1), (2.75342, 1), (-5.40401, 1), (7.11389, 1), (5.74368, 1), (6.78345, 1), (3.83773, 1), (0.70959, 1), (0.57434, 1), (1.5888, 1), (3.94889, 1), (5.8234, 1), (7.78366, 1), (9.08354, 1), (-7.99182, 1), (-2.77033, 1), (-10.29342, 1), (1.76251, 1), (2.09266, 1), (4.20614, 1), (-3.63064, 1), (-2.17794, 1), (-2.66225, 1), (-2.74707, 1), (-1.93431, 1), (1.38629, 1), (4.12816, 1), (-1.58902, 1), (-5.08864, 1), (-2.30491, 1), (2.64605, 1), (1.16158, 1), (2.63534, 1), (1.4956, 1), (-4.60768, 1), (0.60771, 1), (3.29549, 1), (-1.42592, 1), (0.8883, 1), (-1.10612, 1), (-2.57296, 1), (5.88085, 1), (7.40745, 1), (13.48116, 1), (5.53539, 1), (-1.46014, 1), (3.73304, 1), (3.5435, 1), (-3.89151, 1), (4.16265, 1), (2.32663, 1), (5.31735, 1), (6.33485, 1), (2.1339, 1), (0.82708, 1), (-2.95155, 1), (-6.76019, 1), (-4.20179, 1), (8.78354, 1), (1.41863, 1), (7.65689, 1), (-6.52601, 1), (-4.4426, 1), (-4.49483, 1), (-3.91479, 1), (-2.84562, 1), (2.58974, 1), (2.24424, 1), (-4.65846, 1), (8.4062, 1), (8.20262, 1), (-8.63752, 1), (4.97966, 1), (-0.35563, 1), (-4.72116, 1), (-2.95997, 1), (2.73959, 1), (-0.23956, 1), (10.13915, 1), (11.83775, 1), (-2.50332, 1), (-0.58181, 1), (-7.62836, 1), (2.26478, 1), (-3.50179, 1), (-2.08023, 1), (4.07256, 1), (-1.40826, 1), (-2.33644, 1), (3.00197, 1), (4.23668, 1), (-2.24647, 1), (1.0445, 1), (-0.31901, 1), (8.62657, 1), (3.92817, 1), (0.08462, 1), (10.15884, 1), (0.4113, 1), (4.45847, 1), (5.82941, 1), (6.59202, 1), (-3.73441, 1), (-5.86969, 1), (-4.56543, 1), (-1.32636, 1), (-0.17884, 1), (-3.56181, 1), (-0.66932, 1), (6.87538, 1), (0.73527, 1), (-0.24177, 1), (-0.8657, 1), (-0.22977, 1), (1.02095, 1), (6.16311, 1), (-5.68027, 1), (-3.7619, 1), (4.22959, 1), (-1.5249, 1);
SELECT '-2.610898982580138', '0.00916587538237954';
SELECT roundBankers(studentTTest(left, right).1, 6) as t_stat, roundBankers(studentTTest(left, right).2, 6) 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, 0), (8.69444, 1), (3.73628, 0), (3.81414, 1), (-0.39478, 0), (12.38442, 1), (5.15633, 0), (8.9738, 1), (0.50539, 0), (9.19594, 1), (-5.34036, 0), (7.21009, 1), (0.19336, 0), (4.97743, 1), (8.35729, 0), (4.94756, 1), (6.95818, 0), (19.80911, 1), (-2.93812, 0), (13.75358, 1), (8.30807, 0), (16.56373, 1), (-3.3517, 0), (9.72882, 1), (4.16279, 0), (4.64509, 1), (-3.17231, 0), (17.76854, 1), (1.93545, 0), (4.80693, 1), (11.06606, 0), (8.79505, 1), (-4.22678, 0), (10.88868, 1), (-1.99975, 0), (6.21932, 1), (-4.51178, 0), (15.11614, 1), (-4.50711, 0), (13.24703, 1), (1.89786, 0), (14.76476, 1), (-6.19638, 0), (-0.6117, 1), (-3.70188, 0), (17.48993, 1), (5.01334, 0), (12.11847, 1), (1.79036, 0), (4.87439, 1), (2.14435, 0), (18.56479, 1), (3.0282, 0), (1.23712, 1), (2.35528, 0), (5.41596, 1), (-12.18535, 0), (4.54994, 1), (5.59709, 0), (11.37668, 