从Python 3.10开始，Pearson的相关系数(statistics.correlation)可以直接在标准库中获得:

from statistics import correlation

# a = [15, 12, 8, 8, 7, 7, 7, 6, 5, 3]
# b = [10, 25, 17, 11, 13, 17, 20, 13, 9, 15]
correlation(a, b)
# 0.1449981545806852

嗯，很多回复的代码都很长，很难读…

我建议在处理数组时使用numpy及其漂亮的特性:

import numpy as np
def pcc(X, Y):
   ''' Compute Pearson Correlation Coefficient. '''
   # Normalise X and Y
   X -= X.mean(0)
   Y -= Y.mean(0)
   # Standardise X and Y
   X /= X.std(0)
   Y /= Y.std(0)
   # Compute mean product
   return np.mean(X*Y)

# Using it on a random example
from random import random
X = np.array([random() for x in xrange(100)])
Y = np.array([random() for x in xrange(100)])
pcc(X, Y)

你可以看看scipy.stats:

from pydoc import help
from scipy.stats.stats import pearsonr
help(pearsonr)

>>>
Help on function pearsonr in module scipy.stats.stats:

pearsonr(x, y)
 Calculates a Pearson correlation coefficient and the p-value for testing
 non-correlation.

 The Pearson correlation coefficient measures the linear relationship
 between two datasets. Strictly speaking, Pearson's correlation requires
 that each dataset be normally distributed. Like other correlation
 coefficients, this one varies between -1 and +1 with 0 implying no
 correlation. Correlations of -1 or +1 imply an exact linear
 relationship. Positive correlations imply that as x increases, so does
 y. Negative correlations imply that as x increases, y decreases.

 The p-value roughly indicates the probability of an uncorrelated system
 producing datasets that have a Pearson correlation at least as extreme
 as the one computed from these datasets. The p-values are not entirely
 reliable but are probably reasonable for datasets larger than 500 or so.

 Parameters
 ----------
 x : 1D array
 y : 1D array the same length as x

 Returns
 -------
 (Pearson's correlation coefficient,
  2-tailed p-value)

 References
 ----------
 http://www.statsoft.com/textbook/glosp.html#Pearson%20Correlation

下面是mkh答案的一个变体，比它运行得快得多，还有scipy.stats。皮尔逊，使用numba。

import numba

@numba.jit
def corr(data1, data2):
    M = data1.size

    sum1 = 0.
    sum2 = 0.
    for i in range(M):
        sum1 += data1[i]
        sum2 += data2[i]
    mean1 = sum1 / M
    mean2 = sum2 / M

    var_sum1 = 0.
    var_sum2 = 0.
    cross_sum = 0.
    for i in range(M):
        var_sum1 += (data1[i] - mean1) ** 2
        var_sum2 += (data2[i] - mean2) ** 2
        cross_sum += (data1[i] * data2[i])

    std1 = (var_sum1 / M) ** .5
    std2 = (var_sum2 / M) ** .5
    cross_mean = cross_sum / M

    return (cross_mean - mean1 * mean2) / (std1 * std2)

与其依赖numpy/scipy，我认为我的答案应该是最容易编码和理解计算Pearson相关系数(PCC)的步骤。

import math

# calculates the mean
def mean(x):
    sum = 0.0
    for i in x:
         sum += i
    return sum / len(x) 

# calculates the sample standard deviation
def sampleStandardDeviation(x):
    sumv = 0.0
    for i in x:
         sumv += (i - mean(x))**2
    return math.sqrt(sumv/(len(x)-1))

# calculates the PCC using both the 2 functions above
def pearson(x,y):
    scorex = []
    scorey = []

    for i in x: 
        scorex.append((i - mean(x))/sampleStandardDeviation(x)) 

    for j in y:
        scorey.append((j - mean(y))/sampleStandardDeviation(y))

# multiplies both lists together into 1 list (hence zip) and sums the whole list   
    return (sum([i*j for i,j in zip(scorex,scorey)]))/(len(x)-1)

PCC的意义基本上是向你展示两个变量/列表的相关性有多强。 需要注意的是，PCC值的范围是-1到1。 0到1之间的值表示正相关。 0值=最高变异(没有任何相关性)。 -1到0之间的值表示负相关。

从Python 3.10开始，Pearson的相关系数(statistics.correlation)可以直接在标准库中获得:

from statistics import correlation

# a = [15, 12, 8, 8, 7, 7, 7, 6, 5, 3]
# b = [10, 25, 17, 11, 13, 17, 20, 13, 9, 15]
correlation(a, b)
# 0.1449981545806852