Kolmogorov-Smirnov p-value and alpha value in python I am having trouble understanding the scipy.stats documentation against the backdrop of a book that explains the KS-Test.
The documentation (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html) shows that the function gives us a p-Value which shows us wether we can reject the null-hypothesis if the two samples are from the same distribution or not.
How does this compare to the alpha value explained here: https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Two-sample_Kolmogorov%E2%80%93Smirnov_test
For my two sets of data, which look like this:

I get this result:
stats.ks_2samp(original, synth)
Out[366]: KstestResult(statistic=0.05868544600938967, pvalue=3.5569000817378716e-13)

That makes sense to me, since the distributions are fairly similar.
Since I have 8760 samples in each set however, my critical D value is 0.0205, so the KstestResult value is bigger than that. Knowing that the test gets harsher for big sample sizes this also seems legit, since there IS a difference in the distributions, even if it is not that big.
But what exactly does the very small pvalue tell me?

Being a bit loose with the phrasing, I would phrase it as follows.

*

*The distributions are pretty similar.


*The distributions are, however, not the same, and you’re very confident about that.
Being more formal about interpreting the p-value, if the two distributions are the same, you’ve observed an unusual result.
