Randomiserad blockdesign: kontrollera varians

Experimentell design i Python

James Chapman

Curriculum Manager, DataCamp

Förstå blockering

Minska varians genom att gruppera liknande enheter
Varje block får alla behandlingar
Fokus på behandlingseffekter, med kontroll för blockeffekter

Ett exempel på blockrandomisering med två rutnät av orange och vita rutor

Exempel på blockdesigndata

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

Implementera randomiserad blockdesign

Använd .groupby() för att blanda inom block

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

Implementerade randomiserade block

numpy.random.choice() för slumpmässig behandlingstilldelning inom block

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

Visualisera behandlingseffekter inom block

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

Lådagram inom block

ANOVA inom block

Anta en signifikansnivå $\alpha$ på 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

Visualisera effekter över block

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

Lådagram över block

ANOVA mellan block

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)

Nu kör vi en övning!

Experimentell design i Python