A/B testing & experimentation
User bucketing, experiment metrics, statistical comparison, and rollout guardrails.
Bayesian A/B Test Credible Interval in Python
Simulates A/B test data and computes posterior credible intervals and the probability that variant B outperforms A using Bayesian Beta-Binomial inference.
import numpy as np
from scipy import stats
# Simulated A/B test data
n_A = 1000
n_B = 1000
conversions_A = 120
conversions_B = 140
# Prior: Beta(1, 1) uniform
alpha_prior, beta_prior = 1, 1
# Posterior parameters
alpha_A = alpha_prior + conversions_A
beta_A = beta_prior + n_A - conversions_A
alpha_B = alpha_prior +…Benjamini Hochberg FDR Correction in Python
Implement the Benjamini-HHochberg false discovery rate (FDR) procedure in Python to control the expected proportion of false positives among rejected hypotheses.
import numpy as np
def benjamini_hochberg(p_values, alpha=0.05):
p_values = np.array(p_values)
n = len(p_values)
sorted_idx = np.argsort(p_values)
sorted_p = p_values[sorted_idx]
thresholds = (np.arange(1, n + 1) / n) * alpha
significant = sorted_p <= thresholds
if not significan…Check Sample Ratio Mismatch in Python
Estimates the probability that a simple random sample's proportion differs from the population proportion by more than 10% using simulation.
import random
def sample_ratio_mismatch(population_size: int, sample_size: int, p: float) -> float:
"""
Estimate the probability that a simple random sample's proportion
differs from the population proportion by more than 10%.
"""
total_counts = [0, 0]
for _ in range(10000):
sample = …Chi-Square Test in Python for Conversion Mock Data
Compute the chi-square statistic and approximate p-value for a mock A/B conversion test using the standard library.
import math
from collections import Counter
def chi_square_statistic(observed):
"""
Compute chi-square statistic for a mock conversion test.
observed: dict mapping outcomes to observed frequencies.
"""
observed = Counter(observed)
n = sum(observed.values())
expected = n / len(observed) if …Delta Method for Ratio Metrics in A/B Testing with Python
Computes the confidence interval for the difference between two ratio metrics using the delta method, with mock A/B test data.
import numpy as np
from scipy.stats import norm
def delta_method_ratio_delta(control: np.ndarray, treatment: np.ndarray, confidence: float = 0.95):
"""Estimate confidence interval for ratio metric using delta method.
Args:
control: numerator/denominator pairs from control group (n x 2 array)
…Epsilon Greedy Bandit Mock in Python
A simple epsilon-greedy multi-armed bandit simulation that balances exploration and exploitation to estimate true means of several Bernoulli-like reward distributions.
import random
class Bandit:
def __init__(self, true_mean):
self.true_mean = true_mean
self.estimated_mean = 0.0
self.n_pulls = 0
def pull(self):
return random.gauss(self.true_mean, 1.0)
def update(self, reward):
self.n_pulls += 1
self.estimated_mean += (r…How to Compute CUPED Variance Reduction in Python
Implement CUPED in Python to reduce variance of A/B test treatment effect estimates using pre-experiment covariates.
import numpy as np
def compute_cuped_reduction(control, variant, covariate):
"""
Compute variance reduction using CUPED (Controlled Experiment with
Pre-Experiment Data). Uses pre-experiment covariate values to
reduce variance of the treatment effect estimate.
"""
control = np.asarray(control, …How to Compute Mann-Whitney U Test in Python
Compute the Mann-Whitney U statistic and p-value manually in Python with tie correction and a normal approximation for independent samples.
import numpy as np
from scipy import stats
def mann_whitney_u_mock(sample_a, sample_b):
"""Compute Mann-Whitney U and p-value manually."""
# Combine and rank
combined = sample_a + sample_b
n_a, n_b = len(sample_a), len(sample_b)
n_total = n_a + n_b
# Rank with ties handling (average ranks…How to Create an Interrupted Time Series Mock in Python
Generate simulated interrupted time series data with a pre/post-intervention trend, level shift, and noise to test segmented regression models.
import numpy as np
# Mock interrupted time series data
np.random.seed(42)
n_pre = 50
n_post = 50
time = np.arange(0, n_pre + n_post)
# Pre-intervention: linear trend + noise
pre_trend = 0.05 * time[:n_pre] + np.random.normal(0, 0.5, n_pre)
# Post-intervention: new slope + level shift + noise
post_trend = 0.05 * tim…How to Generate an Orthogonal Array for A/B Testing in Python
Generate a mock orthogonal array for multi-layer experiments with NumPy, ensuring balanced level combinations across experiment groups.
import numpy as np
def orthogonal_mock_layers(n_experiments: int, n_layers: int, n_levels: int) -> np.ndarray:
"""Generate an orthogonal array for multi-layer experiment design using base-level logic."""
