Python scipy.stats.anderson_ksamp() Examples

def test_example1a(self):
        # Example data from Scholz & Stephens (1987), originally
        # published in Lehmann (1995, Nonparametrics, Statistical
        # Methods Based on Ranks, p. 309)
        # Pass a mixture of lists and arrays
        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
        assert_warns(UserWarning, stats.anderson_ksamp, (t1, t2, t3, t4),
                     midrank=False)
        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=False)

        assert_almost_equal(Tk, 4.449, 3)
        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
                                  tm, 4)
        assert_almost_equal(p, 0.0021, 4) 

def test_example1b(self):
        # Example data from Scholz & Stephens (1987), originally
        # published in Lehmann (1995, Nonparametrics, Statistical
        # Methods Based on Ranks, p. 309)
        # Pass arrays
        t1 = np.array([38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0])
        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])
        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=True)

        assert_almost_equal(Tk, 4.480, 3)
        assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459],
                                  tm, 4)
        assert_almost_equal(p, 0.0020, 4) 

def test_result_attributes(self):
        # Example data from Scholz & Stephens (1987), originally
        # published in Lehmann (1995, Nonparametrics, Statistical
        # Methods Based on Ranks, p. 309)
        # Pass a mixture of lists and arrays
        t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]
        t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8])
        t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0])
        t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8])

        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            res = stats.anderson_ksamp((t1, t2, t3, t4), midrank=False)

        attributes = ('statistic', 'critical_values', 'significance_level')
        check_named_results(res, attributes) 

def test_example2a(self):
        # Example data taken from an earlier technical report of
        # Scholz and Stephens
        # Pass lists instead of arrays
        t1 = [194, 15, 41, 29, 33, 181]
        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
              118, 25, 156, 310, 76, 26, 44, 23, 62]
        t5 = [130, 208, 70, 101, 208]
        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
               22, 139, 210, 97, 30, 23, 13, 14]
        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
        t12 = [50, 254, 5, 283, 35, 12]
        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
               61, 34]
        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8,
                                              t9, t10, t11, t12, t13, t14),
                                             midrank=False)

        assert_almost_equal(Tk, 3.288, 3)
        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
                                  tm, 4)
        assert_almost_equal(p, 0.0041, 4) 

def test_example2b(self):
        # Example data taken from an earlier technical report of
        # Scholz and Stephens
        t1 = [194, 15, 41, 29, 33, 181]
        t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118]
        t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34]
        t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29,
              118, 25, 156, 310, 76, 26, 44, 23, 62]
        t5 = [130, 208, 70, 101, 208]
        t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27]
        t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33]
        t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5,
              12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95]
        t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82,
              54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24]
        t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36,
               22, 139, 210, 97, 30, 23, 13, 14]
        t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438]
        t12 = [50, 254, 5, 283, 35, 12]
        t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130]
        t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66,
               61, 34]
        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8,
                                              t9, t10, t11, t12, t13, t14),
                                             midrank=True)

        assert_almost_equal(Tk, 3.294, 3)
        assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009],
                                  tm, 4)
        assert_almost_equal(p, 0.0041, 4) 

def test_not_enough_samples(self):
        assert_raises(ValueError, stats.anderson_ksamp, np.ones(5)) 

def test_empty_sample(self):
        assert_raises(ValueError, stats.anderson_ksamp, (np.ones(5), [])) 

def test_overflow(self):
        # when significance_level approximation overflows, should still return
        with suppress_warnings() as sup:
            sup.filter(UserWarning, message='approximate p-value')
            res = stats.anderson_ksamp([[-20, -10] * 100, [-10, 40, 12] * 100])
            assert_almost_equal(res[0], 272.796, 3) 

def anderson_ksamp(self, fD1, fD2):
        """
        Anderson Darling Test
        """
        return stats.anderson_ksamp([fD1, fD2]) 

def _test_impl(self, data1: t.List[Number], data2: t.List[Number]) -> float:
        return max(st.anderson_ksamp([data1, data2])[-1], 1) 

def testCompletedCumulatives(data, method = 'AndersonDarling', offset = None, plot = False):
    """Test if data sets have the same number / intensity distribution by adding max intensity counts to the smaller sized data sets and performing a distribution comparison test"""
    
