Normal Power Comparison

This notebook shows how NormalPowerAnalysis and PowerAnalysis calculators give similar powers for a switchback experiment, and the normal one is way faster.

In [1]:

from datetime import date

import numpy as np
from cluster_experiments import PowerAnalysis, ConstantPerturbator, BalancedClusteredSplitter, ExperimentAnalysis, ClusteredOLSAnalysis, NormalPowerAnalysis
import pandas as pd
from time import time



# Create fake data
N = 10_000
clusters = [f"Cluster {i}" for i in range(10)]
dates = [f"{date(2022, 1, i):%Y-%m-%d}" for i in range(1, 15)]
df = pd.DataFrame(
    {
        "cluster": np.random.choice(clusters, size=N),
        "date": np.random.choice(dates, size=N),
    }
).assign(
    # Target is a linear combination of cluster and day of week, plus some noise
    cluster_id=lambda df: df["cluster"].astype("category").cat.codes,
    day_of_week=lambda df: pd.to_datetime(df["date"]).dt.dayofweek,
    target=lambda df: df["cluster_id"] + df["day_of_week"] + np.random.normal(size=N),
)

from datetime import date import numpy as np from cluster_experiments import PowerAnalysis, ConstantPerturbator, BalancedClusteredSplitter, ExperimentAnalysis, ClusteredOLSAnalysis, NormalPowerAnalysis import pandas as pd from time import time # Create fake data N = 10_000 clusters = [f"Cluster {i}" for i in range(10)] dates = [f"{date(2022, 1, i):%Y-%m-%d}" for i in range(1, 15)] df = pd.DataFrame( { "cluster": np.random.choice(clusters, size=N), "date": np.random.choice(dates, size=N), } ).assign( # Target is a linear combination of cluster and day of week, plus some noise cluster_id=lambda df: df["cluster"].astype("category").cat.codes, day_of_week=lambda df: pd.to_datetime(df["date"]).dt.dayofweek, target=lambda df: df["cluster_id"] + df["day_of_week"] + np.random.normal(size=N), )

In [2]:

df.head()

df.head()

Out[2]:

	cluster	date	cluster_id	day_of_week	target
0	Cluster 3	2022-01-12	3	2	5.206403
1	Cluster 3	2022-01-14	3	4	7.004311
2	Cluster 9	2022-01-06	9	3	11.554722
3	Cluster 1	2022-01-10	1	0	2.697168
4	Cluster 8	2022-01-14	8	4	10.311295

Some clusters have a higher average outcome than others

In [3]:

cluster_cols = ["cluster", "date"]

splitter = BalancedClusteredSplitter(
    cluster_cols=cluster_cols,
)

perturbator = ConstantPerturbator()

analysis = ClusteredOLSAnalysis(
    cluster_cols=cluster_cols,
)

alpha = 0.05
n_simulations = 100
n_simulations_normal = 10

# Simulated power analysis, we use clustered splitter and ols clustered analysis
pw_simulated = PowerAnalysis(
    splitter=splitter,
    perturbator=perturbator,
    alpha=alpha,
    n_simulations=n_simulations,
    analysis=analysis,
)

# Normal power analysis, uses Central limit theorem to estimate power, and needs less simulations
pw_normal = NormalPowerAnalysis(
    splitter=splitter,
    alpha=alpha,
    n_simulations=n_simulations_normal,
    analysis=analysis,
)

cluster_cols = ["cluster", "date"] splitter = BalancedClusteredSplitter( cluster_cols=cluster_cols, ) perturbator = ConstantPerturbator() analysis = ClusteredOLSAnalysis( cluster_cols=cluster_cols, ) alpha = 0.05 n_simulations = 100 n_simulations_normal = 10 # Simulated power analysis, we use clustered splitter and ols clustered analysis pw_simulated = PowerAnalysis( splitter=splitter, perturbator=perturbator, alpha=alpha, n_simulations=n_simulations, analysis=analysis, ) # Normal power analysis, uses Central limit theorem to estimate power, and needs less simulations pw_normal = NormalPowerAnalysis( splitter=splitter, alpha=alpha, n_simulations=n_simulations_normal, analysis=analysis, )

In [4]:

# power line for simulated
effects = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75]
time_pw = time()
pw_simulated_line = pw_simulated.power_line(df, average_effects=effects)
print(f"Simulated power line took {time() - time_pw} seconds")

# power line for simulated effects = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75] time_pw = time() pw_simulated_line = pw_simulated.power_line(df, average_effects=effects) print(f"Simulated power line took {time() - time_pw} seconds")

Simulated power line took 35.480019092559814 seconds

In [5]:

# power line for normal
time_pw = time()
pw_normal_line = pw_normal.power_line(df, average_effects=effects)
print(f"Time for normal power line: {time() - time_pw} seconds")

# power line for normal time_pw = time() pw_normal_line = pw_normal.power_line(df, average_effects=effects) print(f"Time for normal power line: {time() - time_pw} seconds")

Time for normal power line: 0.5191936492919922 seconds

In [6]:

# power line for normal, single simulation
time_pw = time()
pw_normal.n_simulations = 1
pw_normal_line_single = pw_normal.power_line(df, average_effects=effects)
print(f"Time for normal power line single simulation: {time() - time_pw} seconds")

# power line for normal, single simulation time_pw = time() pw_normal.n_simulations = 1 pw_normal_line_single = pw_normal.power_line(df, average_effects=effects) print(f"Time for normal power line single simulation: {time() - time_pw} seconds")

Time for normal power line single simulation: 0.06762981414794922 seconds

In [7]:

pd.DataFrame(
    {
        "Average effect": effects,
        "Simulated power": pw_simulated_line.values(),
        "Normal power": pw_normal_line.values(),
        "Normal power single simulation": pw_normal_line_single.values(),
    }
).plot(
    x="Average effect",
    y=["Simulated power", "Normal power", "Normal power single simulation"],
    title="Power analysis",
    xlabel="Average effect",
    ylabel="Power",
    marker="o",
)

pd.DataFrame( { "Average effect": effects, "Simulated power": pw_simulated_line.values(), "Normal power": pw_normal_line.values(), "Normal power single simulation": pw_normal_line_single.values(), } ).plot( x="Average effect", y=["Simulated power", "Normal power", "Normal power single simulation"], title="Power analysis", xlabel="Average effect", ylabel="Power", marker="o", )

Out[7]:

<AxesSubplot:title={'center':'Power analysis'}, xlabel='Average effect', ylabel='Power'>

In [8]:

# pw_normal can also be used to find MDE
mde = pw_normal.mde(df, power=0.7)
print(f"Minimum detectable effect: {mde:.2f}")

# and we can retrieve the power for a given effect size
power = pw_normal.power_analysis(df, average_effect=mde)
print(f"Power for MDE: {power:.2f}, should be 0.7")

# pw_normal can also be used to find MDE mde = pw_normal.mde(df, power=0.7) print(f"Minimum detectable effect: {mde:.2f}") # and we can retrieve the power for a given effect size power = pw_normal.power_analysis(df, average_effect=mde) print(f"Power for MDE: {power:.2f}, should be 0.7")

Minimum detectable effect: 1.44
Power for MDE: 0.70, should be 0.7