Chi-Square Test in Python for Conversion Mock Data

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 observed else 0

    chi_sq = 0.0
    for count in observed.values():
        chi_sq += (count - expected) ** 2 / expected if expected else 0
    return chi_sq, expected

def chi_square_to_p_value(chi_sq, df):
    """
    Approximate p-value for chi-square distribution using
    Wilson-Hilferty transformation.
    df: degrees of freedom (k-1 for goodness of fit).
    """
    if chi_sq <= 0 or df <= 0:
        return 1.0
    z = ((chi_sq / df) ** (1/3) - (1 - 2/(9*df))) / math.sqrt(2/(9*df))
    p = 0.5 * (1 + math.erf(z / math.sqrt(2)))
    return 1 - p

if __name__ == "__main__":
    # Mock conversion: 100 visitors, 15 converted (success), 85 did not (failure)
    observed = {"converted": 15, "not_converted": 85}
    chi_sq, expected = chi_square_statistic(observed)
    df = len(observed) - 1
    p_value = chi_square_to_p_value(chi_sq, df)

    print(f"Observed: {dict(observed)}")
    print(f"Expected per category: {expected:.2f}")
    print(f"Chi-square statistic: {chi_sq:.4f}")
    print(f"Degrees of freedom: {df}")
    print(f"P-value (approx): {p_value:.4f}")
    print(f"Significant at 0.05: {p_value < 0.05}")