1), (-12.92336, 0), (9.5982, 1), (-0.04281, 0), (6.59822, 1), (-0.16923, 0), (1.16703, 1), (0.88924, 0), (8.88418, 1), (-4.68414, 0), (10.95047, 1), (8.01099, 0), (5.52787, 1), (2.61686, 0), (-1.11647, 1), (-2.76895, 0), (14.49946, 1), (3.32165, 0), (3.27585, 1), (-0.85135, 0), (-0.42025, 1), (1.21368, 0), (6.37906, 1), (4.38673, 0), (2.5242, 1), (6.20964, 0), (8.1405, 1), (-1.23172, 0), (6.46732, 1), (4.65516, 0), (9.89332, 1), (-1.87143, 0), (10.4374, 1), (0.86429, 0), (-1.06465, 1), (2.51184, 0), (6.84902, 1), (-1.88822, 0), (10.96576, 1), (-1.61802, 0), (7.83319, 1), (1.93653, 0), (14.39823, 1), (-3.66631, 0), (7.02594, 1), (-1.05294, 0), (13.46629, 1), (-10.74718, 0), (10.39531, 1), (16.49295, 0), (11.27348, 1), (-7.65494, 0), (9.32187, 1), (-3.39303, 0), (12.32667, 1), (-4.89418, 0), (8.98905, 1), (3.2521, 0), (9.54757, 1), (0.05831, 0), (5.98325, 1), (-3.00409, 0), (3.47248, 1), (5.76702, 0), (9.26966, 1), (2.67674, 0), (5.77816, 1), (10.52623, 0), (6.32966, 1), (-0.54501, 0), (9.49313, 1), (-4.89835, 0), (6.21337, 1), (3.52457, 0), (10.00242, 1), (-0.0451, 0), (6.25167, 1), (-6.61226, 0), (15.64671, 1), (9.02391, 0), (2.78968, 1), (5.52571, 0), (6.55442, 1), (4.54352, 0), (3.68819, 1), (-3.8394, 0), (9.55934, 1), (-7.75295, 0), (4.166, 1), (5.91167, 0), (12.32471, 1), (1.38897, 0), (7.10969, 1), (6.24166, 0), (16.31723, 1), (5.58536, 0), (12.99482, 1), (4.7591, 0), (10.11585, 1), (-2.58336, 0), (10.29455, 1), (-1.91263, 0), (18.27524, 1), (3.31575, 0), (12.84435, 1), (5.3507, 0), (13.11954, 1), (-15.22081, 0), (12.84147, 1), (-0.84775, 0), (15.55658, 1), (-4.538, 0), (11.45329, 1), (6.71177, 0), (7.50912, 1), (0.52882, 0), (8.56226, 1), (2.0242, 0), (8.63104, 1), (5.69146, 0), (15.68026, 1), (4.63328, 0), (21.6361, 1), (0.22984, 0), (6.23925, 1), (-2.84052, 0), (8.65714, 1), (7.91867, 0), (9.9423, 1), (1.11001, 0), (12.28213, 1), (-0.11251, 0), (3.11279, 1), (-0.20905, 0), (13.58128, 1), (0.03287, 0), (16.51407, 1), (-1.59397, 0), (16.60476, 1), (-5.39405, 0), (12.02022, 1), (-7.1233, 0), (12.11035, 1), (4.51517, 0), (9.47832, 1), (-0.70967, 0), (6.40742, 1), (5.67299, 0), (8.87252, 1), (-0.33835, 0), (15.14265, 1), (-1.83047, 0), (2.23572, 1), (-0.62877, 0), (11.57144, 1), (-7.23148, 0), (18.87737, 1), (0.1802, 0), (12.1833, 1), (11.73325, 0), (11.17519, 1), (2.17603, 0), (16.80422, 1), (-0.11683, 0), (6.81423, 1), (-1.29102, 0), (12.12546, 1), (-0.23201, 0), (8.06153, 1), (-6.8643, 0), (10.97228, 1), (-6.85153, 0), (7.30596, 1), (-4.77163, 0), (15.44026, 1), (6.11721, 0), (8.00993, 1), (5.96406, 0), (12.60196, 1), (3.59135, 0), (13.96832, 1), (-0.60095, 0), (14.03207, 1), (3.11163, 0), (4.53758, 1), (-0.18831, 0), (8.08297, 1), (0.67657, 0), (4.90451, 1), (-3.16117, 0), (8.14253, 1), (0.26957, 0), (19.88605, 1), (2.18653, 