1599 lines
66 KiB
Python
1599 lines
66 KiB
Python
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"""
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Tests for the stats.mstats module (support for masked arrays)
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"""
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import warnings
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import platform
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import numpy as np
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from numpy import nan
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import numpy.ma as ma
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from numpy.ma import masked, nomask
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import scipy.stats.mstats as mstats
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from scipy import stats
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from .common_tests import check_named_results
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import pytest
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from pytest import raises as assert_raises
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from numpy.ma.testutils import (assert_equal, assert_almost_equal,
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assert_array_almost_equal, assert_array_almost_equal_nulp, assert_,
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assert_allclose, assert_array_equal)
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from numpy.testing import suppress_warnings
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class TestMquantiles(object):
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def test_mquantiles_limit_keyword(self):
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# Regression test for Trac ticket #867
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data = np.array([[6., 7., 1.],
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[47., 15., 2.],
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[49., 36., 3.],
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[15., 39., 4.],
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[42., 40., -999.],
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[41., 41., -999.],
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[7., -999., -999.],
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[39., -999., -999.],
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[43., -999., -999.],
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[40., -999., -999.],
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[36., -999., -999.]])
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desired = [[19.2, 14.6, 1.45],
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[40.0, 37.5, 2.5],
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[42.8, 40.05, 3.55]]
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quants = mstats.mquantiles(data, axis=0, limit=(0, 50))
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assert_almost_equal(quants, desired)
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def check_equal_gmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
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# Note this doesn't test when axis is not specified
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x = mstats.gmean(array_like, axis=axis, dtype=dtype)
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assert_allclose(x, desired, rtol=rtol)
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assert_equal(x.dtype, dtype)
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def check_equal_hmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
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x = stats.hmean(array_like, axis=axis, dtype=dtype)
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assert_allclose(x, desired, rtol=rtol)
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assert_equal(x.dtype, dtype)
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class TestGeoMean(object):
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def test_1d(self):
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a = [1, 2, 3, 4]
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desired = np.power(1*2*3*4, 1./4.)
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check_equal_gmean(a, desired, rtol=1e-14)
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def test_1d_ma(self):
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# Test a 1d masked array
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a = ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
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desired = 45.2872868812
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check_equal_gmean(a, desired)
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a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
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desired = np.power(1*2*3, 1./3.)
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check_equal_gmean(a, desired, rtol=1e-14)
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def test_1d_ma_value(self):
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# Test a 1d masked array with a masked value
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a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100], mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
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desired = 41.4716627439
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check_equal_gmean(a, desired)
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def test_1d_ma0(self):
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# Test a 1d masked array with zero element
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a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 0])
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desired = 41.4716627439
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with np.errstate(all='ignore'):
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check_equal_gmean(a, desired)
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def test_1d_ma_inf(self):
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# Test a 1d masked array with negative element
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a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, -1])
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desired = 41.4716627439
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with np.errstate(all='ignore'):
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check_equal_gmean(a, desired)
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@pytest.mark.skipif(not hasattr(np, 'float96'), reason='cannot find float96 so skipping')
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def test_1d_float96(self):
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a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
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desired_dt = np.power(1*2*3, 1./3.).astype(np.float96)
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check_equal_gmean(a, desired_dt, dtype=np.float96, rtol=1e-14)
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def test_2d_ma(self):
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a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
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mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
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desired = np.array([1, 2, 3, 4])
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check_equal_gmean(a, desired, axis=0, rtol=1e-14)
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desired = ma.array([np.power(1*2*3*4, 1./4.),
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np.power(2*3, 1./2.),
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np.power(1*4, 1./2.)])
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check_equal_gmean(a, desired, axis=-1, rtol=1e-14)
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# Test a 2d masked array
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a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
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desired = 52.8885199
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check_equal_gmean(np.ma.array(a), desired)
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class TestHarMean(object):
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def test_1d(self):
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a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
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desired = 3. / (1./1 + 1./2 + 1./3)
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check_equal_hmean(a, desired, rtol=1e-14)
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a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
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desired = 34.1417152147
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check_equal_hmean(a, desired)
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a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
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mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
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desired = 31.8137186141
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check_equal_hmean(a, desired)
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@pytest.mark.skipif(not hasattr(np, 'float96'), reason='cannot find float96 so skipping')
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def test_1d_float96(self):
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a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
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desired_dt = np.asarray(3. / (1./1 + 1./2 + 1./3), dtype=np.float96)
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check_equal_hmean(a, desired_dt, dtype=np.float96)
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def test_2d(self):
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a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
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mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
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desired = ma.array([1, 2, 3, 4])
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check_equal_hmean(a, desired, axis=0, rtol=1e-14)
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desired = [4./(1/1.+1/2.+1/3.+1/4.), 2./(1/2.+1/3.), 2./(1/1.+1/4.)]
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check_equal_hmean(a, desired, axis=-1, rtol=1e-14)
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a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
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desired = 38.6696271841
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check_equal_hmean(np.ma.array(a), desired)
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class TestRanking(object):
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def test_ranking(self):
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x = ma.array([0,1,1,1,2,3,4,5,5,6,])
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assert_almost_equal(mstats.rankdata(x),
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[1,3,3,3,5,6,7,8.5,8.5,10])
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x[[3,4]] = masked
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assert_almost_equal(mstats.rankdata(x),
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[1,2.5,2.5,0,0,4,5,6.5,6.5,8])
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assert_almost_equal(mstats.rankdata(x, use_missing=True),
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[1,2.5,2.5,4.5,4.5,4,5,6.5,6.5,8])
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x = ma.array([0,1,5,1,2,4,3,5,1,6,])
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assert_almost_equal(mstats.rankdata(x),
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[1,3,8.5,3,5,7,6,8.5,3,10])
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x = ma.array([[0,1,1,1,2], [3,4,5,5,6,]])
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assert_almost_equal(mstats.rankdata(x),
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[[1,3,3,3,5], [6,7,8.5,8.5,10]])
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assert_almost_equal(mstats.rankdata(x, axis=1),
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[[1,3,3,3,5], [1,2,3.5,3.5,5]])
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assert_almost_equal(mstats.rankdata(x,axis=0),
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[[1,1,1,1,1], [2,2,2,2,2,]])
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class TestCorr(object):
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def test_pearsonr(self):
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# Tests some computations of Pearson's r
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x = ma.arange(10)
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with warnings.catch_warnings():
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# The tests in this context are edge cases, with perfect
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# correlation or anticorrelation, or totally masked data.
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# None of these should trigger a RuntimeWarning.
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warnings.simplefilter("error", RuntimeWarning)
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assert_almost_equal(mstats.pearsonr(x, x)[0], 1.0)
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assert_almost_equal(mstats.pearsonr(x, x[::-1])[0], -1.0)
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x = ma.array(x, mask=True)
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pr = mstats.pearsonr(x, x)
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assert_(pr[0] is masked)
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assert_(pr[1] is masked)
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x1 = ma.array([-1.0, 0.0, 1.0])
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y1 = ma.array([0, 0, 3])
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r, p = mstats.pearsonr(x1, y1)
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assert_almost_equal(r, np.sqrt(3)/2)
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assert_almost_equal(p, 1.0/3)
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# (x2, y2) have the same unmasked data as (x1, y1).
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mask = [False, False, False, True]
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x2 = ma.array([-1.0, 0.0, 1.0, 99.0], mask=mask)
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y2 = ma.array([0, 0, 3, -1], mask=mask)
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r, p = mstats.pearsonr(x2, y2)
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assert_almost_equal(r, np.sqrt(3)/2)
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assert_almost_equal(p, 1.0/3)
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def test_spearmanr(self):
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# Tests some computations of Spearman's rho
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(x, y) = ([5.05,6.75,3.21,2.66], [1.65,2.64,2.64,6.95])
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assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
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(x, y) = ([5.05,6.75,3.21,2.66,np.nan],[1.65,2.64,2.64,6.95,np.nan])
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(x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
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assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
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x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
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1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
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y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
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0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
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assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
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x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
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1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7, np.nan]
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y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
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0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4, np.nan]
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(x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
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assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
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# Next test is to make sure calculation uses sufficient precision.
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# The denominator's value is ~n^3 and used to be represented as an
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# int. 2000**3 > 2**32 so these arrays would cause overflow on
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# some machines.
