Compute the Kolmogorov-Smirnov 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.
- data1, data2 : sequence of 1-D ndarrays
two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different
- statistic : float
- pvalue : 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 >>> np.random.seed(12345678) #fix random seed to get the same result >>> n1 = 200 # size of first sample >>> n2 = 300 # size of second sample
For a 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) >>> stats.ks_2samp(rvs1, rvs2) (0.20833333333333337, 4.6674975515806989e-005)
For a slightly different distribution, we cannot reject the null hypothesis at a 10% or lower alpha since the p-value at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2, loc=0.01, scale=1.0) >>> stats.ks_2samp(rvs1, rvs3) (0.10333333333333333, 0.14498781825751686)
For an identical distribution, we cannot reject the null hypothesis since the p-value is high, 41%:
>>> rvs4 = stats.norm.rvs(size=n2, loc=0.0, scale=1.0) >>> stats.ks_2samp(rvs1, rvs4) (0.07999999999999996, 0.41126949729859719)