Function fisher_exact_test

pattern/metrics.py:672–711

Fast implementation of Fisher's exact test (two-tailed). Returns the significance for the given 2x2 contingency table: < 0.05: significant < 0.01: very significant The following test shows a very significant correlation between gender & dieting: -------------

(a, b, c, d, **kwargs)

#--- FISHER'S EXACT TEST ---------------------------------------------------------------------------

def fisher_exact_test(a, b, c, d, **kwargs):
    """ Fast implementation of Fisher's exact test (two-tailed).
        Returns the significance for the given 2x2 contingency table:
        < 0.05: significant
        < 0.01: very significant
        The following test shows a very significant correlation between gender & dieting:
        -----------------------------
        |             | men | women |
        |     dieting |  1  |   9   |
        | non-dieting | 11  |   3   |
        -----------------------------
        fisher_exact_test(a=1, b=9, c=11, d=3) => 0.0028
    """
    _cache = {}
    # Hypergeometric distribution.
    # (a+b)!(c+d)!(a+c)!(b+d)! / a!b!c!d!n! for n=a+b+c+d
    def p(a, b, c, d):
        return C(a + b, a) * C(c + d, c) / C(a + b + c + d, a + c)
    # Binomial coefficient.
    # n! / k!(n-k)! for 0 <= k <= n
    def C(n, k):
        if len(_cache) > 10000:
            _cache.clear()
        if k > n - k: # 2x speedup.
            k = n - k
        if 0 <= k <= n and (n, k) not in _cache:
            c = 1.0
            for i in range(1, int(k + 1)):
                c *= n - k + i
                c /= i
            _cache[(n, k)] = c # 3x speedup.
        return _cache.get((n, k), 0.0)
    # Probability of the given data.
    cutoff = p(a, b, c, d)
    # Probabilities of "more extreme" data, in both directions (two-tailed).
    # Based on: http://www.koders.com/java/fid868948AD5196B75C4C39FEA15A0D6EAF34920B55.aspx?s=252
    s = [cutoff] + \
        [p(a+i, b-i, c-i, d+i) for i in range(1, min(b, c) + 1)] + \
        [p(a-i, b+i, c+i, d-i) for i in range(1, min(a, d) + 1)]
    return sum(v for v in s if v <= cutoff) or 0.0
    
fisher_test = fisher_exact_test