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# Re: st: Ksmirnov one-sided test interpretation

 From "JVerkuilen (Gmail)" To statalist@hsphsun2.harvard.edu Subject Re: st: Ksmirnov one-sided test interpretation Date Fri, 1 Mar 2013 09:58:37 -0500

```On Fri, Mar 1, 2013 at 4:30 AM, Tsankova, Teodora <TsankovT@ebrd.com> wrote:
> Thank you Joerg, for your comment. I am using the test not as an
> equality of distributions check but as an one-sided (inequality) check.

There is a specialist literature on this topic but it's kind of all
over the place from what little I know.

> In my case I want to check whether a parameter is higher than a random
> uniform distribution would suggest. So, I basically need to prove that
> its values are higher than if they were chosen at random in the range
> observed. I am not using a simple ttest because I would like to prove
> that not only the mean is higher but that also all the values tend to be
> higher than the uniform distribution. Also, it is difficult to deduct
> this information from the CDF graphs as I have a limited number of
> observations which are sometime above and sometimes below the 45 degree
> line which would represent the random uniform distribution.
>
> That being said, most of the interpretation of the KS test are for a
> two-sided test and this is why I have trouble making conclusions.

Sounds like you're interested in the question of stochastic dominance.
The KS test is likely to have very low power for that because its
alternative is so vague, but if you want to work with it I'd suggest
getting a classical nonparametric statistics book such as Gibbons &
Chakraborti as I believe this kind of question could be answered by
inverting a one-sample KS test to generate an appropriate one-sided
confidence interval. There's a literature on this kind of question and
in general you can map stochastic dominance to an ROC analysis. for
which there are some nice tools in Stata already, such as -rocgold-
and associated postestimation. But this is definitely a specialist
literature. As I recall many of the easy methods end up failing pretty

Gibbons, J. D., and S. Chakraborti. 2011. Nonparametric Statistical
Inference. 5th ed. Boca Raton, FL: Chapman & Hall/CRC.

--
JVVerkuilen, PhD
jvverkuilen@gmail.com

"It is like a finger pointing away to the moon. Do not concentrate on
the finger or you will miss all that heavenly glory." --Bruce Lee,
Enter the Dragon (1973)
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