0), (13.85254, 1), (-5.94611, 0), (23.01839, 1), (-4.39352, 0), (6.02084, 1), (-3.71525, 0), (9.60319, 1), (5.11103, 0), (1.90511, 1), (1.33998, 0), (10.35237, 1), (1.01629, 0), (16.27082, 1), (-3.36917, 0), (12.52379, 1), (-3.99661, 0), (11.37435, 1), (8.19336, 0), (13.61823, 1), (2.89168, 0), (15.77622, 1), (-11.10373, 0), (15.17254, 1), (11.68005, 0), (6.711, 1), (3.08282, 0), (4.74205, 1), (-6.81506, 0), (10.09812, 1), (-2.34587, 0), (6.61722, 1), (-2.68725, 0), (10.34164, 1), (0.3577, 0), (8.96602, 1), (-3.05682, 0), (12.32157, 1), (9.08062, 0), (11.75711, 1), (-0.77913, 0), (13.49499, 1), (10.35215, 0), (8.57713, 1), (6.82565, 0), (11.50313, 1), (-1.24674, 0), (1.13097, 1), (5.18822, 0), (7.83205, 1), (-3.70743, 0), (5.77957, 1), (1.40319, 0), (15.5519, 1), (5.89432, 0), (10.82676, 1), (1.43152, 0), (11.51218, 1), (6.70638, 0), (9.29779, 1), (9.76613, 0), (9.77021, 1), (4.27604, 0), (9.94114, 1), (-2.63141, 0), (15.54513, 1), (-7.8133, 0), (19.10736, 1), (-0.06668, 0), (15.04205, 1), (1.05391, 0), (9.03114, 1), (4.41797, 0), (24.0104, 1), (0.09337, 0), (9.94205, 1), (6.16075, 0), (2.5925, 1), (7.49413, 0), (8.82726, 1), (-3.52872, 0), (10.0209, 1), (-2.17126, 0), (8.1635, 1), (-3.87605, 0), (4.24074, 1), (3.26607, 0), (7.67291, 1), (-3.28045, 0), (5.21642, 1), (2.1429, 0), (11.2808, 1), (1.53386, 0), (6.88172, 1), (0.21169, 0), (5.98743, 1), (-0.63674, 0), (17.97249, 1), (5.84893, 0), (6.46323, 1), (-0.63498, 0), (15.37416, 1), (8.29526, 0), (2.89957, 1), (-1.08358, 0), (17.13044, 1), (-2.306, 0), (11.06355, 1), (2.86991, 0), (3.09625, 1), (-0.76074, 0), (-2.33019, 1), (5.49191, 0), (7.42675, 1), (1.82883, 0), (15.06792, 1), (-3.70497, 0), (8.81116, 1), (-0.53232, 0), (19.17446, 1), (-11.49722, 0), (18.77181, 1), (3.44877, 0), (14.06443, 1), (-1.8596, 0), (12.81241, 1), (-10.34851, 0), (2.72299, 1), (1.13093, 0), (18.67739, 1), (-10.93389, 0), (11.63275, 1), (-3.39703, 0), (2.23891, 1), (0.19749, 0), (13.01195, 1), (-3.68389, 0), (7.43402, 1), (-4.67863, 0), (8.14599, 1), (10.78916, 0), (16.65328, 1), (0.37675, 0), (1.362, 1), (3.98094, 0), (3.87957, 1), (-3.64775, 0), (11.16134, 1), (-4.8443, 0), (6.25357, 1), (1.102, 0), (4.21945, 1), (8.72112, 0), (12.50047, 1), (-1.47361, 0), (6.45486, 1), (6.24183, 0), (18.99924, 1), (6.83569, 0), (18.09508, 1), (-3.11684, 0), (13.59528, 1), (4.91306, 0), (3.39681, 1), (-0.03628, 0), (13.33157, 1), (5.1282, 0), (5.8945, 1), (-2.38558, 0), (5.61212, 1), (2.33351, 0), (8.41149, 1), (-0.97191, 0), (13.78608, 1), (-0.05588, 0), (6.08609, 1), (-4.70019, 0), (12.76962, 1), (-5.12371, 0), (3.26206, 1), (0.65606, 0), (0.25528, 1), (-0.11574, 0), (11.9083, 1), (4.4238, 0), (4.35071, 1), (6.93399, 0), (11.19855, 1), (3.68712, 0), (13.87404, 1), (-0.01187, 0), (6.87986, 1), (1.8332, 0), (8.32566, 