A/B testing & experimentation

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 +…

import numpy as np
from scipy import stats

def balance_check(treatment, covariate):
    """Check covariate balance between treatment and control groups."""
    treat_vals = covariate[treatment == 1]
    control_vals = covariate[treatment == 0]
    
    # Standardized mean difference
    pooled_std = np.sqrt((np.var(t…

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 …

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)
       …

import numpy as np
import pandas as pd

# Generate mock panel data: 2 groups (control=0, treatment=1) × 2 periods (pre=0, post=1)
rng = np.random.default_rng(42)
n_per_cell = 50

data = []
for group in [0, 1]:
    for period in [0, 1]:
        # True effect: treatment increases outcome by 5 in the post period
        …

import random
import json

def generate_mock_bandit_report(num_arms=5, num_rounds=100, seed=42):
    random.seed(seed)
    arms = ["A", "B", "C", "D", "E"][:num_arms]
    true_means = {arm: random.uniform(0.3, 0.7) for arm in arms}
    pulls = {arm: 0 for arm in arms}
    rewards = {arm: 0 for arm in arms}

    for _ …

import math
from scipy.stats import norm


def min_sample_size(effect_size, alpha=0.05, power=0.8):
    """
    Calculate minimum sample size for a two-sample t-test (equal groups).

    Args:
        effect_size: Cohen's d (standardized mean difference)
        alpha: significance level (Type I error)
        power: …

import random
import statistics
from collections import Counter

def explore_secondary_metrics(data):
    """Calculate secondary metrics: distribution, variability, and spread."""
    if not data:
        return "No data provided"
    
    total = sum(data)
    mean = statistics.mean(data)
    median = statistics.medi…

def get_physics_grade(exam_score, homework_score):
    """Calculate final grade from exam and homework scores."""
    exam_weight = 0.7
    homework_weight = 0.3
    return (exam_score * exam_weight) + (homework_score * homework_weight)


def mock_note(correct_score, max_score, student_name):
    """Generate a mock no…

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, …

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…

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
…

import random
import math

def mock_ci(n=100, p_true=0.5, z=1.96, seed=42):
    """Simulate a sample proportion and compute its 95% confidence interval."""
    random.seed(seed)
    successes = sum(1 for _ in range(n) if random.random() < p_true)
    p_hat = successes / n
    se = math.sqrt(p_hat * (1 - p_hat) / n)
  …

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, …

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):
       …