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x = list(range(2000))
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y = list(range(2000))
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y[0], y[9] = y[9], y[0]
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y[10], y[434] = y[434], y[10]
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y[435], y[1509] = y[1509], y[435]
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# rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
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# = 1 - (1 / 500)
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# = 0.998
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assert_almost_equal(mstats.spearmanr(x,y)[0], 0.998)
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# test for namedtuple attributes
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res = mstats.spearmanr(x, y)
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attributes = ('correlation', 'pvalue')
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check_named_results(res, attributes, ma=True)
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@pytest.mark.skipif(platform.machine() == 'ppc64le',
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reason="fails/crashes on ppc64le")
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def test_kendalltau(self):
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# check case with with maximum disorder and p=1
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x = ma.array(np.array([9, 2, 5, 6]))
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y = ma.array(np.array([4, 7, 9, 11]))
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [0.0, 1.0]
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assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
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# simple case without ties
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x = ma.array(np.arange(10))
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y = ma.array(np.arange(10))
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [1.0, 5.511463844797e-07]
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assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
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# check exception in case of invalid method keyword
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assert_raises(ValueError, mstats.kendalltau, x, y, method='banana')
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# swap a couple of values
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b = y[1]
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y[1] = y[2]
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y[2] = b
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [0.9555555555555556, 5.511463844797e-06]
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assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
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# swap a couple more
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b = y[5]
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y[5] = y[6]
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y[6] = b
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [0.9111111111111111, 2.976190476190e-05]
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assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
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# same in opposite direction
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x = ma.array(np.arange(10))
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y = ma.array(np.arange(10)[::-1])
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [-1.0, 5.511463844797e-07]
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assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
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# swap a couple of values
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b = y[1]
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y[1] = y[2]
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y[2] = b
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# Cross-check with exact result from R:
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# cor.test(x,y,method="kendall",exact=1)
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expected = [-0.9555555555555556, 5.511463844797e-06]
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|
|
assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
|
||
|
|
|
||
|
|
# swap a couple more
|
||
|
|
b = y[5]
|
||
|
|
y[5] = y[6]
|
||
|
|
y[6] = b
|
||
|
|
# Cross-check with exact result from R:
|
||
|
|
# cor.test(x,y,method="kendall",exact=1)
|
||
|
|
expected = [-0.9111111111111111, 2.976190476190e-05]
|
||
|
|
assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
|
||
|
|
|
||
|
|
# Tests some computations of Kendall's tau
|
||
|
|
x = ma.fix_invalid([5.05, 6.75, 3.21, 2.66, np.nan])
|
||
|
|
y = ma.fix_invalid([1.65, 26.5, -5.93, 7.96, np.nan])
|
||
|
|
z = ma.fix_invalid([1.65, 2.64, 2.64, 6.95, np.nan])
|
||
|
|
assert_almost_equal(np.asarray(mstats.kendalltau(x, y)),
|
||
|
|
[+0.3333333, 0.75])
|
||
|
|
assert_almost_equal(np.asarray(mstats.kendalltau(x, y, method='asymptotic')),
|
||
|
|
[+0.3333333, 0.4969059])
|
||
|
|
assert_almost_equal(np.asarray(mstats.kendalltau(x, z)),
|
||
|
|
[-0.5477226, 0.2785987])
|
||
|
|
#
|
||
|
|
x = ma.fix_invalid([0, 0, 0, 0, 20, 20, 0, 60, 0, 20,
|
||
|
|
10, 10, 0, 40, 0, 20, 0, 0, 0, 0, 0, np.nan])
|
||
|
|
y = ma.fix_invalid([0, 80, 80, 80, 10, 33, 60, 0, 67, 27,
|
||
|
|
25, 80, 80, 80, 80, 80, 80, 0, 10, 45, np.nan, 0])
|
||
|
|
result = mstats.kendalltau(x, y)
|
||
|
|
assert_almost_equal(np.asarray(result), [-0.1585188, 0.4128009])
|
||
|
|
# make sure internal variable use correct precision with
|
||
|
|
# larger arrays
|
||
|
|
x = np.arange(2000, dtype=float)
|
||
|
|
x = ma.masked_greater(x, 1995)
|
||
|
|
y = np.arange(2000, dtype=float)
|
||
|
|
y = np.concatenate((y[1000:], y[:1000]))
|
||
|
|
assert_(np.isfinite(mstats.kendalltau(x, y)[1]))
|
||
|
|
|
||
|
|
# test for namedtuple attributes
|
||
|
|
res = mstats.kendalltau(x, y)
|
||
|
|
attributes = ('correlation', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_kendalltau_seasonal(self):
|
||
|
|
# Tests the seasonal Kendall tau.
|
||
|
|
x = [[nan, nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
|
||
|
|
[4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
|
||
|
|
[3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
|
||
|
|
[nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
|
||
|
|
x = ma.fix_invalid(x).T
|
||
|
|
output = mstats.kendalltau_seasonal(x)
|
||
|
|
assert_almost_equal(output['global p-value (indep)'], 0.008, 3)
|
||
|
|
assert_almost_equal(output['seasonal p-value'].round(2),
|
||
|
|
[0.18,0.53,0.20,0.04])
|
||
|
|
|
||
|
|
def test_pointbiserial(self):
|
||
|
|
x = [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,
|
||
|
|
0,0,0,0,1,-1]
|
||
|
|
y = [14.8,13.8,12.4,10.1,7.1,6.1,5.8,4.6,4.3,3.5,3.3,3.2,3.0,
|
||
|
|
2.8,2.8,2.5,2.4,2.3,2.1,1.7,1.7,1.5,1.3,1.3,1.2,1.2,1.1,
|
||
|
|
0.8,0.7,0.6,0.5,0.2,0.2,0.1,np.nan]
|
||
|
|
assert_almost_equal(mstats.pointbiserialr(x, y)[0], 0.36149, 5)
|
||
|
|
|
||
|
|
# test for namedtuple attributes
|
||
|
|
res = mstats.pointbiserialr(x, y)
|
||
|
|
attributes = ('correlation', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTrimming(object):
|
||
|
|
|
||
|
|
def test_trim(self):
|
||
|
|
a = ma.arange(10)
|
||
|
|
assert_equal(mstats.trim(a), [0,1,2,3,4,5,6,7,8,9])
|
||
|
|
a = ma.arange(10)
|
||
|
|
assert_equal(mstats.trim(a,(2,8)), [None,None,2,3,4,5,6,7,8,None])
|
||
|
|
a = ma.arange(10)
|
||
|
|
assert_equal(mstats.trim(a,limits=(2,8),inclusive=(False,False)),
|
||
|
|
[None,None,None,3,4,5,6,7,None,None])
|
||
|
|
a = ma.arange(10)
|
||
|
|
assert_equal(mstats.trim(a,limits=(0.1,0.2),relative=True),
|
||
|
|
[None,1,2,3,4,5,6,7,None,None])
|
||
|
|
|
||
|
|
a = ma.arange(12)
|
||
|
|
a[[0,-1]] = a[5] = masked
|
||
|
|
assert_equal(mstats.trim(a, (2,8)),
|
||
|
|
[None, None, 2, 3, 4, None, 6, 7, 8, None, None, None])
|
||
|
|
|
||
|
|
x = ma.arange(100).reshape(10, 10)
|
||
|
|
expected = [1]*10 + [0]*70 + [1]*20
|
||
|
|
trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
|
||
|
|
assert_equal(trimx._mask.ravel(), expected)
|
||
|
|
trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
|
||
|
|
assert_equal(trimx._mask.ravel(), expected)
|
||
|
|
trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=-1)
|
||
|
|
assert_equal(trimx._mask.T.ravel(), expected)
|
||
|
|
|
||
|
|
# same as above, but with an extra masked row inserted
|
||
|
|
x = ma.arange(110).reshape(11, 10)
|
||
|
|
x[1] = masked
|
||
|
|
expected = [1]*20 + [0]*70 + [1]*20
|
||
|
|
trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
|
||
|
|
assert_equal(trimx._mask.ravel(), expected)
|
||
|
|
trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
|
||
|
|
assert_equal(trimx._mask.ravel(), expected)
|
||
|
|
trimx = mstats.trim(x.T, (0.1,0.2), relative=True, axis=-1)