1), (5.81322, 0), (22.51334, 1), (-4.04709, 0), (2.5226, 1), (-8.26397, 0), (16.84498, 1), (-2.11273, 0), (6.26108, 1), (5.28396, 0), (13.84824, 1), (0.73054, 0), (6.03262, 1), (6.43559, 0), (14.12668, 1), (4.35565, 0), (16.01939, 1), (-1.05545, 0), (8.19237, 1), (5.00087, 0), (18.01595, 1), (-2.72239, 0), (9.45609, 1), (7.32313, 0), (6.90459, 1), (2.11548, 0), (12.83115, 1), (-3.40953, 0), (10.603, 1), (6.97051, 0), (13.70439, 1), (-0.45567, 0), (6.1633, 1), (1.31699, 0), (4.1151, 1), (-1.49871, 0), (8.20499, 1), (7.14772, 0), (11.67903, 1), (0.79277, 0), (7.30851, 1), (6.9698, 0), (6.50941, 1), (2.08733, 0), (7.3949, 1), (-3.55962, 0), (12.80075, 1), (0.75601, 0), (5.62043, 1), (1.21, 0), (18.2542, 1), (-2.17877, 0), (17.9393, 1), (1.83206, 0), (16.4569, 1), (5.72463, 0), (8.78811, 1), (7.42257, 0), (4.85949, 1), (0.97829, 0), (-3.36394, 1), (7.54238, 0), (5.38683, 1), (9.91081, 0), (12.26083, 1), (-4.61743, 0), (10.27907, 1), (-4.40799, 0), (11.5144, 1), (9.99854, 0), (11.57335, 1), (8.53725, 0), (1.94203, 1), (3.2905, 0), (7.78228, 1), (0.38634, 0), (11.79385, 1), (-2.53374, 0), (10.18415, 1), (4.94758, 0), (14.67613, 1), (4.79624, 0), (4.70301, 1), (5.57664, 0), (12.72151, 1), (-6.44871, 0), (-3.35508, 1), (3.34431, 0), (17.63775, 1), (0.14209, 0), (2.53883, 1), (10.88431, 0), (14.01483, 1), (0.31846, 0), (12.4387, 1), (-0.54703, 0), (11.15408, 1), (-4.67791, 0), (7.74882, 1), (-5.68011, 0), (13.60956, 1), (-4.93362, 0), (7.81991, 1), (1.2271, 0), (10.90969, 1), (5.27512, 0), (8.19828, 1), (-3.84611, 0), (-1.18523, 1), (6.81706, 0), (0.5916, 1), (10.33033, 0), (0.35805, 1), (5.13979, 0), (12.98364, 1), (3.66534, 0), (11.38628, 1), (-2.07219, 0), (13.94644, 1), (10.65442, 0), (2.03781, 1), (-3.31751, 0), (10.74447, 1), (-1.82011, 0), (12.35656, 1), (-0.39886, 0), (7.08701, 1), (1.77052, 0), (2.69871, 1), (1.29049, 0), (19.66653, 1), (7.92344, 0), (7.88636, 1), (-2.92595, 0), (10.36916, 1), (-2.67107, 0), (1.632, 1), (5.64708, 0), (11.86081, 1), (0.34639, 0), (13.47602, 1), (-3.04356, 0), (6.60204, 1), (3.98828, 0), (7.01303, 1), (-1.36695, 0), (20.19992, 1), (-8.48462, 0), (18.88249, 1), (-4.04669, 0), (11.34367, 1), (9.84561, 0), (12.97305, 1), (-6.1537, 0), (9.5776, 1), (0.82433, 0), (17.91364, 1), (1.92449, 0), (18.3247, 1), (2.51288, 0), (9.9211, 1), (0.40965, 0), (7.14257, 1), (2.89183, 0), (6.59133, 1), (3.84347, 0), (12.35274, 1), (0.66829, 0), (10.57523, 1), (-3.45094, 0), (12.12859, 1), (1.3544, 0), (9.47177, 1), (-9.85456, 0), (0.60659, 1), (5.25689, 0), (4.72996, 1), (-5.26018, 0), (4.51121, 1), (-6.16912, 0), (13.28893, 1), (-1.77163, 0), (8.09014, 1), (3.96687, 0), (8.02511, 1), (0.70893, 0), (13.85406, 1), (-5.45342, 0), (1.75412, 1), (-3.89706, 0), (6.00641, 1), (3.11868, 0), (6.35554, 1), (4.41714, 0), (7.11293, 