Two-sample Kolmogorov-Smirnov Test in Python Scipy

You are using the one-sample KS test. You probably want the two-sample test ks_2samp:

>>> from scipy.stats import ks_2samp>>> import numpy as np>>> >>> np.random.seed(12345678)>>> x = np.random.normal(0, 1, 1000)>>> y = np.random.normal(0, 1, 1000)>>> z = np.random.normal(1.1, 0.9, 1000)>>> >>> ks_2samp(x, y)Ks_2sampResult(statistic=0.022999999999999909, pvalue=0.95189016804849647)>>> ks_2samp(x, z)Ks_2sampResult(statistic=0.41800000000000004, pvalue=3.7081494119242173e-77)

Results can be interpreted as following:

1. You can either compare the statistic value given by python to the KS-test critical value table according to your sample size. When statistic value is higher than the critical value, the two distributions are different.

2. Or you can compare the p-value to a level of significance a, usually a=0.05 or 0.01 (you decide, the lower a is, the more significant). If p-value is lower than a, then it is very probable that the two distributions are different.

This is what the scipy docs say:

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.

Cannot reject doesn't mean we confirm.