ortho = np.indices((n_levels,) * n_layers).reshape(n_layers, -1).T
ortho = ortho % n_levels # Classic…How to Mock Mutual Exclusion for A/B Experiment Groups in Python
Simulate mutual exclusion for experiment groups using a thread-safe lock, ensuring only one member updates the shared counter at a time.
import threading
import time
import random
class CountingGate:
"""A mock mutual exclusion gate using a lock."""
def __init__(self):
self.counter = 0
self.lock = threading.Lock()
def enter(self, group_id, member_id):
with self.lock:
current = self.counter
t…How to Mock Time for Cache TTL Testing in Python
This code demonstrates how to test a cache's TTL expiration logic by mocking time.time with unittest.mock to control the passage of time.
import time
from unittest.mock import patch
class ConfigCache:
def __init__(self, ttl=60):
self.ttl = ttl
self._store = {}
self._timestamps = {}
def get(self, key):
if key not in self._store:
return None
if time.time() - self._timestamps[key] > self.ttl:
…How to Perform Intent-to-Treat Analysis in Python
Runs an intent-to-treat analysis on mock A/B test data, comparing outcomes by initial group assignment with a t-test for significance.
import pandas as pd
import numpy as np
def intent_to_treat_analysis(data):
"""Perform intent-to-treat (ITT) analysis.
ITT compares outcomes based on initial treatment assignment,
regardless of whether participants actually received the treatment.
"""
# Create a copy to avoid mutating the origina…How to Run a Permutation Test in Python
Run a Monte Carlo permutation test to compute a p-value for comparing two group means without parametric assumptions.
import random
import statistics
def permutation_test(group_a, group_b, n_permutations=10000, seed=42):
random.seed(seed)
combined = group_a + group_b
observed_diff = abs(statistics.mean(group_a) - statistics.mean(group_b))
count = 0
n = len(group_a)
for _ in range(n_permutations):
…How to Simulate Geo Experiments in Python
Build a mock geo experiment simulator with ramp-up/down periods, measuring weekly lift between treatment and control markets.
import random
import math
from dataclasses import dataclass
@dataclass
class GeoMarket:
name: str
base_demand: float
geo_coefficient: float
def simulate_geo_experiment(markets, weeks=12, control_weeks=6):
"""
Simulates a geo experiment with ramp-up and ramp-down periods.
Returns weekly lift p…How to join assignment logs with outcomes in Python
Merge submission log entries with grading outcomes using left join and full outer join patterns in pure Python.
from datetime import datetime, timedelta
class AssignmentLog:
def __init__(self):
self.logs = [
{"assignment_id": 101, "student_id": "S001", "submitted_at": "2024-03-01 10:30:00"},
{"assignment_id": 101, "student_id": "S002", "submitted_at": "2024-03-02 14:15:00"},
{"as…How to simulate a contextual bandit in Python
Simulate a contextual multi-armed bandit with random features and epsilon-greedy action selection in Python.
import random
class ContextualBandit:
def __init__(self, n_actions=3, n_features=4):
self.n_actions = n_actions
self.n_features = n_features
self.theta = [random.random() for _ in range(n_actions * n_features)]
def mock_context(self):
return [random.uniform(-1, 1) for _ in ra…Synthetic Control in Python: Mock Example
Implements synthetic control from scratch: learns donor weights via ridge regression on pre-period data, then predicts a counterfactual for the treated unit.
import numpy as np
class SyntheticControl:
def __init__(self, data, treated_index, pre_periods, post_periods):
self.data = np.array(data, dtype=float)
self.treated_index = treated_index
self.pre_periods = pre_periods
self.post_periods = post_periods
def fit_weights(sel…Thompson Sampling Mock Bandit in Python
Implement a Thompson sampling multi-armed bandit to explore and exploit reward probabilities across multiple options, updating Beta distributions over time.
import random
class ThompsonSamplingBandit:
def __init__(self, num_arms, alpha=1.0, beta=1.0):
self.num_arms = num_arms
self.alpha = [alpha] * num_arms
self.beta = [beta] * num_arms
def select_arm(self):
samples = [random.betavariate(a, b) for a, b in zip(self.alpha, self.beta…UCB1 Bandit Algorithm in Python
This code implements the UCB1 multi-armed bandit algorithm, balancing exploration and exploitation to identify the best arm while maximizing cumulative reward.
import math
import random
def ucb1(means, n_iterations=1000, exploration_weight=2.0):
"""Run UCB1 bandit algorithm on arms with given true means."""
n_arms = len(means)
counts = [0] * n_arms
rewards = [0.0] * n_arms
for t in range(1, n_iterations + 1):
# UCB1 selection
if t <…Browse by section
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A/B testing & experimentation — Python code examples
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