Diseño en bloques aleatorizados: controlar la varianza

Diseño experimental en Python

James Chapman

Curriculum Manager, DataCamp

Comprender el bloqueo

Reduce la varianza agrupando unidades similares
Cada bloque recibe todos los tratamientos
Enfócate en los efectos del tratamiento, controlando los efectos de bloque

Ejemplo de aleatorización por bloques con dos cuadrículas de cuadros naranjas y blancos

Ejemplo de datos en bloque

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

Implementar un diseño en bloques aleatorizados

Usa .groupby() para mezclar dentro de bloques

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

Bloques aleatorizados implementados

numpy.random.choice() para asignar tratamientos aleatorios dentro de bloques

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

Visualizar efectos por tratamiento dentro de bloques

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

Diagrama de cajas dentro de bloques

ANOVA dentro de bloques

Supón un nivel de significancia $\alpha$ = 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

Visualizar efectos entre bloques

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

Diagrama de cajas entre bloques

ANOVA entre bloques

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)

¡Vamos a practicar!

Diseño experimental en Python