def calc_spearman_t(r,n,tails='two-tailed',eps=1e-10):
"""Calculate the t value, and probability for Spearman correlation
Equation from Wikipedia article on Spearman rank correlation:
http://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient
TODO: verify with additional / published sources.
TODO: want to find the correct handling for the
case of perfect correlation
"""
#Right now I subtract an arbitrarily tiny
#epsilon if r is exactly 1.0 to prevent divide-by-zero
#errors.
if r == 1.0:
r = r-eps
t = r*(((n-2)/(1.0-r**2))**0.5)
if tails == 'two-tailed':
prob = tprob(t,n-2)
elif tails == 'high':
prob = t_high(t,n-2)
elif tails == 'low':
prob = t_low(t,n-2)
else:
raise RuntimeError("Valid prob. methods are 'two-tailed','high',and 'low'")
return prob
def calc_spearman_t(r, n, tails='two-tailed', eps=1e-10):
"""Calculate the t value, and probability for Spearman correlation
Equation from Wikipedia article on Spearman rank correlation:
http://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient
TODO: verify with additional / published sources.
TODO: want to find the correct handling for the
case of perfect correlation
"""
#Right now I subtract an arbitrarily tiny
#epsilon if r is exactly 1.0 to prevent divide-by-zero
#errors.
if r == 1.0:
r = r - eps
t = r * (((n - 2) / (1.0 - r**2))**0.5)
if tails == 'two-tailed':
prob = tprob(t, n - 2)
elif tails == 'high':
prob = t_high(t, n - 2)
elif tails == 'low':
prob = t_low(t, n - 2)
else:
raise RuntimeError(
"Valid prob. methods are 'two-tailed','high',and 'low'")
return prob
def t_tailed_prob(t, df, tails):
"""Return appropriate p-value for given t and df, depending on tails."""
if tails == 'high':
return t_high(t, df)
elif tails == 'low':
return t_low(t, df)
else:
return tprob(t,df)
def correlation(x_items, y_items):
"""Returns Pearson correlation between x and y, and its significance.
WARNING: x_items and y_items must be same length!
"""
r = pearson(x_items, y_items)
n = len(x_items)
if n < 3:
prob = 1
else:
try:
t = r/sqrt((1 - (r*r))/(n-2))
prob = tprob(t, n-2)
except (ZeroDivisionError, FloatingPointError): #r was presumably 1
prob = 0
return (r, prob)
def test_tprob(self):
"""tprob should match twice the t_high probability for abs(t)"""
probs = {
1: [ 2*i for i in
[ 0.500000000, 0.496817007, 0.468274483, 0.352416382,
0.250000000, 0.147583618, 0.062832958, 0.031725517,
0.015902251, 0.010606402, 0.006365349, 0.001591536,
]],
10: [ 2*i for i in
[ 5.000000e-01, 4.961090e-01, 4.611604e-01, 3.139468e-01,
1.704466e-01, 3.669402e-02, 2.686668e-04, 7.947766e-07,
1.073031e-09, 1.980896e-11, 1.237155e-13, 1.200254e-19,
]],
100:[ 2*i for i in
[ 5.000000e-01, 4.960206e-01, 4.602723e-01, 3.090868e-01,
1.598621e-01, 2.410609e-02, 1.225087e-06, 4.950844e-17,
4.997134e-37, 4.190166e-52, 7.236082e-73, 2.774197e-132,
]],
}
for df in self.df:
for x, p in zip(self.values, probs[df]):
self.assertFloatEqualRel(tprob(x, df), p, eps=1e-4)