|
||
|
|
assert_equal(trimx.T._mask.ravel(), expected)
|
||
|
|
|
||
|
|
def test_trim_old(self):
|
||
|
|
x = ma.arange(100)
|
||
|
|
assert_equal(mstats.trimboth(x).count(), 60)
|
||
|
|
assert_equal(mstats.trimtail(x,tail='r').count(), 80)
|
||
|
|
x[50:70] = masked
|
||
|
|
trimx = mstats.trimboth(x)
|
||
|
|
assert_equal(trimx.count(), 48)
|
||
|
|
assert_equal(trimx._mask, [1]*16 + [0]*34 + [1]*20 + [0]*14 + [1]*16)
|
||
|
|
x._mask = nomask
|
||
|
|
x.shape = (10,10)
|
||
|
|
assert_equal(mstats.trimboth(x).count(), 60)
|
||
|
|
assert_equal(mstats.trimtail(x).count(), 80)
|
||
|
|
|
||
|
|
def test_trimr(self):
|
||
|
|
x = ma.arange(10)
|
||
|
|
result = mstats.trimr(x, limits=(0.15, 0.14), inclusive=(False, False))
|
||
|
|
expected = ma.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
|
||
|
|
mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 1])
|
||
|
|
assert_equal(result, expected)
|
||
|
|
assert_equal(result.mask, expected.mask)
|
||
|
|
|
||
|
|
def test_trimmedmean(self):
|
||
|
|
data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
|
||
|
|
296,299,306,376,428,515,666,1310,2611])
|
||
|
|
assert_almost_equal(mstats.trimmed_mean(data,0.1), 343, 0)
|
||
|
|
assert_almost_equal(mstats.trimmed_mean(data,(0.1,0.1)), 343, 0)
|
||
|
|
assert_almost_equal(mstats.trimmed_mean(data,(0.2,0.2)), 283, 0)
|
||
|
|
|
||
|
|
def test_trimmed_stde(self):
|
||
|
|
data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
|
||
|
|
296,299,306,376,428,515,666,1310,2611])
|
||
|
|
assert_almost_equal(mstats.trimmed_stde(data,(0.2,0.2)), 56.13193, 5)
|
||
|
|
assert_almost_equal(mstats.trimmed_stde(data,0.2), 56.13193, 5)
|
||
|
|
|
||
|
|
def test_winsorization(self):
|
||
|
|
data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
|
||
|
|
296,299,306,376,428,515,666,1310,2611])
|
||
|
|
assert_almost_equal(mstats.winsorize(data,(0.2,0.2)).var(ddof=1),
|
||
|
|
21551.4, 1)
|
||
|
|
assert_almost_equal(
|
||
|
|
mstats.winsorize(data, (0.2,0.2),(False,False)).var(ddof=1),
|
||
|
|
11887.3, 1)
|
||
|
|
data[5] = masked
|
||
|
|
winsorized = mstats.winsorize(data)
|
||
|
|
assert_equal(winsorized.mask, data.mask)
|
||
|
|
|
||
|
|
def test_winsorization_nan(self):
|
||
|
|
data = ma.array([np.nan, np.nan, 0, 1, 2])
|
||
|
|
assert_raises(ValueError, mstats.winsorize, data, (0.05, 0.05),
|
||
|
|
nan_policy='raise')
|
||
|
|
# Testing propagate (default behavior)
|
||
|
|
assert_equal(mstats.winsorize(data, (0.4, 0.4)),
|
||
|
|
ma.array([2, 2, 2, 2, 2]))
|
||
|
|
assert_equal(mstats.winsorize(data, (0.8, 0.8)),
|
||
|
|
ma.array([np.nan, np.nan, np.nan, np.nan, np.nan]))
|
||
|
|
assert_equal(mstats.winsorize(data, (0.4, 0.4), nan_policy='omit'),
|
||
|
|
ma.array([np.nan, np.nan, 2, 2, 2]))
|
||
|
|
assert_equal(mstats.winsorize(data, (0.8, 0.8), nan_policy='omit'),
|
||
|
|
ma.array([np.nan, np.nan, 2, 2, 2]))
|
||
|
|
|
||
|
|
class TestMoments(object):
|
||
|
|
# Comparison numbers are found using R v.1.5.1
|
||
|
|
# note that length(testcase) = 4
|
||
|
|
# testmathworks comes from documentation for the
|
||
|
|
# Statistics Toolbox for Matlab and can be found at both
|
||
|
|
# https://www.mathworks.com/help/stats/kurtosis.html
|
||
|
|
# https://www.mathworks.com/help/stats/skewness.html
|
||
|
|
# Note that both test cases came from here.
|
||
|
|
testcase = [1,2,3,4]
|
||
|
|
testmathworks = ma.fix_invalid([1.165, 0.6268, 0.0751, 0.3516, -0.6965,
|
||
|
|
np.nan])
|
||
|
|
testcase_2d = ma.array(
|
||
|
|
np.array([[0.05245846, 0.50344235, 0.86589117, 0.36936353, 0.46961149],
|
||
|
|
[0.11574073, 0.31299969, 0.45925772, 0.72618805, 0.75194407],
|
||
|
|
[0.67696689, 0.91878127, 0.09769044, 0.04645137, 0.37615733],
|
||
|
|
[0.05903624, 0.29908861, 0.34088298, 0.66216337, 0.83160998],
|
||
|
|
[0.64619526, 0.94894632, 0.27855892, 0.0706151, 0.39962917]]),
|
||
|
|
mask=np.array([[True, False, False, True, False],
|
||
|
|
[True, True, True, False, True],
|
||
|
|
[False, False, False, False, False],
|
||
|
|
[True, True, True, True, True],
|
||
|
|
[False, False, True, False, False]], dtype=bool))
|
||
|
|
|
||
|
|
def test_moment(self):
|
||
|
|
y = mstats.moment(self.testcase,1)
|
||
|
|
assert_almost_equal(y,0.0,10)
|
||
|
|
y = mstats.moment(self.testcase,2)
|
||
|
|
assert_almost_equal(y,1.25)
|
||
|
|
y = mstats.moment(self.testcase,3)
|
||
|
|
assert_almost_equal(y,0.0)
|
||
|
|
y = mstats.moment(self.testcase,4)
|
||
|
|
assert_almost_equal(y,2.5625)
|
||
|
|
|
||
|
|
def test_variation(self):
|
||
|
|
y = mstats.variation(self.testcase)
|
||
|
|
assert_almost_equal(y,0.44721359549996, 10)
|
||
|
|
|
||
|
|
def test_skewness(self):
|
||
|
|
y = mstats.skew(self.testmathworks)
|
||
|
|
assert_almost_equal(y,-0.29322304336607,10)
|
||
|
|
y = mstats.skew(self.testmathworks,bias=0)
|
||
|
|
assert_almost_equal(y,-0.437111105023940,10)
|
||
|
|
y = mstats.skew(self.testcase)
|
||
|
|
assert_almost_equal(y,0.0,10)
|
||
|
|
|
||
|
|
def test_kurtosis(self):
|
||
|
|
# Set flags for axis = 0 and fisher=0 (Pearson's definition of kurtosis
|
||
|
|
# for compatibility with Matlab)
|
||
|
|
y = mstats.kurtosis(self.testmathworks, 0, fisher=0, bias=1)
|
||
|
|
assert_almost_equal(y, 2.1658856802973, 10)
|
||
|
|
# Note that MATLAB has confusing docs for the following case
|
||
|
|
# kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
|
||
|
|
# kurtosis(x) gives a biased estimate of Fisher's skewness (Pearson-3)
|
||
|
|
# The MATLAB docs imply that both should give Fisher's
|
||
|
|
y = mstats.kurtosis(self.testmathworks, fisher=0, bias=0)
|
||
|
|
assert_almost_equal(y, 3.663542721189047, 10)
|
||
|
|
y = mstats.kurtosis(self.testcase, 0, 0)
|
||
|
|
assert_almost_equal(y, 1.64)
|
||
|
|
|
||
|
|
# test that kurtosis works on multidimensional masked arrays
|
||
|
|
correct_2d = ma.array(np.array([-1.5, -3., -1.47247052385, 0.,
|
||
|
|
-1.26979517952]),
|
||
|
|
mask=np.array([False, False, False, True,
|
||
|
|
False], dtype=bool))
|
||
|
|
assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1),
|
||
|
|
correct_2d)
|
||
|
|
for i, row in enumerate(self.testcase_2d):
|
||
|
|
assert_almost_equal(mstats.kurtosis(row), correct_2d[i])
|
||
|
|
|
||
|
|
correct_2d_bias_corrected = ma.array(
|
||
|
|
np.array([-1.5, -3., -1.88988209538, 0., -0.5234638463918877]),
|
||
|
|
mask=np.array([False, False, False, True, False], dtype=bool))
|
||
|
|
assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1,
|
||
|
|
bias=False),
|
||
|
|
correct_2d_bias_corrected)
|
||
|
|
for i, row in enumerate(self.testcase_2d):
|
||
|
|
assert_almost_equal(mstats.kurtosis(row, bias=False),
|
||
|
|
correct_2d_bias_corrected[i])
|
||
|
|
|
||
|
|
# Check consistency between stats and mstats implementations
|
||
|
|
assert_array_almost_equal_nulp(mstats.kurtosis(self.testcase_2d[2, :]),
|
||
|
|
stats.kurtosis(self.testcase_2d[2, :]),
|
||
|
|
nulp=4)
|
||
|
|
|
||
|
|
def test_mode(self):
|
||
|
|
a1 = [0,0,0,1,1,1,2,3,3,3,3,4,5,6,7]
|
||
|
|
a2 = np.reshape(a1, (3,5))
|
||
|
|
a3 = np.array([1,2,3,4,5,6])
|
||
|
|
a4 = np.reshape(a3, (3,2))
|
||
|
|
ma1 = ma.masked_where(ma.array(a1) > 2, a1)
|
||
|
|
ma2 = ma.masked_where(a2 > 2, a2)
|
||
|
|
ma3 = ma.masked_where(a3 < 2, a3)
|
||
|
|
ma4 = ma.masked_where(ma.array(a4) < 2, a4)
|
||
|
|
assert_equal(mstats.mode(a1, axis=None), (3,4))
|
||
|
|
assert_equal(mstats.mode(a1, axis=0), (3,4))
|
||
|
|
assert_equal(mstats.mode(ma1, axis=None), (0,3))
|
||
|
|
assert_equal(mstats.mode(a2, axis=None), (3,4))
|
||
|
|
assert_equal(mstats.mode(ma2, axis=None), (0,3))
|
||
|
|
assert_equal(mstats.mode(a3, axis=None), (1,1))
|
||
|
|
assert_equal(mstats.mode(ma3, axis=None), (2,1))
|
||
|
|
assert_equal(mstats.mode(a2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
|
||
|
|
assert_equal(mstats.mode(ma2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
|
||
|
|
assert_equal(mstats.mode(a2, axis=-1), ([[0],[3],[3]], [[3],[3],[1]]))
|
||
|
|
assert_equal(mstats.mode(ma2, axis=-1), ([[0],[1],[0]], [[3],[1],[0]]))
|
||
|
|
assert_equal(mstats.mode(ma4, axis=0), ([[3,2]], [[1,1]]))
|
||
|
|
assert_equal(mstats.mode(ma4, axis=-1), ([[2],[3],[5]], [[1],[1],[1]]))
|
||
|
|
|
||
|
|
a1_res = mstats.mode(a1, axis=None)
|
||
|
|
|
||
|
|
# test for namedtuple attributes
|
||
|
|
attributes = ('mode', 'count')
|
||
|
|
check_named_results(a1_res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_mode_modifies_input(self):
|
||
|
|
# regression test for gh-6428: mode(..., axis=None) may not modify
|
||
|
|
# the input array
|
||
|
|
im = np.zeros((100, 100))
|
||
|
|
im[:50, :] += 1
|
||
|
|
im[:, :50] += 1
|
||
|
|
cp = im.copy()
|
||
|
|
mstats.mode(im, None)
|
||
|
|
assert_equal(im, cp)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPercentile(object):
|
||
|
|
def setup_method(self):
|
||
|
|
self.a1 = [3, 4, 5, 10, -3, -5, 6]
|
||
|
|
self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
|
||
|
|
self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
|
||
|
|
|
||
|
|
def test_percentile(self):
|
||
|
|
x = np.arange(8) * 0.5
|
||
|
|
assert_equal(mstats.scoreatpercentile(x, 0), 0.)
