def ks_test(x, y=None, alt="two sided", exact = None, warn_for_ties = True):
"""Returns the statistic and probability from the Kolmogorov-Smirnov test.
Arguments:
- x, y: vectors of numbers whose distributions are to be compared.
- alt: the alternative hypothesis, default is 2-sided.
- exact: whether to compute the exact probability
- warn_for_ties: warns when values are tied. This should left at True
unless a monte carlo variant, like ks_boot, is being used.
Note the 1-sample cases are not implemented, although their cdf's are
implemented in ks.py"""
# translation from R 2.4
num_x = len(x)
num_y = None
x = zip(x, zeros(len(x), int))
lo = ["less", "lo", "lower", "l", "lt"]
hi = ["greater", "hi", "high", "h", "g", "gt"]
two = ["two sided", "2", 2, "two tailed", "two", "two.sided"]
Pval = None
if y is not None: # in anticipation of actually implementing the 1-sample cases
num_y = len(y)
y = zip(y, ones(len(y), int))
n = num_x * num_y / (num_x + num_y)
combined = x + y
if len(set(combined)) < num_x + num_y:
ties = True
else:
ties = False
combined = array(combined, dtype=[('stat', float), ('sample', int)])
combined.sort(order='stat')
cumsum = zeros(combined.shape[0], float)
scales = array([1/num_x, -1/num_y])
indices = combined['sample']
cumsum = scales.take(indices)
cumsum = cumsum.cumsum()
if exact == None:
exact = num_x * num_y < 1e4
if alt in two:
stat = max(fabs(cumsum))
elif alt in lo:
stat = -cumsum.min()
elif alt in hi:
stat = cumsum.max()
else:
raise RuntimeError, "Unknown alt: %s" % alt
if exact and alt in two and not ties:
Pval = 1 - psmirnov2x(stat, num_x, num_y)
else:
raise NotImplementedError
if Pval == None:
if alt in two:
Pval = 1 - pkstwo(sqrt(n) * stat)
else:
Pval = exp(-2 * n * stat**2)
if ties and warn_for_ties:
warnings.warn("Cannot compute correct KS probability with ties")
try: # if numpy arrays were input, the Pval can be an array of len==1
Pval = Pval[0]
except (TypeError, IndexError):
pass
return stat, Pval
def test_ps2x(self):
"""2 sample 2-sided smirnov should match answers from R"""
self.assertFloatEqual(psmirnov2x(0.48, 20, 50), 0.9982277)
self.assertFloatEqual(psmirnov2x(0.28, 20, 50), 0.8161612)
self.assertFloatEqual(psmirnov2x(0.28, 50, 20), 0.8161612)
def test_ps2x(self):
"""2 sample 2-sided smirnov should match answers from R"""
self.assertFloatEqual(psmirnov2x(0.48, 20, 50), 0.9982277)
self.assertFloatEqual(psmirnov2x(0.28, 20, 50), 0.8161612)
self.assertFloatEqual(psmirnov2x(0.28, 50, 20), 0.8161612)
