Comparing two samples

In the following, we are given two samples, which can come either from the same or from different distributions, and we want to test whether these samples have the same statistical properties.

Comparing means

Test with samples with identical means:

>>> import scipy.stats as stats
>>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500)
>>> rvs2 = stats.norm.rvs(loc=5, scale=10, size=500)
>>> stats.ttest_ind(rvs1, rvs2)
Ttest_indResult(statistic=-0.5489036175088705, pvalue=0.5831943748663959)  # random

Test with samples with different means:

>>> rvs3 = stats.norm.rvs(loc=8, scale=10, size=500)
>>> stats.ttest_ind(rvs1, rvs3)
Ttest_indResult(statistic=-4.533414290175026, pvalue=6.507128186389019e-06)  # random

Kolmogorov-Smirnov test for two samples: ks_2samp

For the example, where both samples are drawn from the same distribution, we cannot reject the null hypothesis, since the pvalue is high

>>> stats.ks_2samp(rvs1, rvs2)
KstestResult(statistic=0.026, pvalue=0.9959527565364388)  # random

In the second example, with different location, i.e., means, we can reject the null hypothesis, since the pvalue is below 1%

>>> stats.ks_2samp(rvs1, rvs3)
KstestResult(statistic=0.114, pvalue=0.00299005061044668)  # random