import numpy as np


def kendall_w(scores):
    """
    :param scores: rows correspond to category levels, e.g., for QS this would be unc. sampling, CAL etc, and the
        columns correspond to the scores.
    :return:
    """
    if scores.ndim!=2:
        raise 'scores  matrix must be 2-dimensional'
    m = scores.shape[0]  # raters/levels
    n = scores.shape[1]  # items rated
    score_ranks = np.argsort(scores, axis=1)
    denom = m**2*(n**3-n)
    rating_sums = np.sum(score_ranks, axis=0)
    S = n*np.var(rating_sums)
    return 12*S/denom