    #idea: fill up data points to the same numbers at the high intensity values and use KS test
    #cf. work in progress on thoouroghly testing the differences in histograms
    
    #fill up the low count data
    n = numpy.array([x.size for x in data]);
    nm = n.max();
    m = numpy.array([x.max() for x in data]);
    mm = m.max();
    k = n.size;
    #print nm, mm, k
    
    if offset is None:
        #assume data starts at 0 !
        offset = mm / nm; #ideall for all statistics this should be mm + eps to have as little influence as possible.
    

    datac = [x.copy() for x in data];
    for i in range(m.size):
        if n[i] < nm:
            datac[i] = numpy.concatenate((datac[i], numpy.ones(nm-n[i], dtype = datac[i].dtype) * (mm + offset))); # + 10E-5 * numpy.random.rand(nm-n[i])));
         
    #test by plotting
    if plot is True:
        import matplotlib.pyplot as plt;
        for i in range(m.size):
            datac[i].sort();
            plt.step(datac[i], numpy.arange(datac[i].size));
    
    #perfomr the tests
    if method == 'KolmogorovSmirnov' or method == 'KS':
        if k == 2:
            (s, p) = stats.ks_2samp(datac[0], datac[1]);
        else:
            raise RuntimeError('KolmogorovSmirnov only for 2 samples not %d' % k);
        
    elif method == 'CramervonMises' or method == 'CM':
        if k == 2:
            (s,p) = stats2.testCramerVonMises2Sample(datac[0], datac[1]);
        else:
            raise RuntimeError('CramervonMises only for 2 samples not %d' % k);
      
    elif method == 'AndersonDarling' or method == 'AD':
        (s,a,p) = stats.anderson_ksamp(datac);

    return (p,s); 

def testCompletedInvertedCumulatives(data, method = 'AndersonDarling', offset = None, plot = False):
    """Test if data sets have the same number / intensity distribution by adding zero intensity counts to the smaller sized data sets and performing a distribution comparison test on the reversed cumulative distribution"""
    
    #idea: fill up data points to the same numbers at the high intensity values and use KS test
    #cf. work in progress on thoouroghly testing the differences in histograms
    
    #fill up the low count data
    n = numpy.array([x.size for x in data]);
    nm = n.max();
    m = numpy.array([x.max() for x in data]);
    mm = m.max();
    k = n.size;
    #print nm, mm, k
    
    if offset is None:
        #assume data starts at 0 !
        offset = mm / nm; #ideall for all statistics this should be mm + eps to have as little influence as possible.
    

    datac = [x.copy() for x in data];
    for i in range(m.size):
        if n[i] < nm:
            datac[i] = numpy.concatenate((-datac[i], numpy.ones(nm-n[i], dtype = datac[i].dtype) * (offset))); # + 10E-5 * numpy.random.rand(nm-n[i])));
        else:
            datac[i] = -datac[i];
         
    #test by plotting
    if plot is True:
        import matplotlib.pyplot as plt;
        for i in range(m.size):
            datac[i].sort();
            plt.step(datac[i], numpy.arange(datac[i].size));
    
    #perfomr the tests
    if method == 'KolmogorovSmirnov' or method == 'KS':
        if k == 2:
            (s, p) = stats.ks_2samp(datac[0], datac[1]);
        else:
            raise RuntimeError('KolmogorovSmirnov only for 2 samples not %d' % k);
        
    elif method == 'CramervonMises' or method == 'CM':
        if k == 2:
            (s,p) = stats2.testCramerVonMises2Sample(datac[0], datac[1]);
        else:
            raise RuntimeError('CramervonMises only for 2 samples not %d' % k);
      
    elif method == 'AndersonDarling' or method == 'AD':
        (s,a,p) = stats.anderson_ksamp(datac);

    return (p,s);