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), 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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, 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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), 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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), 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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;
