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):
self.assertFloatEqual(zprob(z), p)
for z, p in zip(self.negvalues, probs):
self.assertFloatEqual(zprob(z), p)
def z_tailed_prob(z, tails):
"""Returns appropriate p-value for given z, depending on tails."""
if tails == 'high':
return z_high(z)
elif tails == 'low':
return z_low(z)
else:
return zprob(z)
def kendalls_tau(x, y, return_p=True):
"""returns kendall's tau
Arguments:
- return_p: returns the probability from the normal approximation when
True, otherwise just returns tau"""
ranked = as_paired_ranks(x, y)
n = len(ranked)
denom = n * (n - 1) / 2
con = 0
discor = 0
x_tied = 0
y_tied = 0
for i in range(n - 1):
x_1 = ranked[i][0]
y_1 = ranked[i][1]
for j in range(i + 1, n):
x_2 = ranked[j][0]
y_2 = ranked[j][1]
x_diff = x_1 - x_2
y_diff = y_1 - y_2
if x_diff * y_diff > 0:
con += 1
elif x_diff and y_diff:
discor += 1
else:
if x_diff:
y_tied += 1
if y_diff:
x_tied += 1
diff = con - discor
total = con + discor
denom = ((total + y_tied) * (total + x_tied))**0.5
variance = (4 * n + 10) / (9 * n * (n - 1))
tau = diff / denom
stat = tau
if x_tied or y_tied:
x_tied = array([v for v in Freqs(x).itervalues() if v > 1])
y_tied = array([v for v in Freqs(y).itervalues() if v > 1])
t0 = n * (n - 1) / 2
t1 = sum(x_tied * (x_tied - 1)) / 2
t2 = sum(y_tied * (y_tied - 1)) / 2
stat = tau * sqrt((t0 - t1) * (t0 - t2))
v0 = n * (n - 1) * (2 * n + 5)
vt = sum(x_tied * (x_tied - 1) * (2 * x_tied + 5))
vu = sum(y_tied * (y_tied - 1) * (2 * y_tied + 5))
v1 = sum(x_tied * (x_tied - 1)) * sum(y_tied * (y_tied - 1))
v2 = sum(x_tied * (x_tied - 1) * (x_tied - 2)) * \
sum(y_tied * (y_tied - 1) * (y_tied - 2))
variance = (v0 - vt - vu) / 18 + v1 / (2 * n * (n - 1)) + v2 / (9 * n * \
(n - 1) * (n - 2))
if return_p:
return tau, zprob(stat / variance**0.5)
else:
return tau
def kendalls_tau(x, y, return_p=True):
"""returns kendall's tau
Arguments:
- return_p: returns the probability from the normal approximation when
True, otherwise just returns tau"""
ranked = as_paired_ranks(x, y)
n = len(ranked)
denom = n * (n-1) / 2
con = 0
discor = 0
x_tied = 0
y_tied = 0
for i in range(n-1):
x_1 = ranked[i][0]
y_1 = ranked[i][1]
for j in range(i+1, n):
x_2 = ranked[j][0]
y_2 = ranked[j][1]
x_diff = x_1 - x_2
y_diff = y_1 - y_2
if x_diff * y_diff > 0:
con += 1
elif x_diff and y_diff:
discor += 1
else:
if x_diff:
y_tied += 1
if y_diff:
x_tied += 1
diff = con - discor
total = con + discor
denom = ((total + y_tied) * (total + x_tied))**0.5
variance = (4*n+10) / (9*n*(n-1))
tau = diff / denom
stat = tau
if x_tied or y_tied:
x_tied = array([v for v in Freqs(x).itervalues() if v > 1])
y_tied = array([v for v in Freqs(y).itervalues() if v > 1])
t0 = n*(n-1)/2
t1 = sum(x_tied * (x_tied-1)) / 2
t2 = sum(y_tied * (y_tied-1)) / 2
stat = tau * sqrt((t0-t1)*(t0-t2))
v0 = n * (n - 1) * (2 * n + 5)
vt = sum(x_tied * (x_tied - 1) * (2 * x_tied + 5))
vu = sum(y_tied * (y_tied - 1) * (2 * y_tied + 5))
v1 = sum(x_tied * (x_tied - 1)) * sum(y_tied * (y_tied - 1))
v2 = sum(x_tied * (x_tied - 1) * (x_tied - 2)) * \
sum(y_tied * (y_tied - 1) * (y_tied - 2))
variance = (v0 - vt - vu) / 18 + v1 / (2 * n * (n - 1)) + v2 / (9 * n * \
(n - 1) * (n - 2))
if return_p:
return tau, zprob(stat / variance**0.5)
else:
return tau
def mw_test(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, zeros(len(x), int), zeros(len(x), int))
y = zip(y, ones(len(y), int), zeros(len(y), int))
combined = x+y
combined = 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 = 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 = sqrt((prod / (total * (total-1)))*((total**3 - total - T)/12))
z = (numerator/denominator)
p = zprob(z)
return U, p