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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 …
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 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 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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