mirror of
https://github.com/ClickHouse/ClickHouse.git
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3f874af323
(cherry picked from commit 89547e77cf
)
56 lines
59 KiB
SQL
56 lines
59 KiB
SQL
DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right UInt8) ENGINE = Memory;
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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);
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SELECT '0.021378001462867';
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SELECT roundBankers(welchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (30.02, 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);
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SELECT '0.090773324285671';
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SELECT roundBankers(welchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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INSERT INTO welch_ttest VALUES (0.010268, 0), (0.000167, 0), (0.000167, 0), (0.159258, 1), (0.136278, 1), (0.122389, 1);
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SELECT '0.00339907162713746';
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SELECT roundBankers(welchTTest(left, right).2, 16) from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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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), 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SELECT '-0.5028215369186904', '0.6152361677168877';
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SELECT roundBankers(welchTTest(left, right).1, 16) as t_stat, roundBankers(welchTTest(left, right).2, 16) as p_value from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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CREATE TABLE welch_ttest (left Float64, right Float64) ENGINE = Memory;
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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, 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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);
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SELECT '14.971190998235835', '5.898143508382202e-44';
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SELECT roundBankers(welchTTest(left, right).1, 16) as t_stat, roundBankers(welchTTest(left, right).2, 16) as p_value from welch_ttest;
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DROP TABLE IF EXISTS welch_ttest;
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DROP TABLE IF EXISTS student_ttest;
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/*Check t-stat and p-value and compare it with scipy.stat implementation
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First: a=1, sigma (not sigma^2)=5, size=500
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Second: a=1, sigma = 5, size = 500 */
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CREATE TABLE student_ttest (left Float64, right Float64) ENGINE = Memory;
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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, 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(-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);
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SELECT '-2.610898982580138', '0.00916587538237954';
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SELECT roundBankers(studentTTest(left, right).1, 16) as t_stat, roundBankers(studentTTest(left, right).2, 16) as p_value from student_ttest;
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DROP TABLE IF EXISTS student_ttest;
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/*Check t-stat and p-value and compare it with scipy.stat implementation
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First: a=1, sigma (not sigma^2)=5, size=500
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Second: a=1, sigma = 5, size = 500 */
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CREATE TABLE student_ttest (left Float64, right Float64) ENGINE = Memory;
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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), 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(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);
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SELECT '-28.740781574102936', '7.667329672103986e-133';
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SELECT roundBankers(studentTTest(left, right).1, 16) as t_stat, roundBankers(studentTTest(left, right).2, 16) as p_value from student_ttest;
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DROP TABLE IF EXISTS student_ttest;
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