def test_contingency_table_with_zero_rows_cols(self):
# test that zero rows/cols in contingency table don't affect result
N = 100
shape = 4, 6
size = np.prod(shape)
np.random.seed(0)
s = stats.multinomial.rvs(N, p=np.ones(size) / size).reshape(shape)
res = stats.somersd(s)
s2 = np.insert(s, 2, np.zeros(shape[1]), axis=0)
res2 = stats.somersd(s2)
s3 = np.insert(s, 2, np.zeros(shape[0]), axis=1)
res3 = stats.somersd(s3)
s4 = np.insert(s2, 2, np.zeros(shape[0] + 1), axis=1)
res4 = stats.somersd(s4)
# Cross-check with result from SAS FREQ:
assert_allclose(res.statistic, -0.116981132075470, atol=1e-15)
assert_allclose(res.statistic, res2.statistic)
assert_allclose(res.statistic, res3.statistic)
assert_allclose(res.statistic, res4.statistic)
assert_allclose(res.pvalue, 0.156376448188150, atol=1e-15)
assert_allclose(res.pvalue, res2.pvalue)
assert_allclose(res.pvalue, res3.pvalue)
assert_allclose(res.pvalue, res4.pvalue)
def test_asymmetry(self):
# test that somersd is asymmetric w.r.t. input order and that
# convention is as described: first input is row variable & independent
# data is from Wikipedia:
# https://en.wikipedia.org/wiki/Somers%27_D
# but currently that example contradicts itself - it says X is
# independent yet take D_XY
x = [
1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3,
3, 3
]
y = [
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2
]
# Cross-check with result from SAS FREQ:
d_cr = 0.272727272727270
d_rc = 0.342857142857140
p = 0.092891940883700 # same p-value for either direction
res = stats.somersd(x, y)
assert_allclose(res.statistic, d_cr, atol=1e-15)
assert_allclose(res.pvalue, p, atol=1e-4)
assert_equal(res.table.shape, (3, 2))
res = stats.somersd(y, x)
assert_allclose(res.statistic, d_rc, atol=1e-15)
assert_allclose(res.pvalue, p, atol=1e-15)
assert_equal(res.table.shape, (2, 3))
def test_only_ranks_matter(self):
# only ranks of input data should matter
x = [1, 2, 3]
x2 = [-1, 2.1, np.inf]
y = [3, 2, 1]
y2 = [0, -0.5, -np.inf]
res = stats.somersd(x, y)
res2 = stats.somersd(x2, y2)
assert_equal(res.statistic, res2.statistic)
assert_equal(res.pvalue, res2.pvalue)
def test_somers_original(self):
# test against Somers' original paper [1]
# Table 5A
# Somers' convention was column IV
table = np.array([[8, 2], [6, 5], [3, 4], [1, 3], [2, 3]])
# Our convention (and that of SAS FREQ) is row IV
table = table.T
dyx = 129 / 340
assert_allclose(stats.somersd(table).statistic, dyx)
# table 7A - d_yx = 1
table = np.array([[25, 0], [85, 0], [0, 30]])
dxy, dyx = 3300 / 5425, 3300 / 3300
assert_allclose(stats.somersd(table).statistic, dxy)
assert_allclose(stats.somersd(table.T).statistic, dyx)
# table 7B - d_yx < 0
table = np.array([[25, 0], [0, 30], [85, 0]])
dyx = -1800 / 3300
assert_allclose(stats.somersd(table.T).statistic, dyx)
def test_contingency_table_return(self):
# check that contingency table is returned
x = np.arange(10)
y = np.arange(10)
res = stats.somersd(x, y)
assert_equal(res.table, np.eye(10))
def test_invalid_contingency_tables(self):
N = 100
shape = 4, 6
size = np.prod(shape)
np.random.seed(0)
# start with a valid contingency table
s = stats.multinomial.rvs(N, p=np.ones(size) / size).reshape(shape)
s5 = s - 2
message = "All elements of the contingency table must be non-negative"
with assert_raises(ValueError, match=message):
stats.somersd(s5)
s6 = s + 0.01
message = "All elements of the contingency table must be integer"
with assert_raises(ValueError, match=message):
stats.somersd(s6)
message = ("At least two elements of the contingency "
"table must be nonzero.")