|
||
|
|
assert_equal(mstats.scoreatpercentile(x, 100), 3.5)
|
||
|
|
assert_equal(mstats.scoreatpercentile(x, 50), 1.75)
|
||
|
|
|
||
|
|
def test_2D(self):
|
||
|
|
x = ma.array([[1, 1, 1],
|
||
|
|
[1, 1, 1],
|
||
|
|
[4, 4, 3],
|
||
|
|
[1, 1, 1],
|
||
|
|
[1, 1, 1]])
|
||
|
|
assert_equal(mstats.scoreatpercentile(x, 50), [1, 1, 1])
|
||
|
|
|
||
|
|
|
||
|
|
class TestVariability(object):
|
||
|
|
""" Comparison numbers are found using R v.1.5.1
|
||
|
|
note that length(testcase) = 4
|
||
|
|
"""
|
||
|
|
testcase = ma.fix_invalid([1,2,3,4,np.nan])
|
||
|
|
|
||
|
|
def test_sem(self):
|
||
|
|
# This is not in R, so used: sqrt(var(testcase)*3/4) / sqrt(3)
|
||
|
|
y = mstats.sem(self.testcase)
|
||
|
|
assert_almost_equal(y, 0.6454972244)
|
||
|
|
n = self.testcase.count()
|
||
|
|
assert_allclose(mstats.sem(self.testcase, ddof=0) * np.sqrt(n/(n-2)),
|
||
|
|
mstats.sem(self.testcase, ddof=2))
|
||
|
|
|
||
|
|
def test_zmap(self):
|
||
|
|
# This is not in R, so tested by using:
|
||
|
|
# (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
|
||
|
|
y = mstats.zmap(self.testcase, self.testcase)
|
||
|
|
desired_unmaskedvals = ([-1.3416407864999, -0.44721359549996,
|
||
|
|
0.44721359549996, 1.3416407864999])
|
||
|
|
assert_array_almost_equal(desired_unmaskedvals,
|
||
|
|
y.data[y.mask == False], decimal=12)
|
||
|
|
|
||
|
|
def test_zscore(self):
|
||
|
|
# This is not in R, so tested by using:
|
||
|
|
# (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
|
||
|
|
y = mstats.zscore(self.testcase)
|
||
|
|
desired = ma.fix_invalid([-1.3416407864999, -0.44721359549996,
|
||
|
|
0.44721359549996, 1.3416407864999, np.nan])
|
||
|
|
assert_almost_equal(desired, y, decimal=12)
|
||
|
|
|
||
|
|
|
||
|
|
class TestMisc(object):
|
||
|
|
|
||
|
|
def test_obrientransform(self):
|
||
|
|
args = [[5]*5+[6]*11+[7]*9+[8]*3+[9]*2+[10]*2,
|
||
|
|
[6]+[7]*2+[8]*4+[9]*9+[10]*16]
|
||
|
|
result = [5*[3.1828]+11*[0.5591]+9*[0.0344]+3*[1.6086]+2*[5.2817]+2*[11.0538],
|
||
|
|
[10.4352]+2*[4.8599]+4*[1.3836]+9*[0.0061]+16*[0.7277]]
|
||
|
|
assert_almost_equal(np.round(mstats.obrientransform(*args).T, 4),
|
||
|
|
result, 4)
|
||
|
|
|
||
|
|
def test_ks_2samp(self):
|
||
|
|
x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
|
||
|
|
[4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
|
||
|
|
[3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
|
||
|
|
[nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
|
||
|
|
x = ma.fix_invalid(x).T
|
||
|
|
(winter, spring, summer, fall) = x.T
|
||
|
|
|
||
|
|
assert_almost_equal(np.round(mstats.ks_2samp(winter, spring), 4),
|
||
|
|
(0.1818, 0.9628))
|
||
|
|
assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'g'), 4),
|
||
|
|
(0.1469, 0.6886))
|
||
|
|
assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'l'), 4),
|
||
|
|
(0.1818, 0.6011))
|
||
|
|
|
||
|
|
def test_friedmanchisq(self):
|
||
|
|
# No missing values
|
||
|
|
args = ([9.0,9.5,5.0,7.5,9.5,7.5,8.0,7.0,8.5,6.0],
|
||
|
|
[7.0,6.5,7.0,7.5,5.0,8.0,6.0,6.5,7.0,7.0],
|
||
|
|
[6.0,8.0,4.0,6.0,7.0,6.5,6.0,4.0,6.5,3.0])
|
||
|
|
result = mstats.friedmanchisquare(*args)
|
||
|
|
assert_almost_equal(result[0], 10.4737, 4)
|
||
|
|
assert_almost_equal(result[1], 0.005317, 6)
|
||
|
|
# Missing values
|
||
|
|
x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
|
||
|
|
[4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
|
||
|
|
[3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
|
||
|
|
[nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
|
||
|
|
x = ma.fix_invalid(x)
|
||
|
|
result = mstats.friedmanchisquare(*x)
|
||
|
|
assert_almost_equal(result[0], 2.0156, 4)
|
||
|
|
assert_almost_equal(result[1], 0.5692, 4)
|
||
|
|
|
||
|
|
# test for namedtuple attributes
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(result, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
def test_regress_simple():
|
||
|
|
# Regress a line with sinusoidal noise. Test for #1273.
|
||
|
|
x = np.linspace(0, 100, 100)
|
||
|
|
y = 0.2 * np.linspace(0, 100, 100) + 10
|
||
|
|
y += np.sin(np.linspace(0, 20, 100))
|
||
|
|
|
||
|
|
slope, intercept, r_value, p_value, sterr = mstats.linregress(x, y)
|
||
|
|
assert_almost_equal(slope, 0.19644990055858422)
|
||
|
|
assert_almost_equal(intercept, 10.211269918932341)
|
||
|
|
|
||
|
|
# test for namedtuple attributes
|
||
|
|
res = mstats.linregress(x, y)
|
||
|
|
attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
def test_theilslopes():
|
||
|
|
# Test for basic slope and intercept.
|
||
|
|
slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1])
|
||
|
|
assert_almost_equal(slope, 0.5)
|
||
|
|
assert_almost_equal(intercept, 0.5)
|
||
|
|
|
||
|
|
# Test for correct masking.
|
||
|
|
y = np.ma.array([0, 1, 100, 1], mask=[False, False, True, False])
|
||
|
|
slope, intercept, lower, upper = mstats.theilslopes(y)
|
||
|
|
assert_almost_equal(slope, 1./3)
|
||
|
|
assert_almost_equal(intercept, 2./3)
