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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 Conduct a Two-Sample T-Test in Python
Performs Welch's t-test for two independent samples, computing the t-statistic, degrees of freedom, and p-value using NumPy and SciPy.
import numpy as np
def two_sample_t_test(sample1, sample2):
"""Perform Welch's t-test for two independent samples."""
n1, n2 = len(sample1), len(sample2)
mean1, mean2 = np.mean(sample1), np.mean(sample2)
var1, var2 = np.var(sample1, ddof=1), np.var(sample2, ddof=1)
# Standard error of difference
…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 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 Sequential Calls in Python with unittest.mock
Use Mock.side_effect to return a different result for each sequential call and verify the call order with assert_has_calls.
import unittest
from unittest.mock import Mock
class Service:
def fetch(self, item_id):
raise NotImplementedError
def process_items(service, ids):
results = []
for item_id in ids:
result = service.fetch(item_id)
results.append(result)
return results
if __name__ == "__main__":…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 Perform Welch's t-Test in Python
Calculate the Welch t-statistic and degrees of freedom for two samples with unequal variances using Python's statistics module.
import math
from statistics import mean, variance
def welch_t_test(sample1, sample2):
n1, n2 = len(sample1), len(sample2)
mean1, mean2 = mean(sample1), mean(sample2)
var1, var2 = variance(sample1), variance(sample2)
# Welch's t statistic
t_stat = (mean1 - mean2) / math.sqrt(var1 / n1 + var2 / n2…How to Run a Fisher Exact Test in Python
Compute the two-sided Fisher exact test p-value for a 2x2 contingency table using pure Python and the math module.
from math import comb, factorial
from itertools import combinations
def hypergeometric_probability(a, b, c, d):
"""Probability of observing table [[a, b], [c, d]] under the null."""
row1 = a + b
row2 = c + d
col1 = a + c
col2 = b + d
total = row1 + row2
return (comb(row1, a) * comb(row2, …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 <…Approximate Count with HyperLogLog in Python
A mock HyperLogLog implementation uses hash-based registers to estimate cardinality of large datasets with sublinear memory.
import hashlib
class HyperLogLog:
def __init__(self, precision=4):
if precision < 4 or precision > 16:
raise ValueError("precision must be between 4 and 16")
self.precision = precision
self.registers = [0] * (1 << precision)
def _hash(self, value):
return int(hashl…Build a Full Text Search Index in Python
Create a simple inverted index for full-text search with the standard library, supporting multi-word AND queries across documents.
import re
from collections import defaultdict
class SimpleTextIndex:
def __init__(self):
self.index = defaultdict(list)
self.documents = {}
def add_document(self, doc_id, text):
self.documents[doc_id] = text
words = set(re.findall(r'\w+', text.lower()))
for word in wo…Composite index leftmost prefix in Python
Simulate a composite index in SQLite and check whether query columns match the leftmost prefix rule for index usage.
import sqlite3
def get_indexed_columns(table_name):
"""Simulate a composite index by reading column names that start with 'idx_'."""
conn = sqlite3.connect(":memory:")
conn.execute(f"CREATE TABLE {table_name} (id INTEGER, idx_col1 TEXT, idx_col2 INTEGER, other TEXT)")
conn.execute(f"CREATE INDEX idx_…Consistent Hashing with Virtual Buckets in Python
This code maps many virtual buckets onto a few physical buckets using a consistent hashing ring, ensuring balanced distribution with minimal remapping when physical buckets change.
import random
class VirtualBuckets:
"""Maps many virtual buckets onto few physical buckets using consistent hashing."""
def __init__(self, physical_buckets, virtual_factor=100):
self.physical = list(physical_buckets)
self.virtual_factor = virtual_factor
self.ring = []
self…How to Build a Connection Pool Reuse Mock in Python
Build a mock connection pool with context manager to track connection reuse, acquires, and releases in Python.
import time
from contextlib import contextmanager
class Connection:
def __init__(self, name):
self.name = name
self.in_use = False
self.busy_since = None
def fetch(self):
return f"data from {self.name}"
class ConnectionPool:
def __init__(self, size=3):
self.conn…How to Build a Shard Map Mock Dict in Python
Implement a dictionary-like class that distributes keys across multiple shards using Python's hash() for realistic data partitioning.
class ShardMap:
def __init__(self, shard_count):
self.shards = {i: {} for i in range(shard_count)}
self.shard_count = shard_count
def _shard_for(self, key):
return hash(key) % self.shard_count
def __getitem__(self, key):
return self.shards[self._shard_for(key)][key]
d…How to Create a Covering Index with INCLUDE Columns in Python
Create a covering index with INCLUDE columns in SQLite from Python and inspect the query plan to confirm the index covers the query.
import sqlite3
def create_covering_index_mock():
conn = sqlite3.connect(":memory:")
cursor = conn.cursor()
cursor.execute("""
CREATE TABLE employees (
id INTEGER PRIMARY KEY,
name TEXT,
department TEXT,
salary INTEGER
)
""")
employe…How to Eager Load with JOIN to Reduce N+1 Queries in Python
Demonstrates eager loading with a SQL JOIN to reduce N+1 query patterns down to a single database call when fetching related data.
import sqlite3
def eager_load_join_reduce(mock_db_path=":memory:"):
"""Demonstrate eager loading where joins reduce query count from N+1 to 1."""
conn = sqlite3.connect(mock_db_path)
cursor = conn.cursor()
cursor.executescript(
"""
CREATE TABLE authors (id INTEGER PRIMARY KEY, name TE…How to Implement Consistent Hashing in Python
Build a consistent hash ring in Python that distributes keys across nodes and minimizes remapping when nodes are added or removed.
import hashlib
from bisect import bisect_right
class ConsistentHashRing:
def __init__(self, nodes, replicas=3):
self.replicas = replicas
self.ring = {}
self.sorted_keys = []
for node in nodes:
self.add_node(node)
def _hash(self, key):
return int(hashlib.md…Browse by section
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