Rancangan blok acak: mengendalikan varians

Perancangan Eksperimen dengan Python

James Chapman

Curriculum Manager, DataCamp

Memahami blocking

Kurangi varians dengan mengelompokkan unit serupa
Setiap blok menerima semua perlakuan
Fokus pada efek perlakuan sambil mengendalikan efek blok

Contoh pengacakan blok dengan dua kisi kotak oranye dan putih

Contoh data rancangan blok

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

Menerapkan rancangan blok acak

Gunakan .groupby() untuk mengacak dalam tiap blok

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

Blok acak diterapkan

numpy.random.choice() untuk penugasan perlakuan acak dalam blok

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

Memvisualisasikan efek perlakuan dalam blok

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

Boxplot dalam setiap blok

ANOVA di dalam blok

Gunakan tingkat signifikansi $\alpha$ = 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

Memvisualisasikan efek antar blok

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

Boxplot antar blok

ANOVA antar blok

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)

Ayo berlatih!

Perancangan Eksperimen dengan Python