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Detect Concept Drift in Python with a Simple Statistical Test
Detect concept drift by comparing the mean of recent data against a reference distribution using a z-score-like threshold.
import random
import statistics
def detect_drift(recent, reference, threshold=1.5):
ref_mean = statistics.mean(reference)
ref_std = statistics.stdev(reference)
recent_mean = statistics.mean(recent)
drift_score = abs(recent_mean - ref_mean) / (ref_std if ref_std > 0 else 1)
drifted = drif…How to Impute Missing Values with Mean in Python
Replace None values in a list with the mean of the existing values using Python's statistics module.
import statistics
from statistics import mean
def impute_mean(values):
"""Replace None with the mean of the non-None values."""
# Filter out None to compute the mean of existing values
valid = [v for v in values if v is not None]
if not valid:
return values # nothing to impute if all are Non…How to Mock ROC AUC in Python
Compute ROC AUC from scratch in Python using pairwise comparisons between positive and negative score distributions, ideal for testing ML models without sklearn.
import random
from math import comb
def mock_roc_auc(scores, labels):
"""Compute mock ROC AUC by simulating a classifier's score distribution."""
random.seed(42)
n = len(labels)
pos_scores = [scores[i] for i in range(n) if labels[i] == 1]
neg_scores = [scores[i] for i in range(n) if labels[i] == …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…Bonferroni Correction in Python
Applies the Bonferroni correction to a list of p-values to control the family-wise error rate when performing multiple comparisons.
import numpy as np
def bonferroni_correction(p_values, alpha=0.05):
"""Apply Bonferroni correction to a list of p-values."""
n = len(p_values)
corrected_alpha = alpha / n
significant = [p < corrected_alpha for p in p_values]
return corrected_alpha, significant
if __name__ == "__main__":
# Moc…Bootstrap Confidence Interval in Python
Estimates a confidence interval for a statistic (like the mean) using bootstrap resampling in pure Python.
import random
def bootstrap_ci(data, statistic, n_bootstraps=1000, ci_level=0.95, seed=42):
random.seed(seed)
n = len(data)
boot_stats = []
for _ in range(n_bootstraps):
sample = [random.choice(data) for _ in range(n)]
boot_stats.append(statistic(sample))
boot_stats.sort()
l…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)
…Generate a Mock Multi-Armed Bandit Report in Python
Simulate a multi-armed bandit experiment with random pulls and rewards, then output a JSON report with per-arm statistics.
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 _ …How to Build a Guardrail Metrics Monitor in Python
This code implements a mock monitor that records metric values, checks them against thresholds, and summarizes pass/alert statistics.
import random
import time
from collections import defaultdict
class GuardrailMetricsMonitor:
def __init__(self):
self.metrics = defaultdict(list)
self.thresholds = {
"prompt_toxicity": 0.8,
"response_length": 500,
"latency_ms": 1000,
}
def record(s…How to Calculate Minimum Sample Size for a T-Test in Python
Compute the minimum sample size per group for a two-sample t-test using effect size, significance level, and statistical power.
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: …How to Calculate Secondary Metrics in Python
Computes distribution, variability, and spread of a numeric dataset using Python's statistics and collections modules.
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…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 Mock a Confidence Interval for a Proportion in Python
Simulate a Bernoulli sample and compute a 95% confidence interval for a proportion using the normal approximation in Python.
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)
…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 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):
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