How to Run a Fisher Exact Test in Python

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, c)) / comb(total, col1)


def fisher_exact_test(a, b, c, d):
    """Two-sided Fisher exact test p-value for 2x2 contingency table."""
    observed = [a, b, c, d]
    row1 = a + b
    row2 = c + d
    col1 = a + c
    col2 = b + d

    if min(row1, row2, col1, col2) < 0:
        raise ValueError("Table entries must be non-negative")
    if row1 == 0 or row2 == 0 or col1 == 0 or col2 == 0:
        return 1.0  # Degenerate table

    prob_observed = hypergeometric_probability(a, b, c, d)
    p_value = 0.0
    max_a = min(row1, col1)
    min_a = max(0, col1 - row2)

    for x in range(min_a, max_a + 1):
        y = row1 - x
        z = col1 - x
        w = row2 - z
        if y >= 0 and z >= 0 and w >= 0:
            prob = hypergeometric_probability(x, y, z, w)
            if prob <= prob_observed:
                p_value += prob
    return p_value


if __name__ == "__main__":
    # Example: [[6, 2], [1, 5]]
    table = [6, 2, 1, 5]
    p = fisher_exact_test(*table)
    print(f"Table: {table}")
    print(f"Two-sided p-value: {p:.6f}")