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mannwhitney.py
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mannwhitney.py
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import pandas as pd
import numpy as np
from scipy.stats import tiecorrect, rankdata, norm
class mannWhitney():
def __init__(self, data1, data2, tail = 'two', significant_level=0.05):
"""
Function for Mann-Whitney U test
Parameters
----------
data1 : interable object of float
e.g. list, [1,2,3]
data2 : interable object of float
e.g. list, [1,2,3]
tail : string, define which tail test
e.g 'two' : two-tailed test
'less': one-tailed test (smaller)
'more': one-tailed test (larger)
significant_level: float
e.g. 0.05 or 0.1
"""
Critical_05 = pd.DataFrame({'2': [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0, 5.0, 5.0, 5.0, 5.0, 5.0, 6.0, 6.0, 6.0, 6.0, 7.0, 7.0] ,
'3': [-1.0, -1.0, -1.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0, 9.0, 9.0, 10.0, 10.0, 11.0, 11.0, 12.0, 13.0, 13.0, 14.0, 14.0, 15.0, 15.0, 16.0, 16.0, 17.0, 17.0, 18.0, 18.0] ,
'4': [-1.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 11.0, 12.0, 13.0, 13.0, 15.0, 16.0, 17.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0, 31.0, 31.0] ,
'5': [-1.0, 0.0, 1.0, 2.0, 3.0, 5.0, 6.0, 7.0, 8.0, 9.0, 11.0, 12.0, 13.0, 14.0, 15.0, 17.0, 18.0, 19.0, 20.0, 22.0, 23.0, 24.0, 25.0, 27.0, 28.0, 29.0, 30.0, 32.0, 33.0, 34.0, 35.0, 37.0, 38.0, 39.0, 40.0, 41.0, 43.0, 44.0, 45.0] ,
'6': [-1.0, 1.0, 2.0, 3.0, 5.0, 6.0, 8.0, 10.0, 11.0, 13.0, 14.0, 16.0, 17.0, 19.0, 21.0, 22.0, 24.0, 25.0, 27.0, 29.0, 30.0, 32.0, 33.0, 35.0, 37.0, 38.0, 40.0, 42.0, 43.0, 45.0, 46.0, 48.0, 50.0, 51.0, 53.0, 55.0, 56.0, 58.0, 59.0] ,
'7': [-1.0, 1.0, 3.0, 5.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0, 22.0, 24.0, 26.0, 28.0, 30.0, 32.0, 34.0, 36.0, 38.0, 40.0, 42.0, 44.0, 46.0, 48.0, 50.0, 52.0, 54.0, 56.0, 58.0, 60.0, 62.0, 64.0, 66.0, 68.0, 70.0, 72.0, 74.0] ,
'8': [0, 2, 4, 6, 7, 10, 13, 15, 17, 19, 22, 24, 26, 29, 31, 34, 36, 38, 41, 43, 45, 48, 50, 53, 55, 57, 60, 62, 65, 67, 69, 72, 74, 77, 79, 81, 84, 86, 89] ,
'9': [0, 2, 4, 7, 10, 12, 15, 17, 20, 23, 26, 28, 31, 34, 37, 39, 42, 45, 48, 50, 53, 56, 59, 62, 64, 67, 70, 73, 76, 78, 81, 84, 87, 89, 92, 95, 98, 101, 103] ,
'10': [0, 3, 5, 8, 11, 14, 17, 20, 23, 26, 29, 33, 36, 39, 42, 45, 48, 52, 55, 58, 61, 64, 67, 71, 74, 77, 80, 83, 87, 90, 93, 96, 99, 103, 106, 109, 112, 115, 119] ,
'11': [0, 3, 6, 9, 13, 16, 19, 23, 26, 30, 33, 37, 40, 44, 47, 51, 55, 58, 62, 65, 69, 73, 76, 80, 83, 87, 90, 94, 98, 101, 105, 108, 112, 116, 119, 123, 127, 130, 134] ,
'12': [1, 4, 7, 11, 14, 18, 22, 26, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149] ,
'13': [1, 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 50, 54, 59, 63, 67, 72, 76, 80, 85, 89, 94, 98, 102, 107, 111, 116, 120, 125, 129, 133, 138, 142, 147, 151, 156, 160, 165] ,
'14': [1, 5, 9, 13, 17, 22, 26, 31, 36, 40, 45, 50, 55, 59, 64, 67, 74, 78, 83, 88, 93, 98, 102, 107, 112, 117, 122, 127, 131, 136, 141, 146, 151, 156, 161, 165, 170, 175, 180] ,
'15': [1, 5, 10, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 70, 75, 80, 85, 90, 96, 101, 106, 111, 117, 122, 127, 132, 138, 143, 148, 153, 159, 164, 169, 174, 180, 185, 190, 196] ,
