Kolmogorov-Smirnov

#1
Hi,

I have used a two sample kolmogorov-smirnov test to compare the distributions of two sets of data. I know that the K-S test is a non parametric test, however the distributions of data i'm comparing has turned out to be normally distributed...

I know there is probably a number of tests that could be used to compare normally distributed data, but is there a reason not to use the K-S test? Are there any disadvantages (with regard to type1 and 2 errors perhaps)? Is it ok to use it?

I've sort of gone down this route with my data analysis, but the question has come up: why use a non parametric test to compare parametric data? Hopefully K-S is unconventional rather than completely wrong.

Advice would be helpful. Thanks in advance!!!
 

BGM

TS Contributor
#2
I just give my two cents on the parametric / non-parametric issue.

One of the most obvious pro for parametric (hypothesis testing) approach is that it has a higher power over the non-parametric alternative. The other merit may include it is more elegant and has closed form solution.


On the other hand for non-parametric approach, it avoid the model mis-specification error. The "higher power" merit for parametric approach only holds when you correctly specify the model. And you may also say that for a non-parametric approach you can be applied to different kind of distributions without assuming one. For parametric approach you may need to derive one for each (type of) distribution.
 
#3
The Kolmogorov-Smirnov tests the distributions of a sample, for example the normal distribution.

The most usual thing is that someone want to compare if two population means are the same, by comparing the sample means. This is most often done with a t-test.