【统计学】如何计算 离散变量 的相关系数，及python实现

如何计算 离散变量 的相关系数

1 离散变量与离散变量的相关系数（克莱姆Cramer’ s V系数）

参考文章：

相关性检验-Cramer’ s V系数

文章内容预览

Python实现

• 示例数据

import pandas as pd

df = pd.DataFrame([
    [12,12,8,8,0],
    [4,4,20,6,6],
    [2,2,8,30,18],
    [2,2,4,16,36],
], index=['Psychology','Econominc','Law','Other'], columns=['Pop','Rock','jazz','classical','other'])

df

index	Pop	Rock	jazz	classical	other
Psychology	12	12	8	8	0
Econominc	4	4	20	6	6
Law	2	2	8	30	18
Other	2	2	4	16	36

# 数据格式转换，及公式计算

df = df.stack().to_frame().reset_index()
df.columns = ['study','music_preferenct', 'cnts']

def cramer_corr(df:pd.DataFrame, colname1:str, colname2:str, value:str) -> float:

    df = df[[colname1,colname2,value]]
    df.columns = ['col1','col2','cnts']

    df['E-col1'] = df['col1'].map(df.groupby(['col1'])['cnts'].sum())
    df['E-col2'] = df['col2'].map(df.groupby(['col2'])['cnts'].sum())
    df['E'] = df['E-col1'] * df['E-col2'] / df['cnts'].sum()

    x2 = (pow(df['E']-df['cnts'],2) / df['E']).sum()
    corr = pow( x2 / df['cnts'].sum() / (min(df['col1'].nunique(),df['col2'].nunique())-1), 0.5)
    return corr

cramer_corr(df, 'study', 'music_preferenct','cnts')

结果：0.4337604732431808

2 离散变量与连续变量的相关系数

参考文章：

某乎回答

文章内容预览

Python实现

import pandas as pd

df = pd.DataFrame([
    [27,33,16,29,32,23,25,28,22,18,26,26,15,29,26],
    'tcbbctctbbctbcb',
]).T
df.columns = ['age','brand']

df

index	age	brand
0	27	t
1	33	c
2	16	b
3	29	b
4	32	c
5	23	t
6	25	c
7	28	t
8	22	b
9	18	b
10	26	c
11	26	t
12	15	b
13	29	c
14	26	b

def corr_ratio(df:pd.DataFrame, str_colname, value_colname)->float:
    std = df.groupby([str_colname])[value_colname].std()
    var = df.groupby([str_colname])[value_colname].var(0)
    cnt = df.groupby([str_colname])[value_colname].count()
    mean = df.groupby([str_colname])[value_colname].mean()
    delta_mean = df.groupby([str_colname])[value_colname].mean() - df[value_colname].mean()
    corr = (pow(delta_mean,2)*cnt).sum() / ( (var * cnt).sum() + (pow(delta_mean,2)*cnt).sum() )

    return corr

corr_ratio(df, 'brand', 'age')

结果：0.44554455445544555