|
||
|
|
|
||
|
|
# Test of confidence intervals from example in Sen (1968).
|
||
|
|
x = [1, 2, 3, 4, 10, 12, 18]
|
||
|
|
y = [9, 15, 19, 20, 45, 55, 78]
|
||
|
|
slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07)
|
||
|
|
assert_almost_equal(slope, 4)
|
||
|
|
assert_almost_equal(upper, 4.38, decimal=2)
|
||
|
|
assert_almost_equal(lower, 3.71, decimal=2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_siegelslopes():
|
||
|
|
# method should be exact for straight line
|
||
|
|
y = 2 * np.arange(10) + 0.5
|
||
|
|
assert_equal(mstats.siegelslopes(y), (2.0, 0.5))
|
||
|
|
assert_equal(mstats.siegelslopes(y, method='separate'), (2.0, 0.5))
|
||
|
|
|
||
|
|
x = 2 * np.arange(10)
|
||
|
|
y = 5 * x - 3.0
|
||
|
|
assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
|
||
|
|
assert_equal(mstats.siegelslopes(y, x, method='separate'), (5.0, -3.0))
|
||
|
|
|
||
|
|
# method is robust to outliers: brekdown point of 50%
|
||
|
|
y[:4] = 1000
|
||
|
|
assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
|
||
|
|
|
||
|
|
# if there are no outliers, results should be comparble to linregress
|
||
|
|
np.random.seed(231)
|
||
|
|
x = np.arange(10)
|
||
|
|
y = -2.3 + 0.3*x + stats.norm.rvs(size=10)
|
||
|
|
slope_ols, intercept_ols, _, _, _ = stats.linregress(x, y)
|
||
|
|
|
||
|
|
slope, intercept = mstats.siegelslopes(y, x)
|
||
|
|
assert_allclose(slope, slope_ols, rtol=0.1)
|
||
|
|
assert_allclose(intercept, intercept_ols, rtol=0.1)
|
||
|
|
|
||
|
|
slope, intercept = mstats.siegelslopes(y, x, method='separate')
|
||
|
|
assert_allclose(slope, slope_ols, rtol=0.1)
|
||
|
|
assert_allclose(intercept, intercept_ols, rtol=0.1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_plotting_positions():
|
||
|
|
# Regression test for #1256
|
||
|
|
pos = mstats.plotting_positions(np.arange(3), 0, 0)
|
||
|
|
assert_array_almost_equal(pos.data, np.array([0.25, 0.5, 0.75]))
|
||
|
|
|
||
|
|
|
||
|
|
class TestNormalitytests():
|
||
|
|
|
||
|
|
def test_vs_nonmasked(self):
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
assert_array_almost_equal(mstats.normaltest(x),
|
||
|
|
stats.normaltest(x))
|
||
|
|
assert_array_almost_equal(mstats.skewtest(x),
|
||
|
|
stats.skewtest(x))
|
||
|
|
assert_array_almost_equal(mstats.kurtosistest(x),
|
||
|
|
stats.kurtosistest(x))
|
||
|
|
|
||
|
|
funcs = [stats.normaltest, stats.skewtest, stats.kurtosistest]
|
||
|
|
mfuncs = [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]
|
||
|
|
x = [1, 2, 3, 4]
|
||
|
|
for func, mfunc in zip(funcs, mfuncs):
|
||
|
|
assert_raises(ValueError, func, x)
|
||
|
|
assert_raises(ValueError, mfunc, x)
|
||
|
|
|
||
|
|
def test_axis_None(self):
|
||
|
|
# Test axis=None (equal to axis=0 for 1-D input)
|
||
|
|
x = np.array((-2,-1,0,1,2,3)*4)**2
|
||
|
|
assert_allclose(mstats.normaltest(x, axis=None), mstats.normaltest(x))
|
||
|
|
assert_allclose(mstats.skewtest(x, axis=None), mstats.skewtest(x))
|
||
|
|
assert_allclose(mstats.kurtosistest(x, axis=None),
|
||
|
|
mstats.kurtosistest(x))
|
||
|
|
|
||
|
|
def test_maskedarray_input(self):
|
||
|
|
# Add some masked values, test result doesn't change
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
xm = np.ma.array(np.r_[np.inf, x, 10],
|
||
|
|
mask=np.r_[True, [False] * x.size, True])
|
||
|
|
assert_allclose(mstats.normaltest(xm), stats.normaltest(x))
|
||
|
|
assert_allclose(mstats.skewtest(xm), stats.skewtest(x))
|
||
|
|
assert_allclose(mstats.kurtosistest(xm), stats.kurtosistest(x))
|
||
|
|
|
||
|
|
def test_nd_input(self):
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
x_2d = np.vstack([x] * 2).T
|
||
|
|
for func in [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]:
|
||
|
|
res_1d = func(x)
|
||
|
|
res_2d = func(x_2d)
|
||
|
|
assert_allclose(res_2d[0], [res_1d[0]] * 2)
|
||
|
|
assert_allclose(res_2d[1], [res_1d[1]] * 2)
|
||
|
|
|
||
|
|
def test_normaltest_result_attributes(self):
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
res = mstats.normaltest(x)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_kurtosistest_result_attributes(self):
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
res = mstats.kurtosistest(x)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def regression_test_9033(self):
|
||
|
|
# x cleary non-normal but power of negtative denom needs
|
||
|
|
# to be handled correctly to reject normality
|
||
|
|
counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
|
||
|
|
x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
|
||
|
|
assert_equal(mstats.kurtosistest(x)[1] < 0.01, True)
|
||
|
|
|
||
|
|
|
||
|
|
class TestFOneway():
|
||
|
|
def test_result_attributes(self):
|
||
|
|
a = np.array([655, 788], dtype=np.uint16)
|
||
|
|
b = np.array([789, 772], dtype=np.uint16)
|
||
|
|
res = mstats.f_oneway(a, b)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
class TestMannwhitneyu():
|
||
|
|
def test_result_attributes(self):
|
||
|
|
x = np.array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1.])
|
||
|
|
|
||
|
|
y = np.array([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
|
||
|
|
2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
|
||
|
|
1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
|
||
|
|
2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
|
||
|
|
2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
|
||
|
|
2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
|
||
|
|
1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
|
||
|
|
1., 1., 1., 1.])
|
||
|
|
|
||
|
|
res = mstats.mannwhitneyu(x, y)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
class TestKruskal():
|
||
|
|
def test_result_attributes(self):
|
||
|
|
x = [1, 3, 5, 7, 9]
|
||
|
|
y = [2, 4, 6, 8, 10]
|
||
|
|
|
||
|
|
res = mstats.kruskal(x, y)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
|
||
|
|
#TODO: for all ttest functions, add tests with masked array inputs
|
||
|
|
class TestTtest_rel():
|
||
|
|
def test_vs_nonmasked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
# 1-D inputs
|
||
|
|
res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1])
|
||
|
|
res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# 2-D inputs
|
||
|
|
res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
res1 = stats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
res2 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# Check default is axis=0
|
||
|
|
res3 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:])
|
||
|
|
assert_allclose(res2, res3)
|
||
|
|
|
||
|
|
def test_fully_masked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = ma.masked_array(np.random.randn(3, 2),
|
||
|
|
mask=[[1, 1, 1], [0, 0, 0]])
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
for pair in [(outcome[:, 0], outcome[:, 1]), ([np.nan, np.nan], [1.0, 2.0])]:
|
||
|
|
t, p = mstats.ttest_rel(*pair)
|
||
|
|
assert_array_equal(t, (np.nan, np.nan))
|
||
|
|
assert_array_equal(p, (np.nan, np.nan))
|
||
|
|
|
||
|
|
def test_result_attributes(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
res = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_invalid_input_size(self):
|
||
|
|
assert_raises(ValueError, mstats.ttest_rel,
|
||
|
|
np.arange(10), np.arange(11))
|
||
|
|
x = np.arange(24)
|
||
|
|
assert_raises(ValueError, mstats.ttest_rel,
|
||
|
|
x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=1)
|
||
|
|
assert_raises(ValueError, mstats.ttest_rel,
|
||
|
|
x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=2)
|
||
|
|
|
||
|
|
def test_empty(self):
|
||
|
|
res1 = mstats.ttest_rel([], [])
|
||
|
|
assert_(np.all(np.isnan(res1)))
