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.
a, b : sequence of 1-D ndarrays
D : float
p-value : float
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.
>>> 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)