ANOVA 后的事后分析

Python 实验设计

James Chapman

Curriculum Manager, DataCamp

何时使用事后检验

在 ANOVA 显著后使用
用于探查两两组间差异

一只卡通手拉开蓝色舞台幕布，露出四个标有 A、B、C、D 的彩色圆点网络，线条表示成对比较。部分连接以星号标注显著差异，部分标注为不显著。该图示意 ANOVA 发现总体效应后，事后检验揭示具体哪些组存在差异。

事后方法要点

Tukey 的 HSD（诚实显著性差异）
- 适用于多重比较，稳健
- 最适合全组间比较
Bonferroni 校正
- 调整 p 值以控制 I 类错误
- 最适合特定成对比较

John Tukey

Carlo Emilio Bonferroni

¹ https://www.amphilsoc.org/item-detail/photograph-john-wilder-tukey ² https://en.wikipedia.org/wiki/Carlo_Emilio_Bonferroni

数据集：营销广告活动

ad_campaigns

              Ad_Campaign  Click_Through_Rate
1300    Seasonal Discount        2.1659547732
1661          New Arrival        2.9409657365
2762       Loyalty Reward        3.2476777154
571     Seasonal Discount        3.3382186561
775     Seasonal Discount        1.7148876401

用透视表整理数据

pivot_table = ad_campaigns.pivot_table(values='Click_Through_Rate',
                                       index='Ad_Campaign',
                                       aggfunc="mean")
print(pivot_table)

                   Click_Through_Rate
Ad_Campaign                          
Loyalty Reward               2.792716
New Arrival                  3.013843
Seasonal Discount            2.518917

执行 ANOVA

from scipy.stats import f_oneway
campaign_types = ['Seasonal Discount', 'New Arrival', 'Loyalty Reward']

groups = [ad_campaigns[ad_campaigns['Ad_Campaign'] == campaign]['Click_Through_Rate']
              for campaign in campaign_types]


f_stat, p_val = f_oneway(*groups)
print(p_val)

4.484124496940693e-134

Tukey HSD 检验

from statsmodels.stats.multicomp import pairwise_tukeyhsd

tukey_results = pairwise_tukeyhsd(ad_campaigns['Click_Through_Rate'],

                                  ad_campaigns['Ad_Campaign'],

                                  alpha=0.05)

print(tukey_results)

         Multiple Comparison of Means - Tukey HSD, FWER=0.05          
===========================================================================
        group1             group2  meandiff  p-adj   lower    upper  reject
<hr />---------------------------------------------------------------------
Loyalty Reward        New Arrival    0.2211   0.0    0.176   0.2663    True
Loyalty Reward  Seasonal Discount   -0.2738   0.0  -0.3189  -0.2287    True
   New Arrival  Seasonal Discount   -0.4949   0.0  -0.5401  -0.4498    True
<hr />---------------------------------------------------------------------

Bonferroni 校正设置

from scipy.stats import ttest_ind
from statsmodels.sandbox.stats.multicomp import multipletests

p_values = []


comparisons = [('Seasonal Discount', 'New Arrival'),
               ('Seasonal Discount', 'Loyalty Reward'), 
               ('New Arrival', 'Loyalty Reward')]


for comp in comparisons:
    group1 = ad_campaigns[ad_campaigns['Ad_Campaign'] == comp[0]]['Click_Through_Rate']
    group2 = ad_campaigns[ad_campaigns['Ad_Campaign'] == comp[1]]['Click_Through_Rate']

    t_stat, p_val = ttest_ind(group1, group2)

    p_values.append(p_val)

执行 Bonferroni 校正

p_adjusted = multipletests(p_values, alpha=0.05, method='bonferroni')

print(f"Adjusted P-values: {p_adjusted[1]}")

Adjusted P-values: [5.33634403e-133 2.17627991e-043 5.62590083e-029]

Passons à la pratique !

Python 实验设计