|
||
|
|
|
||
|
|
def test_zero_division(self):
|
||
|
|
t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
|
||
|
|
assert_equal((np.abs(t), p), (np.inf, 0))
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
|
||
|
|
assert_array_equal(t, np.array([np.nan, np.nan]))
|
||
|
|
assert_array_equal(p, np.array([np.nan, np.nan]))
|
||
|
|
|
||
|
|
|
||
|
|
class TestTtest_ind():
|
||
|
|
def test_vs_nonmasked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
# 1-D inputs
|
||
|
|
res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1])
|
||
|
|
res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# 2-D inputs
|
||
|
|
res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
res1 = stats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
res2 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# Check default is axis=0
|
||
|
|
res3 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:])
|
||
|
|
assert_allclose(res2, res3)
|
||
|
|
|
||
|
|
# Check equal_var
|
||
|
|
res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
|
||
|
|
res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
|
||
|
|
assert_allclose(res4, res5)
|
||
|
|
res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
|
||
|
|
res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
|
||
|
|
assert_allclose(res4, res5)
|
||
|
|
|
||
|
|
def test_fully_masked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = ma.masked_array(np.random.randn(3, 2), mask=[[1, 1, 1], [0, 0, 0]])
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
for pair in [(outcome[:, 0], outcome[:, 1]), ([np.nan, np.nan], [1.0, 2.0])]:
|
||
|
|
t, p = mstats.ttest_ind(*pair)
|
||
|
|
assert_array_equal(t, (np.nan, np.nan))
|
||
|
|
assert_array_equal(p, (np.nan, np.nan))
|
||
|
|
|
||
|
|
def test_result_attributes(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
res = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_empty(self):
|
||
|
|
res1 = mstats.ttest_ind([], [])
|
||
|
|
assert_(np.all(np.isnan(res1)))
|
||
|
|
|
||
|
|
def test_zero_division(self):
|
||
|
|
t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
|
||
|
|
assert_equal((np.abs(t), p), (np.inf, 0))
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
|
||
|
|
assert_array_equal(t, (np.nan, np.nan))
|
||
|
|
assert_array_equal(p, (np.nan, np.nan))
|
||
|
|
|
||
|
|
t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1], equal_var=False)
|
||
|
|
assert_equal((np.abs(t), p), (np.inf, 0))
|
||
|
|
assert_array_equal(mstats.ttest_ind([0, 0, 0], [0, 0, 0],
|
||
|
|
equal_var=False), (np.nan, np.nan))
|
||
|
|
|
||
|
|
|
||
|
|
class TestTtest_1samp():
|
||
|
|
def test_vs_nonmasked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
# 1-D inputs
|
||
|
|
res1 = stats.ttest_1samp(outcome[:, 0], 1)
|
||
|
|
res2 = mstats.ttest_1samp(outcome[:, 0], 1)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# 2-D inputs
|
||
|
|
res1 = stats.ttest_1samp(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
res2 = mstats.ttest_1samp(outcome[:, 0], outcome[:, 1], axis=None)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
res1 = stats.ttest_1samp(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
res2 = mstats.ttest_1samp(outcome[:, :2], outcome[:, 2:], axis=0)
|
||
|
|
assert_allclose(res1, res2)
|
||
|
|
|
||
|
|
# Check default is axis=0
|
||
|
|
res3 = mstats.ttest_1samp(outcome[:, :2], outcome[:, 2:])
|
||
|
|
assert_allclose(res2, res3)
|
||
|
|
|
||
|
|
def test_fully_masked(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = ma.masked_array(np.random.randn(3), mask=[1, 1, 1])
|
||
|
|
expected = (np.nan, np.nan)
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
for pair in [((np.nan, np.nan), 0.0), (outcome, 0.0)]:
|
||
|
|
t, p = mstats.ttest_1samp(*pair)
|
||
|
|
assert_array_equal(p, expected)
|
||
|
|
assert_array_equal(t, expected)
|
||
|
|
|
||
|
|
def test_result_attributes(self):
|
||
|
|
np.random.seed(1234567)
|
||
|
|
outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
|
||
|
|
|
||
|
|
res = mstats.ttest_1samp(outcome[:, 0], 1)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_empty(self):
|
||
|
|
res1 = mstats.ttest_1samp([], 1)
|
||
|
|
assert_(np.all(np.isnan(res1)))
|
||
|
|
|
||
|
|
def test_zero_division(self):
|
||
|
|
t, p = mstats.ttest_1samp([0, 0, 0], 1)
|
||
|
|
assert_equal((np.abs(t), p), (np.inf, 0))
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "invalid value encountered in absolute")
|
||
|
|
t, p = mstats.ttest_1samp([0, 0, 0], 0)
|
||
|
|
assert_(np.isnan(t))
|
||
|
|
assert_array_equal(p, (np.nan, np.nan))
|
||
|
|
|
||
|
|
|
||
|
|
class TestCompareWithStats(object):
|
||
|
|
"""
|
||
|
|
Class to compare mstats results with stats results.
|
||
|
|
|
||
|
|
It is in general assumed that scipy.stats is at a more mature stage than
|
||
|
|
stats.mstats. If a routine in mstats results in similar results like in
|
||
|
|
scipy.stats, this is considered also as a proper validation of scipy.mstats
|
||
|
|
routine.
|
||
|
|
|
||
|
|
Different sample sizes are used for testing, as some problems between stats
|
||
|
|
and mstats are dependent on sample size.
|
||
|
|
|
||
|
|
Author: Alexander Loew
|
||
|
|
|
||
|
|
NOTE that some tests fail. This might be caused by
|
||
|
|
a) actual differences or bugs between stats and mstats
|
||
|
|
b) numerical inaccuracies
|
||
|
|
c) different definitions of routine interfaces
|
||
|
|
|
||
|
|
These failures need to be checked. Current workaround is to have disabled these tests,
|
||
|
|
but issuing reports on scipy-dev
|
||
|
|
|
||
|
|
"""
|
||
|
|
def get_n(self):
|
||
|
|
""" Returns list of sample sizes to be used for comparison. """
|
||
|
|
return [1000, 100, 10, 5]
|
||
|
|
|
||
|
|
def generate_xy_sample(self, n):
|
||
|
|
# This routine generates numpy arrays and corresponding masked arrays
|
||
|
|
# with the same data, but additional masked values
|
||
|
|
np.random.seed(1234567)
|
||
|
|
x = np.random.randn(n)
|
||
|
|
y = x + np.random.randn(n)
|
||
|
|
xm = np.full(len(x) + 5, 1e16)
|
||
|
|
ym = np.full(len(y) + 5, 1e16)
|
||
|
|
xm[0:len(x)] = x
|
||
|
|
ym[0:len(y)] = y
|
||
|
|
mask = xm > 9e15
|
||
|
|
xm = np.ma.array(xm, mask=mask)
|
||
|
|
ym = np.ma.array(ym, mask=mask)
|
||
|
|
return x, y, xm, ym
|
||
|
|
|
||
|
|
def generate_xy_sample2D(self, n, nx):
|
||
|
|
x = np.full((n, nx), np.nan)
|
||
|
|
y = np.full((n, nx), np.nan)
|
||
|
|
xm = np.full((n+5, nx), np.nan)
|
||
|
|
ym = np.full((n+5, nx), np.nan)
|
||
|
|
|
||
|
|
for i in range(nx):
|
||
|
|
x[:, i], y[:, i], dx, dy = self.generate_xy_sample(n)
|
||
|
|
|
||
|
|
xm[0:n, :] = x[0:n]
|
||
|
|
ym[0:n, :] = y[0:n]
|
||
|
|
xm = np.ma.array(xm, mask=np.isnan(xm))
|
||
|
|
ym = np.ma.array(ym, mask=np.isnan(ym))
|
||
|
|
return x, y, xm, ym
|
||
|
|
|
||
|
|
def test_linregress(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
res1 = stats.linregress(x, y)
|
||
|
|
res2 = stats.mstats.linregress(xm, ym)
|
||
|
|
assert_allclose(np.asarray(res1), np.asarray(res2))
|
||
|
|
|
||
|
|
def test_pearsonr(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r, p = stats.pearsonr(x, y)
|
||
|
|
rm, pm = stats.mstats.pearsonr(xm, ym)
|
||
|
|
|
||
|
|
assert_almost_equal(r, rm, decimal=14)
|
||
|
|
assert_almost_equal(p, pm, decimal=14)
|
||
|
|
|
||
|
|
def test_spearmanr(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r, p = stats.spearmanr(x, y)
|
||
|
|
rm, pm = stats.mstats.spearmanr(xm, ym)
|
||
|
|
assert_almost_equal(r, rm, 14)
|
||
|
|
assert_almost_equal(p, pm, 14)
|
||
|
|
|
||
|
|
def test_spearmanr_backcompat_useties(self):