with assert_raises(ValueError, match=message):
stats.somersd([[]])
with assert_raises(ValueError, match=message):
stats.somersd([[1]])
s7 = np.zeros((3, 3))
with assert_raises(ValueError, match=message):
stats.somersd(s7)
s7[0, 1] = 1
with assert_raises(ValueError, match=message):
stats.somersd(s7)
def test_like_kendalltau(self):
# All tests correspond with one in test_stats.py `test_kendalltau`
# case without ties, con-dis equal zero
x = [5, 2, 1, 3, 6, 4, 7, 8]
y = [5, 2, 6, 3, 1, 8, 7, 4]
# Cross-check with result from SAS FREQ:
expected = (0.000000000000000, 1.000000000000000)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# case without ties, con-dis equal zero
x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
# Cross-check with result from SAS FREQ:
expected = (0.000000000000000, 1.000000000000000)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# case without ties, con-dis close to zero
x = [5, 2, 1, 3, 6, 4, 7]
y = [5, 2, 6, 3, 1, 7, 4]
# Cross-check with result from SAS FREQ:
expected = (-0.142857142857140, 0.630326953157670)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# simple case without ties
x = np.arange(10)
y = np.arange(10)
# Cross-check with result from SAS FREQ:
# SAS p value is not provided.
expected = (1.000000000000000, 0)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# swap a couple values and a couple more
x = np.arange(10)
y = np.array([0, 2, 1, 3, 4, 6, 5, 7, 8, 9])
# Cross-check with result from SAS FREQ:
expected = (0.911111111111110, 0.000000000000000)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# same in opposite direction
x = np.arange(10)
y = np.arange(10)[::-1]
# Cross-check with result from SAS FREQ:
# SAS p value is not provided.
expected = (-1.000000000000000, 0)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# swap a couple values and a couple more
x = np.arange(10)
y = np.array([9, 7, 8, 6, 5, 3, 4, 2, 1, 0])
# Cross-check with result from SAS FREQ:
expected = (-0.9111111111111111, 0.000000000000000)
res = stats.somersd(x, y)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# with some ties
x1 = [12, 2, 1, 12, 2]
x2 = [1, 4, 7, 1, 0]
# Cross-check with result from SAS FREQ:
expected = (-0.500000000000000, 0.304901788178780)
res = stats.somersd(x1, x2)
assert_allclose(res.statistic, expected[0], atol=1e-15)
assert_allclose(res.pvalue, expected[1], atol=1e-15)
# with only ties in one or both inputs
# SAS will not produce an output for these:
# NOTE: No statistics are computed for x * y because x has fewer
# than 2 nonmissing levels.
# WARNING: No OUTPUT data set is produced for this table because a
# row or column variable has fewer than 2 nonmissing levels and no
# statistics are computed.
res = stats.somersd([2, 2, 2], [2, 2, 2])
assert_allclose(res.statistic, np.nan)
assert_allclose(res.pvalue, np.nan)
res = stats.somersd([2, 0, 2], [2, 2, 2])
assert_allclose(res.statistic, np.nan)
assert_allclose(res.pvalue, np.nan)
res = stats.somersd([2, 2, 2], [2, 0, 2])
assert_allclose(res.statistic, np.nan)
assert_allclose(res.pvalue, np.nan)
res = stats.somersd([0], [0])
assert_allclose(res.statistic, np.nan)
assert_allclose(res.pvalue, np.nan)
# empty arrays provided as input
res = stats.somersd([], [])
assert_allclose(res.statistic, np.nan)
assert_allclose(res.pvalue, np.nan)
# test unequal length inputs
x = np.arange(10.)
y = np.arange(20.)
assert_raises(ValueError, stats.somersd, x, y)
def time_somersd(self, n_size):
res = stats.somersd(self.x, self.y)