1), (7.64841, 0), (8.30442, 1), (0.00489, 0), (12.63024, 1), (3.2263, 0), (12.38966, 1), (-5.33042, 0), (7.6801, 1), (2.52189, 0), (11.33744, 1), (-7.40308, 0), (4.67713, 1), (0.67891, 0), (7.62276, 1), (2.49343, 0), (2.14478, 1), (5.43133, 0), (15.32988, 1), (-0.67541, 0), (1.52299, 1), (-0.60299, 0), (17.00017, 1), (-6.32903, 0), (8.29701, 1), (-3.44336, 0), (10.92961, 1), (-0.23963, 0), (6.78449, 1), (6.94686, 0), (7.02698, 1), (6.59442, 0), (11.51719, 1), (-4.18532, 0), (9.97926, 1), (-1.8228, 0), (7.44251, 1), (-0.29443, 0), (7.58541, 1), (2.99821, 0), (4.76058, 1), (2.51942, 0), (12.88959, 1), (-3.49176, 0), (9.974, 1), (-0.57979, 0), (17.03689, 1), (8.69471, 0), (11.14554, 1), (-1.19427, 0), (11.7392, 1), (-3.17119, 0), (11.50029, 1), (-2.99566, 0), (19.41759, 1), (-3.34493, 0), (9.65127, 1), (-2.33826, 0), (9.87673, 1), (-5.04164, 0), (14.13485, 1), (-0.48214, 0), (9.78034, 1), (7.45097, 0), (1.57826, 1), (3.04787, 0), (3.72091, 1), (2.92632, 0), (9.4054, 1), (1.39694, 0), (23.22816, 1), (4.38686, 0), (-0.12571, 1), (3.25753, 0), (6.97343, 1), (7.14218, 0), (10.09049, 1), (-4.04341, 0), (11.78393, 1), (-9.19352, 0), (3.01909, 1), (2.78473, 0), (16.09448, 1), (0.33331, 0), (6.25485, 1), (9.89238, 0), (7.13164, 1), (6.00566, 0), (7.75879, 1), (-1.7511, 0), (9.56834, 1), (4.77815, 0), (6.14824, 1), (5.07457, 0), (13.53454, 1), (2.56132, 0), (8.26364, 1), (2.38317, 0), (8.7095, 1), (-1.63486, 0), (10.61607, 1), (-1.46871, 0), (10.64418, 1), (-5.8681, 0), (23.9106, 1), (-2.96227, 0), (11.38978, 1), (-1.90638, 0), (11.4383, 1), (-13.3052, 0), (18.41498, 1), (-2.14705, 0), (3.70959, 1), (-9.62069, 0), (19.95918, 1), (2.29313, 0), (9.53847, 1), (0.22162, 0), (14.04957, 1), (-1.83956, 0), (13.70151, 1), (4.1853, 0), (5.45046, 1), (6.05965, 0), (10.95061, 1), (-0.23737, 0), (9.55156, 1), (6.07452, 0), (17.92345, 1), (4.34629, 0), (6.23976, 1), (4.02922, 0), (8.71029, 1), (3.62622, 0), (13.58736, 1), (-3.95825, 0), (8.78527, 1), (-1.63412, 0), (11.14213, 1), (-1.25727, 0), (12.23717, 1), (5.06323, 0), (16.44557, 1), (-0.66176, 0), (0.47144, 1), (2.36606, 0), (9.7198, 1), (-5.77792, 0), (13.50981, 1), (4.535, 0), (14.27806, 1), (1.02031, 0), (13.50793, 1), (4.49345, 0), (7.47381, 1), (-4.99791, 0), (11.07844, 1), (2.46716, 0), (9.89844, 1), (3.65471, 0), (21.48548, 1), (11.2283, 0), (6.92085, 1), (6.69743, 0), (4.44074, 1), (-5.60375, 0), (19.98074, 1), (0.28683, 0), (7.92826, 1), (-0.85737, 0), (16.6313, 1), (4.26726, 0), (17.17618, 1), (-3.4322, 0), (13.80807, 1), (-2.07039, 0), (5.37083, 1), (-2.26798, 0), (9.73962, 1), (-0.99818, 0), (10.66273, 1), (0.41335, 0), (8.90639, 1), (5.18124, 0), (12.24596, 1), (-5.01858, 0), (16.89203, 1), (2.05561, 0), (12.69184, 1), (-0.12117, 0), (15.59077, 1), (0.99471, 0), (6.94287, 1), (6.89979, 