|
||
|
|
# A regression test to ensure we don't break backwards compat
|
||
|
|
# more than we have to (see gh-9204).
|
||
|
|
x = np.arange(6)
|
||
|
|
assert_raises(ValueError, mstats.spearmanr, x, x, False)
|
||
|
|
|
||
|
|
def test_gmean(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.gmean(abs(x))
|
||
|
|
rm = stats.mstats.gmean(abs(xm))
|
||
|
|
assert_allclose(r, rm, rtol=1e-13)
|
||
|
|
|
||
|
|
r = stats.gmean(abs(y))
|
||
|
|
rm = stats.mstats.gmean(abs(ym))
|
||
|
|
assert_allclose(r, rm, rtol=1e-13)
|
||
|
|
|
||
|
|
def test_hmean(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
|
||
|
|
r = stats.hmean(abs(x))
|
||
|
|
rm = stats.mstats.hmean(abs(xm))
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
r = stats.hmean(abs(y))
|
||
|
|
rm = stats.mstats.hmean(abs(ym))
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
def test_skew(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
|
||
|
|
r = stats.skew(x)
|
||
|
|
rm = stats.mstats.skew(xm)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
r = stats.skew(y)
|
||
|
|
rm = stats.mstats.skew(ym)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
def test_moment(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
|
||
|
|
r = stats.moment(x)
|
||
|
|
rm = stats.mstats.moment(xm)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
r = stats.moment(y)
|
||
|
|
rm = stats.mstats.moment(ym)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
def test_zscore(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
|
||
|
|
# reference solution
|
||
|
|
zx = (x - x.mean()) / x.std()
|
||
|
|
zy = (y - y.mean()) / y.std()
|
||
|
|
|
||
|
|
# validate stats
|
||
|
|
assert_allclose(stats.zscore(x), zx, rtol=1e-10)
|
||
|
|
assert_allclose(stats.zscore(y), zy, rtol=1e-10)
|
||
|
|
|
||
|
|
# compare stats and mstats
|
||
|
|
assert_allclose(stats.zscore(x), stats.mstats.zscore(xm[0:len(x)]),
|
||
|
|
rtol=1e-10)
|
||
|
|
assert_allclose(stats.zscore(y), stats.mstats.zscore(ym[0:len(y)]),
|
||
|
|
rtol=1e-10)
|
||
|
|
|
||
|
|
def test_kurtosis(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.kurtosis(x)
|
||
|
|
rm = stats.mstats.kurtosis(xm)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
r = stats.kurtosis(y)
|
||
|
|
rm = stats.mstats.kurtosis(ym)
|
||
|
|
assert_almost_equal(r, rm, 10)
|
||
|
|
|
||
|
|
def test_sem(self):
|
||
|
|
# example from stats.sem doc
|
||
|
|
a = np.arange(20).reshape(5, 4)
|
||
|
|
am = np.ma.array(a)
|
||
|
|
r = stats.sem(a, ddof=1)
|
||
|
|
rm = stats.mstats.sem(am, ddof=1)
|
||
|
|
|
||
|
|
assert_allclose(r, 2.82842712, atol=1e-5)
|
||
|
|
assert_allclose(rm, 2.82842712, atol=1e-5)
|
||
|
|
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=0),
|
||
|
|
stats.sem(x, axis=None, ddof=0), decimal=13)
|
||
|
|
assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=0),
|
||
|
|
stats.sem(y, axis=None, ddof=0), decimal=13)
|
||
|
|
assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=1),
|
||
|
|
stats.sem(x, axis=None, ddof=1), decimal=13)
|
||
|
|
assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=1),
|
||
|
|
stats.sem(y, axis=None, ddof=1), decimal=13)
|
||
|
|
|
||
|
|
def test_describe(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.describe(x, ddof=1)
|
||
|
|
rm = stats.mstats.describe(xm, ddof=1)
|
||
|
|
for ii in range(6):
|
||
|
|
assert_almost_equal(np.asarray(r[ii]),
|
||
|
|
np.asarray(rm[ii]),
|
||
|
|
decimal=12)
|
||
|
|
|
||
|
|
def test_describe_result_attributes(self):
|
||
|
|
actual = mstats.describe(np.arange(5))
|
||
|
|
attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness',
|
||
|
|
'kurtosis')
|
||
|
|
check_named_results(actual, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_rankdata(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.rankdata(x)
|
||
|
|
rm = stats.mstats.rankdata(x)
|
||
|
|
assert_allclose(r, rm)
|
||
|
|
|
||
|
|
def test_tmean(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.tmean(x),stats.mstats.tmean(xm), 14)
|
||
|
|
assert_almost_equal(stats.tmean(y),stats.mstats.tmean(ym), 14)
|
||
|
|
|
||
|
|
def test_tmax(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.tmax(x,2.),
|
||
|
|
stats.mstats.tmax(xm,2.), 10)
|
||
|
|
assert_almost_equal(stats.tmax(y,2.),
|
||
|
|
stats.mstats.tmax(ym,2.), 10)
|
||
|
|
|
||
|
|
assert_almost_equal(stats.tmax(x, upperlimit=3.),
|
||
|
|
stats.mstats.tmax(xm, upperlimit=3.), 10)
|
||
|
|
assert_almost_equal(stats.tmax(y, upperlimit=3.),
|
||
|
|
stats.mstats.tmax(ym, upperlimit=3.), 10)
|
||
|
|
|
||
|
|
def test_tmin(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_equal(stats.tmin(x), stats.mstats.tmin(xm))
|
||
|
|
assert_equal(stats.tmin(y), stats.mstats.tmin(ym))
|
||
|
|
|
||
|
|
assert_almost_equal(stats.tmin(x, lowerlimit=-1.),
|
||
|
|
stats.mstats.tmin(xm, lowerlimit=-1.), 10)
|
||
|
|
assert_almost_equal(stats.tmin(y, lowerlimit=-1.),
|
||
|
|
stats.mstats.tmin(ym, lowerlimit=-1.), 10)
|
||
|
|
|
||
|
|
def test_zmap(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
z = stats.zmap(x, y)
|
||
|
|
zm = stats.mstats.zmap(xm, ym)
|
||
|
|
assert_allclose(z, zm[0:len(z)], atol=1e-10)
|
||
|
|
|
||
|
|
def test_variation(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.variation(x), stats.mstats.variation(xm),
|
||
|
|
decimal=12)
|
||
|
|
assert_almost_equal(stats.variation(y), stats.mstats.variation(ym),
|
||
|
|
decimal=12)
|
||
|
|
|
||
|
|
def test_tvar(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.tvar(x), stats.mstats.tvar(xm),
|
||
|
|
decimal=12)
|
||
|
|
assert_almost_equal(stats.tvar(y), stats.mstats.tvar(ym),
|
||
|
|
decimal=12)
|
||
|
|
|
||
|
|
def test_trimboth(self):
|
||
|
|
a = np.arange(20)
|
||
|
|
b = stats.trimboth(a, 0.1)
|
||
|
|
bm = stats.mstats.trimboth(a, 0.1)
|
||
|
|
assert_allclose(np.sort(b), bm.data[~bm.mask])
|
||
|
|
|
||
|
|
def test_tsem(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
assert_almost_equal(stats.tsem(x), stats.mstats.tsem(xm),
|
||
|
|
decimal=14)
|
||
|
|
assert_almost_equal(stats.tsem(y), stats.mstats.tsem(ym),
|
||
|
|
decimal=14)
|
||
|
|
assert_almost_equal(stats.tsem(x, limits=(-2., 2.)),
|
||
|
|
stats.mstats.tsem(xm, limits=(-2., 2.)),
|
||
|
|
decimal=14)
|
||
|
|
|
||
|
|
def test_skewtest(self):
|
||
|
|
# this test is for 1D data
|
||
|
|
for n in self.get_n():
|
||
|
|
if n > 8:
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.skewtest(x)
|
||
|
|
rm = stats.mstats.skewtest(xm)
|
||
|
|
assert_allclose(r[0], rm[0], rtol=1e-15)
|
||
|
|
# TODO this test is not performed as it is a known issue that
|
||
|
|
# mstats returns a slightly different p-value what is a bit
|
||
|
|
# strange is that other tests like test_maskedarray_input don't
|
||
|
|
# fail!
|
||
|
|
#~ assert_almost_equal(r[1], rm[1])
|
||
|
|
|
||
|
|
def test_skewtest_result_attributes(self):
|
||
|
|
x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
|
||
|
|
res = mstats.skewtest(x)
|
||
|
|
attributes = ('statistic', 'pvalue')
|
||
|
|
check_named_results(res, attributes, ma=True)
|
||
|
|
|
||
|
|
def test_skewtest_2D_notmasked(self):
|
||
|
|
# a normal ndarray is passed to the masked function
|
||
|
|
x = np.random.random((20, 2)) * 20.
|
||
|
|
r = stats.skewtest(x)
|
||
|
|
rm = stats.mstats.skewtest(x)
|
||
|
|
assert_allclose(np.asarray(r), np.asarray(rm))
|
||
|
|
|
||
|
|
def test_skewtest_2D_WithMask(self):
|
||
|
|
nx = 2
|
||
|
|
for n in self.get_n():
|
||
|
|
if n > 8:
|
||
|
|
x, y, xm, ym = self.generate_xy_sample2D(n, nx)
|
||
|
|
r = stats.skewtest(x)
|
||
|
|
rm = stats.mstats.skewtest(xm)
|
||
|
|
|
||
|
|
assert_equal(r[0][0], rm[0][0])
|
||
|
|
assert_equal(r[0][1], rm[0][1])
|
||
|
|
|
||
|
|
def test_normaltest(self):
|
||
|
|
with np.errstate(over='raise'), suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "kurtosistest only valid for n>=20")
|
||
|
|
for n in self.get_n():
|
||
|
|
if n > 8:
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.normaltest(x)
|
||
|
|
rm = stats.mstats.normaltest(xm)
|
||
|
|
assert_allclose(np.asarray(r), np.asarray(rm))
|
||
|
|
|
||
|
|
def test_find_repeats(self):
|
||
|
|
x = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4]).astype('float')
|
||
|
|
tmp = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]).astype('float')
|
||
|
|
mask = (tmp == 5.)
