def ks_2samp(data1, data2):
"""
Computes the Kolmogorov-Smirnof statistic on 2 samples.
This is a two-sided test for the null hypothesis that 2 independent samples
are drawn from the same continuous distribution.
Parameters
----------
a, b : sequence of 1-D ndarrays
two arrays of sample observations assumed to be drawn from a continuous
distribution, sample sizes can be different
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(np.asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1, data2])
#reminder: searchsorted inserts 2nd into 1st array
cdf1 = np.searchsorted(data1, data_all, side='right') / (1.0 * n1)
cdf2 = (np.searchsorted(data2, data_all, side='right')) / (1.0 * n2)
d = np.max(np.absolute(cdf1 - cdf2))
#Note: d absolute not signed distance
en = np.sqrt(n1 * n2 / float(n1 + n2))
try:
prob = ksprob((en + 0.12 + 0.11 / en) * d)
except:
prob = 1.0
return d, prob
def ks_2samp(data1, data2):
"""
Computes the Kolmogorov-Smirnof statistic on 2 samples.
This is a two-sided test for the null hypothesis that 2 independent samples
are drawn from the same continuous distribution.
Parameters
----------
a, b : sequence of 1-D ndarrays
two arrays of sample observations assumed to be drawn from a continuous
distribution, sample sizes can be different
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(np.asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1,data2])
#reminder: searchsorted inserts 2nd into 1st array
cdf1 = np.searchsorted(data1,data_all,side='right')/(1.0*n1)
cdf2 = (np.searchsorted(data2,data_all,side='right'))/(1.0*n2)
d = np.max(np.absolute(cdf1-cdf2))
#Note: d absolute not signed distance
en = np.sqrt(n1*n2/float(n1+n2))
try:
prob = ksprob((en+0.12+0.11/en)*d)
except:
prob = 1.0
return d, prob