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

如果你不喜欢安装scipy，我使用了这个快速的hack，稍微修改了Programming Collective Intelligence:

def pearsonr(x, y):
  # Assume len(x) == len(y)
  n = len(x)
  sum_x = float(sum(x))
  sum_y = float(sum(y))
  sum_x_sq = sum(xi*xi for xi in x)
  sum_y_sq = sum(yi*yi for yi in y)
  psum = sum(xi*yi for xi, yi in zip(x, y))
  num = psum - (sum_x * sum_y/n)
  den = pow((sum_x_sq - pow(sum_x, 2) / n) * (sum_y_sq - pow(sum_y, 2) / n), 0.5)
  if den == 0: return 0
  return num / den

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。

您可能想知道如何在寻找特定方向的相关性(负相关或正相关)的上下文中解释您的概率。这是我写的一个函数。它甚至可能是正确的!

这是基于我从http://www.vassarstats.net/rsig.html和http://en.wikipedia.org/wiki/Student%27s_t_distribution上收集到的信息，感谢这里发布的其他答案。

# Given (possibly random) variables, X and Y, and a correlation direction,
# returns:
#  (r, p),
# where r is the Pearson correlation coefficient, and p is the probability
# that there is no correlation in the given direction.
#
# direction:
#  if positive, p is the probability that there is no positive correlation in
#    the population sampled by X and Y
#  if negative, p is the probability that there is no negative correlation
#  if 0, p is the probability that there is no correlation in either direction
def probabilityNotCorrelated(X, Y, direction=0):
    x = len(X)
    if x != len(Y):
        raise ValueError("variables not same len: " + str(x) + ", and " + \
                         str(len(Y)))
    if x < 6:
        raise ValueError("must have at least 6 samples, but have " + str(x))
    (corr, prb_2_tail) = stats.pearsonr(X, Y)

    if not direction:
        return (corr, prb_2_tail)

    prb_1_tail = prb_2_tail / 2
    if corr * direction > 0:
        return (corr, prb_1_tail)

    return (corr, 1 - prb_1_tail)

def correlation_score(y_true, y_pred):
    """Scores the predictions according to the competition rules. 
    
    It is assumed that the predictions are not constant.
    
    Returns the average of each sample's Pearson correlation coefficient"""
    
    y2 = y_pred.copy()
    y2 -= y2.mean(axis=0);    y2 /= y2.std(axis=0) 
    y1 = y_true.copy(); 
    y1 -= y1.mean(axis=0);    y1 /= y1.std(axis=0) 
        
    c = (y1*y2).mean().mean()# Correlation for rescaled matrices is just matrix product and average 
        
    return c

你可以用pandas.DataFrame这样做。相关系数:

import pandas as pd
a = [[1, 2, 3],
     [5, 6, 9],
     [5, 6, 11],
     [5, 6, 13],
     [5, 3, 13]]
df = pd.DataFrame(data=a)
df.corr()

这给了

          0         1         2
0  1.000000  0.745601  0.916579
1  0.745601  1.000000  0.544248
2  0.916579  0.544248  1.000000