|
||
|
|
xm = np.ma.array(tmp, mask=mask)
|
||
|
|
x_orig, xm_orig = x.copy(), xm.copy()
|
||
|
|
|
||
|
|
r = stats.find_repeats(x)
|
||
|
|
rm = stats.mstats.find_repeats(xm)
|
||
|
|
|
||
|
|
assert_equal(r, rm)
|
||
|
|
assert_equal(x, x_orig)
|
||
|
|
assert_equal(xm, xm_orig)
|
||
|
|
|
||
|
|
# This crazy behavior is expected by count_tied_groups, but is not
|
||
|
|
# in the docstring...
|
||
|
|
_, counts = stats.mstats.find_repeats([])
|
||
|
|
assert_equal(counts, np.array(0, dtype=np.intp))
|
||
|
|
|
||
|
|
def test_kendalltau(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.kendalltau(x, y)
|
||
|
|
rm = stats.mstats.kendalltau(xm, ym)
|
||
|
|
assert_almost_equal(r[0], rm[0], decimal=10)
|
||
|
|
assert_almost_equal(r[1], rm[1], decimal=7)
|
||
|
|
|
||
|
|
def test_obrientransform(self):
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
r = stats.obrientransform(x)
|
||
|
|
rm = stats.mstats.obrientransform(xm)
|
||
|
|
assert_almost_equal(r.T, rm[0:len(x)])
|
||
|
|
|
||
|
|
def test_ks_1samp(self):
|
||
|
|
"""Checks that mstats.ks_1samp and stats.ks_1samp agree on masked arrays."""
|
||
|
|
for mode in ['auto', 'exact', 'asymp']:
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
for alternative in ['less', 'greater', 'two-sided']:
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
res1 = stats.ks_1samp(x, stats.norm.cdf, alternative=alternative, mode=mode)
|
||
|
|
res2 = stats.mstats.ks_1samp(xm, stats.norm.cdf, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res2))
|
||
|
|
res3 = stats.ks_1samp(xm, stats.norm.cdf, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res3))
|
||
|
|
|
||
|
|
def test_kstest_1samp(self):
|
||
|
|
"""Checks that 1-sample mstats.kstest and stats.kstest agree on masked arrays."""
|
||
|
|
for mode in ['auto', 'exact', 'asymp']:
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
for alternative in ['less', 'greater', 'two-sided']:
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
res1 = stats.kstest(x, 'norm', alternative=alternative, mode=mode)
|
||
|
|
res2 = stats.mstats.kstest(xm, 'norm', alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res2))
|
||
|
|
res3 = stats.kstest(xm, 'norm', alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res3))
|
||
|
|
|
||
|
|
def test_ks_2samp(self):
|
||
|
|
"""Checks that mstats.ks_2samp and stats.ks_2samp agree on masked arrays.
|
||
|
|
gh-8431"""
|
||
|
|
for mode in ['auto', 'exact', 'asymp']:
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
if mode in ['auto', 'exact']:
|
||
|
|
sup.filter(RuntimeWarning,
|
||
|
|
"ks_2samp: Exact calculation unsuccessful. Switching to mode=asymp.")
|
||
|
|
for alternative in ['less', 'greater', 'two-sided']:
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
res1 = stats.ks_2samp(x, y, alternative=alternative, mode=mode)
|
||
|
|
res2 = stats.mstats.ks_2samp(xm, ym, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res2))
|
||
|
|
res3 = stats.ks_2samp(xm, y, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res3))
|
||
|
|
|
||
|
|
def test_kstest_2samp(self):
|
||
|
|
"""Checks that 2-sample mstats.kstest and stats.kstest agree on masked arrays."""
|
||
|
|
for mode in ['auto', 'exact', 'asymp']:
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
if mode in ['auto', 'exact']:
|
||
|
|
sup.filter(RuntimeWarning,
|
||
|
|
"ks_2samp: Exact calculation unsuccessful. Switching to mode=asymp.")
|
||
|
|
for alternative in ['less', 'greater', 'two-sided']:
|
||
|
|
for n in self.get_n():
|
||
|
|
x, y, xm, ym = self.generate_xy_sample(n)
|
||
|
|
res1 = stats.kstest(x, y, alternative=alternative, mode=mode)
|
||
|
|
res2 = stats.mstats.kstest(xm, ym, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res2))
|
||
|
|
res3 = stats.kstest(xm, y, alternative=alternative, mode=mode)
|
||
|
|
assert_equal(np.asarray(res1), np.asarray(res3))
|
||
|
|
|
||
|
|
def test_nametuples_agree(self):
|
||
|
|
result = stats.kstest([1, 2], [3, 4])
|
||
|
|
assert_(isinstance(result, stats.stats.KstestResult))
|
||
|
|
result2 = stats.stats.Ks_2sampResult(result.statistic, result.pvalue)
|
||
|
|
assert_(isinstance(result2, stats.stats.Ks_2sampResult))
|
||
|
|
assert_equal(result, result2)
|
||
|
|
|
||
|
|
|
||
|
|
class TestBrunnerMunzel(object):
|
||
|
|
# Data from (Lumley, 1996)
|
||
|
|
X = np.ma.masked_invalid([1, 2, 1, 1, 1, np.nan, 1, 1,
|
||
|
|
1, 1, 1, 2, 4, 1, 1, np.nan])
|
||
|
|
Y = np.ma.masked_invalid([3, 3, 4, 3, np.nan, 1, 2, 3, 1, 1, 5, 4])
|
||
|
|
significant = 14
|
||
|
|
|
||
|
|
def test_brunnermunzel_one_sided(self):
|
||
|
|
# Results are compared with R's lawstat package.
|
||
|
|
u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='less')
|
||
|
|
u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='greater')
|
||
|
|
u3, p3 = mstats.brunnermunzel(self.X, self.Y, alternative='greater')
|
||
|
|
u4, p4 = mstats.brunnermunzel(self.Y, self.X, alternative='less')
|
||
|
|
|
||
|
|
assert_almost_equal(p1, p2, decimal=self.significant)
|
||
|
|
assert_almost_equal(p3, p4, decimal=self.significant)
|
||
|
|
assert_(p1 != p3)
|
||
|
|
assert_almost_equal(u1, 3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u2, -3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u3, 3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u4, -3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(p1, 0.0028931043330757342,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(p3, 0.99710689566692423,
|
||
|
|
decimal=self.significant)
|
||
|
|
|
||
|
|
def test_brunnermunzel_two_sided(self):
|
||
|
|
# Results are compared with R's lawstat package.
|
||
|
|
u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='two-sided')
|
||
|
|
u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='two-sided')
|
||
|
|
|
||
|
|
assert_almost_equal(p1, p2, decimal=self.significant)
|
||
|
|
assert_almost_equal(u1, 3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u2, -3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(p1, 0.0057862086661515377,
|
||
|
|
decimal=self.significant)
|
||
|
|
|
||
|
|
def test_brunnermunzel_default(self):
|
||
|
|
# The default value for alternative is two-sided
|
||
|
|
u1, p1 = mstats.brunnermunzel(self.X, self.Y)
|
||
|
|
u2, p2 = mstats.brunnermunzel(self.Y, self.X)
|
||
|
|
|
||
|
|
assert_almost_equal(p1, p2, decimal=self.significant)
|
||
|
|
assert_almost_equal(u1, 3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u2, -3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(p1, 0.0057862086661515377,
|
||
|
|
decimal=self.significant)
|
||
|
|
|
||
|
|
def test_brunnermunzel_alternative_error(self):
|
||
|
|
alternative = "error"
|
||
|
|
distribution = "t"
|
||
|
|
assert_(alternative not in ["two-sided", "greater", "less"])
|
||
|
|
assert_raises(ValueError,
|
||
|
|
mstats.brunnermunzel,
|
||
|
|
self.X,
|
||
|
|
self.Y,
|
||
|
|
alternative,
|
||
|
|
distribution)
|
||
|
|
|
||
|
|
def test_brunnermunzel_distribution_norm(self):
|
||
|
|
u1, p1 = mstats.brunnermunzel(self.X, self.Y, distribution="normal")
|
||
|
|
u2, p2 = mstats.brunnermunzel(self.Y, self.X, distribution="normal")
|
||
|
|
assert_almost_equal(p1, p2, decimal=self.significant)
|
||
|
|
assert_almost_equal(u1, 3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(u2, -3.1374674823029505,
|
||
|
|
decimal=self.significant)
|
||
|
|
assert_almost_equal(p1, 0.0017041417600383024,
|
||
|
|
decimal=self.significant)
|
||
|
|
|
||
|
|
def test_brunnermunzel_distribution_error(self):
|
||
|
|
alternative = "two-sided"
|
||
|
|
distribution = "error"
|
||
|
|
assert_(alternative not in ["t", "normal"])
|
||
|
|
assert_raises(ValueError,
|
||
|
|
mstats.brunnermunzel,
|
||
|
|
self.X,
|
||
|
|
self.Y,
|
||
|
|
alternative,
|
||
|
|
distribution)
|
||
|
|
|
||
|
|
def test_brunnermunzel_empty_imput(self):
|
||
|
|
u1, p1 = mstats.brunnermunzel(self.X, [])
|
||
|
|
u2, p2 = mstats.brunnermunzel([], self.Y)
|
||
|
|
u3, p3 = mstats.brunnermunzel([], [])
|
||
|
|
|
||
|
|
assert_(np.isnan(u1))
|
||
|
|
assert_(np.isnan(p1))
|
||
|
|
assert_(np.isnan(u2))
|
||
|
|
assert_(np.isnan(p2))
|
||
|
|
assert_(np.isnan(u3))
|
||
|
|
assert_(np.isnan(p3))
|