Source code for ClearMap.Analysis.Statistics.StatisticalTests

# -*- coding: utf-8 -*-
"""
statisticalTests
================

Colelction of some statistics tests
"""
__author__    = 'Christoph Kirst <christoph.kirst.ck@gmail.com>'
__license__   = 'GPLv3 - GNU General Pulic License v3 (see LICENSE.txt)'
__copyright__ = 'Copyright © 2020 by Christoph Kirst'
__webpage__   = 'http://idisco.info'
__download__  = 'http://www.github.com/ChristophKirst/ClearMap2'

import sys
import numpy as np

from scipy.stats import rankdata
from scipy.stats import distributions


[docs] def test_cramer_von_mises_2_sample(x, y): """ Computes the Cramer von Mises two sample test. Arguments --------- x, y : 1-D ndarrays Two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different. Returns ------- t_statistic : float The t-statistic. p_value : float Two-tailed p-value. Notes ----- This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. References ---------- * modified from https://github.com/scipy/scipy/pull/3659 """ #following notation of Anderson et al. doi:10.1214/aoms/1177704477 N = len(x) M = len(y) assert N * M * (N + M) < sys.float_info.max alldata = np.concatenate((x,y)) allranks = rankdata(alldata) ri = allranks[:N] sj = allranks[-M:] i = rankdata(x) j = rankdata(y) #Anderson et al. Eqn 10 U = N*np.sum((ri - i)**2) + M*np.sum((sj - j)**2) #print U #Anderson et al. Eqn 9 T = U/(N * M * (N + M)) - (4 * M * N - 1)/(6 * (M + N)) #print T Texpected = 1./6 + 1./(6 * (M + N)) Tvariance = 1./45 * (M + N + 1)/(M + N)**2 * (4 * M * N * (M+N) - 3*(M**2 + N**2) - 2*M*N)/(4 * M * N) zscore = np.abs(T - Texpected) / np.sqrt(Tvariance) #print zscore return T, 2*distributions.norm.sf(zscore)