ClickHouse/tests/queries/0_stateless/01558_ttest.sql

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, 16) 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, 16) 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, 16) 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)
SELECT '-0.5028215369186904', '0.6152361677168877';
SELECT roundBankers(welchTTest(left, right).1, 16) as t_stat, roundBankers(welchTTest(left, right).2, 16) 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), (11.82
SELECT '14.971190998235835', '5.898143508382202e-44';
SELECT roundBankers(welchTTest(left, right).1, 16) as t_stat, roundBankers(welchTTest(left, right).2, 16) 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.
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, 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), (10.0981
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;