'16': [1, 6, 11, 15, 21, 26, 31, 37, 42, 47, 53, 59, 64, 70, 75, 81, 86, 92, 98, 103, 109, 115, 120, 126, 132, 137, 143, 149, 154, 160, 166, 171, 177, 183, 188, 194, 200, 206, 211] ,
'17': [2, 6, 11, 17, 22, 28, 34, 39, 45, 51, 57, 63, 67, 75, 81, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 154, 160, 166, 172, 178, 184, 190, 196, 202, 209, 215, 221, 227] ,
'18': [2, 7, 12, 18, 24, 30, 36, 42, 48, 55, 61, 67, 74, 80, 86, 93, 99, 106, 112, 119, 125, 132, 138, 145, 151, 158, 164, 171, 177, 184, 190, 197, 203, 210, 216, 223, 230, 236, 243] ,
'19': [2, 7, 13, 19, 25, 32, 38, 45, 52, 58, 65, 72, 78, 85, 92, 99, 106, 113, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 258] ,
'20': [2, 8, 14, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 98, 105, 112, 119, 127, 134, 141, 149, 156, 163, 171, 178, 186, 193, 200, 208, 215, 222, 230, 237, 245, 252, 259, 267, 274]
})
Critical_1 = pd.DataFrame({'2': [-1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 5.0, 5.0, 5.0, 6.0, 6.0, 6.0, 7.0, 7.0, 7.0, 7.0, 8.0, 8.0, 8.0, 9.0, 9.0, 9.0, 10.0, 10.0, 10.0, 11.0] ,
'3': [-1.0, -1.0, 0.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 5.0, 5.0, 6.0, 7.0, 7.0, 8.0, 9.0, 9.0, 10.0, 11.0, 11.0, 12.0, 13.0, 13.0, 14.0, 15.0, 15.0, 16.0, 17.0, 17.0, 18.0, 19.0, 19.0, 20.0, 21.0, 21.0, 22.0, 23.0, 23.0, 24.0] ,
'4': [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0, 31.0, 32.0, 33.0, 34.0, 35.0, 36.0, 38.0, 39.0] ,
'5': [0, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 40, 42, 43, 45, 46, 48, 49, 50, 52, 53] ,
'6': [0, 2, 3, 5, 7, 8, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 37, 39, 41, 43, 45, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 68] ,
'7': [0, 2, 4, 6, 8, 11, 13, 15, 17, 19, 21, 24, 26, 28, 30, 33, 35, 37, 39, 41, 44, 46, 48, 50, 53, 55, 57, 59, 61, 64, 66, 68, 70, 73, 75, 77, 79, 82, 84] ,
'8': [1, 3, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 36, 39, 41, 44, 47, 49, 52, 54, 57, 60, 62, 65, 68, 70, 73, 76, 78, 81, 84, 86, 89, 91, 94, 97, 99] ,
'9': [1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115] ,
'10': [1, 4, 7, 11, 14, 17, 20, 24, 27, 31, 34, 37, 41, 44, 48, 51, 55, 58, 62, 65, 68, 72, 75, 79, 82, 86, 89, 93, 96, 100, 103, 107, 110, 114, 117, 121, 124, 128, 131] ,
'11': [1, 5, 8, 12, 16, 19, 23, 27, 31, 34, 38, 42, 46, 50, 54, 57, 61, 65, 69, 73, 77, 81, 85, 89, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 131, 135, 139, 143, 147] ,
'12': [2, 5, 9, 13, 17, 21, 26, 30, 34, 38, 42, 47, 51, 55, 60, 64, 68, 72, 77, 81, 85, 90, 94, 98, 103, 107, 111, 116, 120, 124, 128, 133, 137, 141, 146, 150, 154, 159, 163] ,
'13': [2, 6, 10, 15, 19, 24, 28, 33, 37, 42, 47, 51, 56, 61, 65, 70, 75, 80, 84, 89, 94, 98, 103, 108, 113, 117, 122, 127, 132, 136, 141, 146, 151, 156, 160, 165, 170, 175, 179] ,
'14': [2, 7, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 77, 82, 87, 92, 97, 102, 107, 113, 118, 123, 128, 133, 138, 144, 149, 154, 159, 164, 170, 175, 180, 185, 190, 196] ,
'15': [3, 7, 12, 18, 23, 28, 33, 39, 44, 50, 55, 61, 66, 72, 77, 83, 88, 94, 100, 105, 111, 116, 122, 128, 133, 139, 144, 150, 156, 161, 167, 172, 178, 184, 189, 195, 201, 206, 212] ,
