# Interpreting Kolmogorov Smirnoff Test

I have two sets of data and I want to determine whether they come from similar distributions or not so I am using the Kolmogorov-Smirnoff Test.

So I understand that if I get a p-value of less than 0.05 I can say that i'm 95% confident that they come from different distributions?

So my question is if I get a p-value of 0.33 am I 67% confident that they come from different distributions? Is that a correct interpretation?

And conversely, how do I say how confident I am that they come from the same distribution, do I need a different test for that? Or is it just the inverse of above?

Thanks

• In Russian, the names Kolmogorov and Smirnov end with the same letter and so should end with the same letter when transliterated. The transliteration -off is very old-fashioned; regardless of that there can be no grounds for inconsistency. Mar 29, 2016 at 13:22
• Rather than wanting to be assured of what form of words you might use, which seems more a question of diplomacy, etiquette or liturgy, the key question is surely how far and in what ways your distributions differ. A quantile-quantile plot will tell you immensely more than any such test. Mar 29, 2016 at 13:24

want to determine whether they come from similar distributions

A goodness of fit test doesn't say how similar two distributions are; once you pin down a suitable way to measure similarity (suitable to your particular purpose), that would be more like some kind of effect size.

So I understand that if I get a p-value of less than 0.05 I can say that i'm 95% confident that they come from different distributions?

No. That's not a correct interpretation of what a p-value tells you.

So my question is if I get a p-value of 0.33 am I 67% confident that they come from different distributions? Is that a correct interpretation?

No.

And conversely, how do I say how confident I am that they come from the same distribution,

You can't. (Well, possibly you can make a statement vaguely sort of similar to that if you're a Bayesian, but then you wouldn't be doing a Kolmogorov-Smirnoff test. And it shouldn't contain the word "confidence" since that has a particular meaning in statistics that wouldn't really apply.)

Or is it just the inverse of above?

Nope.