隨機區組設計：控制變異

Python 的實驗設計

James Chapman

Curriculum Manager, DataCamp

理解區組化

以相似單位分組，降低變異
每個區組包含所有處理
聚焦處理效果，控制區組效果

區組隨機化範例，顯示兩個由橘色與白色方格組成的網格

區組設計資料範例

athletes.head()

   Athlete_ID Initial_Fitness_Level  Muscle_Gain_kg
0         113              Beginner        3.225102
1          30              Advanced        3.976548
2         183          Intermediate        5.165449
3         200              Beginner        2.188297
4         194              Beginner        4.724162

實作隨機區組設計

使用 .groupby() 在區組內隨機抽樣

blocks = athletes.groupby('Initial_Fitness_Level').apply(

    lambda x: x.sample(frac=1)

)

blocks = blocks.reset_index(drop=True)
blocks

     Athlete_ID Initial_Fitness_Level  Muscle_Gain_kg
0           198              Advanced           5.742
1           146              Advanced           6.248
2           157              Advanced           6.049
..          ...                   ...             ...
198         164          Intermediate           6.134
199         178          Intermediate           6.591

完成的隨機區組

使用 numpy.random.choice() 在區組內隨機指派處理

blocks['Treatment'] = np.random.choice(
    ['Cardio', 'Strength Training', 'Mixed'],
    size=len(blocks))

blocks.sample(n=5)

     Athlete_ID  Initial_Fitness_Level  Muscle_Gain_kg          Treatment
 87         194               Beginner           4.724             Cardio
 54           3               Advanced           3.731  Strength Training
177          80           Intermediate           6.758              Mixed
146         183           Intermediate           5.165  Strength Training          
 60         190               Advanced           3.763             Cardio

區組內視覺化處理效果

import seaborn as sns
sns.boxplot(x='Initial_Fitness_Level', y='Muscle_Gain_kg', hue='Treatment', data=blocks)
plt.show()

區組內的盒鬚圖

區組內 ANOVA

假設顯著水準 $\alpha$ 為 0.05

from scipy.stats import f_oneway
blocks.groupby('Initial_Fitness_Level').apply(
  lambda x: f_oneway(x[x['Treatment'] == 'Cardio']['Muscle_Gain_kg'], 
                     x[x['Treatment'] == 'Mixed']['Muscle_Gain_kg'],
                     x[x['Treatment'] == 'Strength Training']['Muscle_Gain_kg'])
)

Block
Initial_Fitness_Level
Advanced        (0.7951054385317405, 0.4555687666120679)
Beginner        (0.1085790370950905, 0.8972754969684291)
Intermediate    (0.5678877824942661, 0.5698403547950377)
dtype: object

跨區組視覺化效果

import seaborn as sns
sns.boxplot(x='Initial_Fitness_Level', y='Muscle_Gain_kg', data=blocks)
plt.show()

跨區組的盒鬚圖

區組間 ANOVA

f_oneway(
  blocks[blocks['Initial_Fitness_Level'] == "Advanced"]['Muscle_Gain_kg'], 
  blocks[blocks['Initial_Fitness_Level'] == "Beginner"]['Muscle_Gain_kg'], 
  blocks[blocks['Initial_Fitness_Level'] == "Intermediate"]['Muscle_Gain_kg']
)

F_onewayResult(statistic=2.325058605244051, pvalue=0.10045536062209368)

一起來練習吧！

Python 的實驗設計