'16': [3, 8, 14, 19, 25, 30, 36, 42, 48, 54, 60, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228] ,
'17': [3, 9, 15, 20, 26, 33, 39, 45, 51, 57, 64, 70, 77, 83, 89, 96, 102, 109, 115, 121, 128, 134, 141, 147, 154, 160, 167, 173, 180, 186, 193, 199, 206, 212, 219, 225, 232, 238, 245] ,
'18': [4, 9, 16, 22, 28, 35, 41, 48, 55, 61, 68, 75, 82, 88, 95, 102, 109, 116, 123, 130, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 212, 219, 226, 233, 240, 247, 254, 261] ,
'19': [4, 10, 17, 23, 30, 37, 44, 51, 58, 65, 72, 80, 87, 94, 101, 109, 116, 123, 130, 138, 145, 152, 160, 167, 174, 182, 189, 196, 204, 211, 218, 226, 233, 241, 248, 255, 263, 270, 278] ,
'20': [4, 11, 18, 25, 32, 39, 47, 54, 62, 69, 77, 84, 92, 100, 107, 115, 123, 130, 138, 146, 154, 161, 169, 177, 185, 192, 200, 208, 216, 224, 231, 239, 247, 255, 263, 271, 278, 286, 294] })
self.critical05 = Critical_05
self.critical1 = Critical_1
# Mann Whitney Test
x = np.asarray(data1)
y = np.asarray(data2)
n1 = len(x)
n2 = len(y)
ranked = rankdata(np.concatenate((x, y)))
rankx = ranked[0:n1] # get the x-ranks
u1 = n1*n2 + (n1*(n1+1))/2.0 - np.sum(rankx, axis=0) # calc U for x
u2 = n1*n2 - u1 # remainder is U for y
# use the min(u1, u2) as u-stat
if u1 <= u2:
stat_a, larger = u1, 1
else:
stat_a, larger = u2, 2
# compute the effect size
effect = 1 - (2*stat_a)/(n1*n2)
# Mann-Whitney test
if min(n1, n2) < 2: # sample size too small - cannot do test
return 'Sorry, sample size is too small to test significance. Please collect more data...'
# Do test for small sample size
elif 2<=min(n1, n2) <= 20 and 2 <= max(n1, n2) <= 40:
if tail != 'two': # only have data for two tail testing
return 'Sorry, sample size too small, only two-tailed test available...'
u_05 = Critical_05[str(min(n1, n2))][max(n1, n2)-2] # u=critical at signif level .05
u_1 = Critical_1[str(min(n1, n2))][max(n1, n2)-2] # u=critical at signif level .1
if significant_level == 0.05 and stat_a <= u_05:
self.significance = True
self.sample_size = 'Small'
self.n1 = n1
self.n2 = n2
self.criticalu = u_05
self.u = stat_a
self.effectsize = effect
self.largergroup = larger
elif significant_level == 0.1 and stat_a <= u_1:
self.significance = True
self.sample_size = 'Small'
self.n1 = n1
self.n2 = n2
self.criticalu = u_1
self.u = stat_a
self.effectsize = effect
self.largergroup = larger
elif significant_level == 0.05:
self.significance = False
self.sample_size = 'Small'
self.n1 = n1
self.n2 = n2
self.criticalu = u_05
self.u = stat_a
self.effectsize = effect
self.largergroup = larger
else:
self.significance = False
self.sample_size = 'Small'
self.n1 = n1
self.n2 = n2
self.criticalu = u_1
self.u = stat_a
self.effectsize = effect
self.largergroup = larger
else:
T = tiecorrect(ranked)
sd = np.sqrt(T * n1 * n2 * (n1+n2+1) / 12.0)
if T == 0:
raise ValueError('All numbers are identical in mannwhitneyu')
meanrank = n1*n2/2.0 + 0.5
if tail == 'two':
bigu = max(u1, u2)
elif tail == 'less':
bigu = u1
elif tail == 'more':
bigu = u2
z = (bigu - meanrank) / sd
if tail == 'two':
p = 2 * norm.sf(abs(z))
else:
p = norm.sf(z)
if p <= significant_level:
self.significance = True
else:
self.significance = False
self.sample_size = 'Large'
self.n1 = n1
self.n2 = n2
self.p = p
self.u = stat_a
self.effectsize = effect
self.largergroup = larger