0), (-0.1801, 1), (-4.18527, 0), (3.25318, 1), (-6.35104, 0), (8.08804, 1), (3.89734, 0), (13.78384, 1), (-1.979, 0), (0.46434, 1), (3.15404, 0), (7.78224, 1), (3.52672, 0), (9.10987, 1), (2.48372, 0), (-0.89391, 1), (-6.13089, 0), (14.3696, 1), (2.2968, 0), (3.01763, 1), (-2.74324, 0), (8.03559, 1), (-0.12876, 0), (7.24609, 1), (-1.51135, 0), (11.86271, 1), (-3.92434, 0), (6.28196, 1), (-1.71254, 0), (8.9725, 1), (-1.25878, 0), (14.46114, 1), (2.03021, 0), (9.50216, 1), (4.31726, 0), (16.30413, 1), (-3.02908, 0), (1.02795, 1), (9.7093, 0), (1.88717, 1), (-3.36284, 0), (9.80106, 1), (6.70938, 0), (4.53487, 1), (0.42762, 0), (16.34543, 1), (5.04726, 0), (7.71098, 1), (2.78386, 0), (2.74639, 1), (6.83022, 0), (6.51875, 1), (-3.02109, 0), (10.42308, 1), (-0.65382, 0), (13.57901, 1), (-15.58675, 0), (0.52784, 1), (5.89746, 0), (4.4708, 1), (-4.11598, 0), (6.39619, 1), (-1.37208, 0), (14.57666, 1), (10.08082, 0), (2.71602, 1), (5.35686, 0), (12.53905, 1), (1.93331, 0), (11.4292, 1), (10.47444, 0), (12.44641, 1), (-2.36872, 0), (14.50894, 1), (6.50752, 0), (17.64374, 1), (2.54603, 0), (11.03218, 1), (-0.4332, 0), (9.82789, 1), (5.26572, 0), (10.11104, 1), (2.09016, 0), (2.16137, 1), (1.15513, 0), (10.24054, 1), (14.95941, 0), (12.86909, 1), (-3.85505, 0), (15.22845, 1), (-2.36239, 0), (5.05411, 1), (1.64338, 0), (10.84836, 1), (-4.25074, 0), (11.15717, 1), (7.29744, 0), (0.91782, 1), (-1.18964, 0), (13.29961, 1), (5.60612, 0), (15.11314, 1), (-3.77011, 0), (11.54004, 1), (6.67642, 0), (-0.94238, 1), (-0.06862, 0), (19.32581, 1), (5.60514, 0), (10.20744, 1), (3.7341, 0), (6.54857, 1), (9.59001, 0), (8.69108, 1), (3.30093, 0), (8.2296, 1), (-2.75658, 0), (8.4474, 1), (4.71994, 0), (6.81178, 1), (0.74699, 0), (5.99415, 1), (2.91095, 0), (13.99336, 1), (-7.36829, 0), (8.7469, 1), (-5.29487, 0), (8.62349, 1), (3.31079, 0), (1.84212, 1), (1.06974, 0), (4.4762, 1), (-1.18424, 0), (9.25421, 1), (-7.415, 0), (10.44229, 1), (3.40595, 0), (12.21649, 1), (-7.63085, 0), (10.45968, 1), (1.13336, 0), (15.34722, 1), (-0.0096, 0), (5.50868, 1), (0.8928, 0), (10.93609, 1), (-0.5943, 0), (2.78631, 1), (7.48306, 0), (11.86145, 1), (10.11943, 0), (18.67385, 1), (5.60459, 0), (10.64051, 1), (4.00189, 0), (12.75565, 1), (2.35823, 0), (6.63666, 1), (0.33475, 0), (12.19343, 1), (3.47072, 0), (9.08636, 1), (-6.68867, 0), (11.67256, 1), (3.31031, 0), (20.31392, 1), (2.17159, 0), (11.66443, 1);
SELECT '-28.740781574102936', '7.667329672103986e-133';
SELECT roundBankers(studentTTest(left, right).1, 6) as t_stat, roundBankers(studentTTest(left, right).2, 6) as p_value from student_ttest;
SELECT roundBankers(studentTTest(0.95)(left, right).3, 6) as t_stat, roundBankers(studentTTest(0.95)(left, right).4, 6) as p_value from student_ttest;
DROP TABLE IF EXISTS student_ttest;