Function pearson_chi_squared_test

pattern/metrics.py:747–773

Returns (X2, P) for the n x m observed and expected data (containing absolute frequencies). If expected is None, an equal distribution over all classes is assumed. If df is None, it is the number of classes-1 (i.e., len(observed[0]) - 1). P < 0.05: significant P < 0.

(observed=[], expected=[], df=None, tail=UPPER)

    return [[n[i] * m[j] / s for j in range(len(O[i]))] for i in range(len(O))]

def pearson_chi_squared_test(observed=[], expected=[], df=None, tail=UPPER):
    """ Returns (X2, P) for the n x m observed and expected data (containing absolute frequencies).
        If expected is None, an equal distribution over all classes is assumed.
        If df is None, it is the number of classes-1 (i.e., len(observed[0]) - 1).
        P < 0.05: significant
        P < 0.01: very significant
        This means that if P < 5%, the data is unevenly distributed (e.g., biased).
        The following test shows that the die is fair:
        ---------------------------------------
        |       | 1  | 2  | 3  | 4  | 5  | 6  | 
        | rolls | 22 | 21 | 22 | 27 | 22 | 36 |
        ---------------------------------------
        chi2([[22, 21, 22, 27, 22, 36]]) => (6.72, 0.24)
    """
    # The P-value (upper tail area) is obtained from the incomplete gamma integral:
    # P(X2 | v) = gammai(v/2, x/2) with v degrees of freedom.
    # See: Cephes, https://github.com/scipy/scipy/blob/master/scipy/special/cephes/chdtr.c
    O  = observed
    E  = expected or _expected(observed)
    df = df or (len(O) > 0 and len(O[0])-1 or 0)
    X2 = 0.0
    for i in range(len(O)):
        for j in range(len(O[i])):
            if O[i][j] != 0 and E[i][j] != 0:
                X2 += (O[i][j] - E[i][j]) ** 2.0 / E[i][j]
    P = gammai(df * 0.5, X2 * 0.5, tail)
    return (X2, P)
    
chi2 = chi_squared = pearson_chi_squared_test