te_f_oneway.py

# -*- coding: utf-8 -*-


def get_total_mean(*args):
    """ obtaining the mean value of total data.
    """
    tmp_sum, item_number = 0.0, 0.0
    for e in args:
        tmp_sum += sum(e)
        item_number += len(e)

    return tmp_sum / item_number


def get_group_mean(group):
    """ obtaining the mean value of a group.
    """
    return float(sum(group)) / len(group)


def te_f_oneway(*args):
    """ ANOVA
        return F
    """
    total_mean = get_total_mean(*args)

    QA = sum([len(e) * ((get_group_mean(e) - total_mean)**2) for e in args])
    S2A = QA / (len(args) - 1)

    QE = sum([(i - get_group_mean(e))**2 for e in args for i in e])
    S2E = QE / (sum([len(e) for e in args]) - len(args))

    # QT can be use to check the correct : QT = QA + QE
    QT = sum([(i - total_mean)**2 for e in args for i in e])

    F = S2A / S2E
    return F


if __name__ == '__main__':
    a1 = [1600, 1610, 1650, 1680, 1700, 1720, 1800]  # mean = 2
    a2 = [1580, 1640, 1640, 1700, 1750]  # mean = 3
    a3 = [1460, 1550, 1600, 1620, 1640, 1660, 1740, 1820]  # mean = 3
    a4 = [1510, 1520, 1530, 1570, 1600, 1680]
    f = te_f_oneway(a1, a2, a3, a4)

    from scipy.stats import f_oneway
    print f_oneway(a1, a2, a3, a4)