卡方适配度检验

Python 假设检验

James Chapman

Curriculum Manager, DataCamp

紫色链接

当您发现自己已访问过顶部资源时有何感受？

purple_link_counts = stack_overflow['purple_link'].value_counts()

purple_link_counts = purple_link_counts.rename_axis('purple_link')\
                                       .reset_index(name='n')\
                                       .sort_values('purple_link')

         purple_link     n
2             Amused   368
3            Annoyed   263
0  Hello, old friend  1225
1        Indifferent   405

提出假设

hypothesized = pd.DataFrame({
  'purple_link': ['Amused', 'Annoyed', 'Hello, old friend', 'Indifferent'], 
  'prop': [1/6, 1/6, 1/2, 1/6]})

         purple_link      prop
0             Amused  0.166667
1            Annoyed  0.166667
2  Hello, old friend  0.500000
3        Indifferent  0.166667

$H_{0}$：样本符合假设分布

$H_{A}$：样本不符合假设分布

$\chi^{2}$ 衡量各组观测值与期望的偏离程度

alpha = 0.01

按类别的假设计数

n_total = len(stack_overflow)
hypothesized["n"] = hypothesized["prop"] * n_total

         purple_link      prop            n
0             Amused  0.166667   376.833333
1            Annoyed  0.166667   376.833333
2  Hello, old friend  0.500000  1130.500000
3        Indifferent  0.166667   376.833333

可视化计数

import matplotlib.pyplot as plt

plt.bar(purple_link_counts['purple_link'], purple_link_counts['n'], 
        color='red', label='Observed')

plt.bar(hypothesized['purple_link'], hypothesized['n'], alpha=0.5, 
        color='blue', label='Hypothesized')

plt.legend()
plt.show()

可视化计数

按 purple_link 答案的条形图：红色为观测计数，蓝色为假设计数。

卡方适配度检验

print(hypothesized)

         purple_link      prop            n
0             Amused  0.166667   376.833333
1            Annoyed  0.166667   376.833333
2  Hello, old friend  0.500000  1130.500000
3        Indifferent  0.166667   376.833333

from scipy.stats import chisquare
chisquare(f_obs=purple_link_counts['n'], f_exp=hypothesized['n'])

Power_divergenceResult(statistic=44.59840778416629, pvalue=1.1261810719413759e-09)

让我们来练习！

Python 假设检验