背景
大家都知道现在大数据非常火爆，在大数据还没有出现时，用的都是“小数据”，这些“小数据”在分析时大部分用的都是Excel、SPSS等工具，直到现在把Excel运用的很熟练的人，仍然很受青睐。但是Python的到来，使处理大数据比较方便。那么之前在Excel、SPSS中的描述统计、假设检验在Python中怎么使用呢？下面将进行详细介绍，前提是已经掌握numpy、pandas这两个库，并且对统计知识有所了解
加载数据
这里引用的是GitHub上的一个CSV数据文件，insurance.csv 保险数据
，可以下载下来参考练习
网址：https://github.com/stedy/Machine-Learning-with-R-datasets
>>> import numpy as np
>>> import pandas as pd
>>> data=pd.read_csv('F:/Machine-Learning datasets/insurance.csv')
>>> data
age sex bmi children smoker region charges
0 19 female 27.900 0 yes southwest 16884.92400
1 18 male 33.770 1 no southeast 1725.55230
2 28 male 33.000 3 no southeast 4449.46200
3 33 male 22.705 0 no northwest 21984.47061
4 32 male 28.880 0 no northwest 3866.85520
... ... ... ... ... ... ... ...
1333 50 male 30.970 3 no northwest 10600.54830
1334 18 female 31.920 0 no northeast 2205.98080
1335 18 female 36.850 0 no southeast 1629.83350
1336 21 female 25.800 0 no southwest 2007.94500
1337 61 female 29.070 0 yes northwest 29141.36030
[1338 rows x 7 columns]
>>> data.isnull().sum()
age 0
sex 0
bmi 0
children 0
smoker 0
region 0
charges 0
dtype: int64
>>> data.dtypes
age int64
sex object
bmi float64
children int64
smoker object
region object
charges float64
dtype: object
描述统计各指标
-
最大值、最小值
>>> data['age'].max()
64
>>> data['age'].min()
18
-
均值
>>> data['age'].mean()
39.20702541106129
-
方差
>>> data['age'].std()
14.049960379216172
-
中位数
>>> data['age'].median()
39.0
-
众数
众数有时会有多个，这里是全部返回
>>> data['age'].mode()
0 18
dtype: int64
>>> d=pd.DataFrame([1,1,1,2,2,2,3,4,4,4,5,5,6],columns=['a'])
>>> d['a'].mode()
0 1
1 2
2 4
dtype: int64
-
分位数
>>> data['age'].quantile([0,0.25,0.5,0.75,1])
0.00 18.0
0.25 27.0
0.50 39.0
0.75 51.0
1.00 64.0
Name: age, dtype: float64
-
频数统计
>>> data['region'].value_counts()
southeast 364
northwest 325
southwest 325
northeast 324
Name: region, dtype: int64
-
极差
>>> data['age'].max()-data['age'].min()
46
-
四分位差
>>> data['age'].quantile(0.75)-data['age'].quantile(0.25)
24.0
-
变异系数
>>> data['age'].std()/data['age'].mean()
0.3583531326824994
假设检验
-
单样本t检验
>>> data
age sex bmi children smoker region charges
0 19 female 27.900 0 yes southwest 16884.92400
1 18 male 33.770 1 no southeast 1725.55230
2 28 male 33.000 3 no southeast 4449.46200
3 33 male 22.705 0 no northwest 21984.47061
4 32 male 28.880 0 no northwest 3866.85520
... ... ... ... ... ... ... ...
1333 50 male 30.970 3 no northwest 10600.54830
1334 18 female 31.920 0 no northeast 2205.98080
1335 18 female 36.850 0 no southeast 1629.83350
1336 21 female 25.800 0 no southwest 2007.94500
1337 61 female 29.070 0 yes northwest 29141.36030
[1338 rows x 7 columns]
>>> data['age'].mean()
39.20702541106129
>>>
>>> import statsmodels.api as sm #加载分析库
>>> t=sm.stats.DescrStatsW(data['age']) #构造统计量对象
>>> t.ttest_mean(38) #t检验，假设总体均值为38，返回t值、P值、自由度
(3.142457193279878, 0.0017121567548687802, 1337.0)
>>> t.ttest_mean(39) #假设总体均值为39，p>0.05，接受原假设
(0.5389849179805168, 0.5899869939488361, 1337.0)
>>> t.ttest_mean(18) #假设总体均值为18，p<0.05，小于0.05拒绝原假设
(55.21190269926711, 0.0, 1337.0)
-
双样本t检验
>>> data.groupby('sex').mean()['charges']
sex
female 12569.578844
male 13956.751178
Name: charges, dtype: float64
>>> sex0=data[data['sex']=='female']['charges']
>>> sex1=data[data['sex']=='male']['charges']
>>> from scipy import stats
>>> leveneTestRes=stats.levene(sex0,sex1) #方差齐性检验
>>> leveneTestRes #p值<0.05，说明方差非齐性
LeveneResult(statistic=9.90925122305512, pvalue=0.0016808765833903443)
>>> stats.stats.ttest_ind(sex0,sex1,equal_var=False) #双样本T检验
Ttest_indResult(statistic=-2.1008878232359565, pvalue=0.035841014956016645)
相关系数
>>> data[['age','charges']].corr(method='pearson') #皮尔逊相关系数
age charges
age 1.000000 0.299008
charges 0.299008 1.000000
>>> data[['age','charges']].corr(method='spearman') #斯皮尔曼等级相关系数
age charges
age 1.000000 0.534392
charges 0.534392 1.000000
>>> data[['age','charges']].corr(method='kendall') #肯德尔相关系数
age charges
age 1.000000 0.475302
charges 0.475302 1.000000
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