def test_zprob(self):
"""zprob should match twice the z_high probability for abs(z)"""
probs = [2 * i for i in [
5.000000e-01, 4.960106e-01, 4.601722e-01, 3.085375e-01,
1.586553e-01, 2.275013e-02, 2.866516e-07, 7.619853e-24,
2.753624e-89, 4.906714e-198, 0.000000e+00, 0.000000e+00]]
for z, p in zip(self.values, probs):
np.testing.assert_allclose(zprob(z), p, atol=10e-7)
for z, p in zip(self.negvalues, probs):
np.testing.assert_allclose(zprob(z), p, atol=10e-7)
def test_zprob(self):
"""zprob should match twice the z_high probability for abs(z)"""
probs = [
2 * i for i in [
5.000000e-01, 4.960106e-01, 4.601722e-01, 3.085375e-01,
1.586553e-01, 2.275013e-02, 2.866516e-07, 7.619853e-24,
2.753624e-89, 4.906714e-198, 0.000000e+00, 0.000000e+00
]
]
for z, p in zip(self.values, probs):
np.testing.assert_allclose(zprob(z), p, atol=10e-7)
for z, p in zip(self.negvalues, probs):
np.testing.assert_allclose(zprob(z), p, atol=10e-7)
def mw_t(x, y):
"""computes the Mann-Whitney U statistic and the probability using the
normal approximation"""
if len(x) > len(y):
x, y = y, x
num_x = len(x)
num_y = len(y)
x = zip(x, np.zeros(len(x), int), np.zeros(len(x), int))
y = zip(y, np.ones(len(y), int), np.zeros(len(y), int))
combined = x + y
combined = np.array(combined, dtype=[('stat', float), ('sample', int),
('rank', float)])
combined.sort(order='stat')
prev = None
start = None
ties = False
T = 0.0
for index in range(combined.shape[0]):
value = combined['stat'][index]
sample = combined['sample'][index]
if value == prev and start is None:
start = index
continue
if value != prev and start is not None:
ties = True
ave_rank = _average_rank(start, index)
num_tied = index - start + 1
T += (num_tied ** 3 - num_tied)
for i in range(start - 1, index):
combined['rank'][i] = ave_rank
start = None
combined['rank'][index] = index + 1
prev = value
if start is not None:
ave_rank = _average_rank(start, index)
num_tied = index - start + 2
T += (num_tied ** 3 - num_tied)
for i in range(start - 1, index + 1):
combined['rank'][i] = ave_rank
total = combined.shape[0]
x_ranks_sum = np.sum(combined['rank'][i]
for i in range(total) if combined['sample'][i] == 0)
prod = num_x * num_y
U1 = prod + (num_x * (num_x + 1) / 2) - x_ranks_sum
U2 = prod - U1
U = max([U1, U2])
numerator = U - prod / 2
denominator = np.sqrt((prod / (total * (total - 1))) *
((total ** 3 - total - T) / 12))
z = (numerator / denominator)
p = zprob(z)
return U, p
