Python：Kendall tau相关系数的计算

关于Kendall correlation coefficient的介绍可参见：

维基百科：https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient

scipy库：https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html

写了两个版本的代码：

import numpy as np
from scipy.stats import kendalltau

data = np.array([[0.7,0.2,0.5,0],
                 [0.6,0.1,0.1,0],
                 [0.8,0.2,0.3,0],
                 [0.6,0.3,0.5,0],
                 [0.5,0.4,0.2,1],
                 [0.4,0.5,0.3,1],
                 [0.5,0.6,0.3,1],
                 [0.4,0.5,0.1,1],
                 [0.2,0.9,0.4,2],
                 [0.2,1,0.6,2],
                 [0.2,0.8,0.5,2],
                 [0.1,1,0.1,2]])

Lens =len(data)
count = 0
for i in range(Lens-1):
    for j in range(i+1,Lens):
        count = count + np.sign(data[i][0] - data[j][0]) * np.sign(data[i][2] - data[j][2])
    print('-----')
kendallCorrelation = count/((Lens*(Lens-1))/2)
kendallCorrelation_1,p_value = kendalltau(data[:,0],data[:,2])

print(kendallCorrelation)
print(kendallCorrelation_1)

from scipy.stats import kendalltau
import numpy as np
a = [1,2,3,4,5,6,7,8,9,10]
b = [4,7,2,10,3,6,8,1,5,9]
# a = [12,2,1,12,2]
# b = [1,4,7,1,0]
Lens = len(a)
count = 0
number = 0
for i in range(Lens-1):
    for j in range(i+1,Lens):
        count = count + np.sign(a[i] - a[j]) * np.sign(b[i] - b[j])
        number += 1

Kendallta1 = count/(Lens*(Lens-1)/2)
Kendallta2,p_value = kendalltau(a,b)
print(number)
print(count)
print(Kendallta1)
print(Kendallta2)

 

结果为啥算出来不一样呢？【原因：自己写的是1938年的tau系数，scipy库里面的1945年版本的tau】

下面是1945年版本的代码：

from scipy.stats import kendalltau
import numpy as np
a = [1,1,2,2,5,5,8,8,9,10]
b = [2,7,2,3,3,6,8,4,5,5]
# a = [12,2,1,12,2]
# b = [1,4,7,1,0]
Lens = len(a)

ties_onlyin_x = 0
ties_onlyin_y = 0
con_pair = 0
dis_pair = 0
for i in range(Lens-1):
    for j in range(i+1,Lens):
        test_tying_x = np.sign(a[i] - a[j])
        test_tying_y = np.sign(b[i] - b[j])
        panduan =test_tying_x * test_tying_y
        if panduan == 1:
            con_pair +=1
        elif panduan == -1:
            dis_pair +=1

        if test_tying_y ==0 and test_tying_x != 0:
            ties_onlyin_y += 1
        elif test_tying_x == 0 and test_tying_y !=0:
            ties_onlyin_x += 1

Kendallta1 = (con_pair - dis_pair)/np.sqrt((con_pair + dis_pair + ties_onlyin_x)*(dis_pair +con_pair + ties_onlyin_y))
Kendallta2,p_value = kendalltau(a,b)

print(Kendallta1)
print(Kendallta2)

跑出来结果是一样的：

0.33737388489831593
0.33737388489831593