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[SciPy-User] KS 2-sample p-value

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Moy
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[SciPy-User] KS 2-sample p-value

Moy
Hi folks.

I'm curious about the p-value computation for the 2-sample KS test
(lines 4298-4302 here [1], link below).

Can someone please give me a reference for this, in particular for the
mysterious "en + 0.12 + 0.11 / en" piece?  I've looked at the MIT
OpenCourseWare notes on KS [2] and at the SciPy docs for kstwobign but
I'm still totally confuzzled by that piece.

Thanks for your time!

Moy

1: https://github.com/scipy/scipy/blob/master/scipy/stats/stats.py#L4298
2:
http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture14.pdf


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Re: KS 2-sample p-value

josef.pktd


On Fri, Jun 10, 2016 at 3:02 PM, Moy <[hidden email]> wrote:
Hi folks.

I'm curious about the p-value computation for the 2-sample KS test
(lines 4298-4302 here [1], link below).

Can someone please give me a reference for this, in particular for the
mysterious "en + 0.12 + 0.11 / en" piece?  I've looked at the MIT
OpenCourseWare notes on KS [2] and at the SciPy docs for kstwobign but
I'm still totally confuzzled by that piece.

Thanks for your time!

Moy

1: https://github.com/scipy/scipy/blob/master/scipy/stats/stats.py#L4298
2:
http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture14.pdf


I don't think I ever looked at the details for that, or don't remember. For similar one-sample test Stephens had several articles with similar small sample corrections as a function of the number of observations.

I don't find anything related in a brief google search. My guess would be that this is from an old (older than 30 or 40 years) study that found that the fractional polynomial provides a good approximation.

Some of the nonparametric tests in scipy.stats also referred to older (maybe 1980s) books on nonparametric testing where I never had access to.

Sometimes another statistics package, R, SAS, Stata, has a relevant original reference in the documentation.


Josef
 



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Re: KS 2-sample p-value

josef.pktd


On Fri, Jun 10, 2016 at 4:06 PM, <[hidden email]> wrote:


On Fri, Jun 10, 2016 at 3:02 PM, Moy <[hidden email]> wrote:
Hi folks.

I'm curious about the p-value computation for the 2-sample KS test
(lines 4298-4302 here [1], link below).

Can someone please give me a reference for this, in particular for the
mysterious "en + 0.12 + 0.11 / en" piece?  I've looked at the MIT
OpenCourseWare notes on KS [2] and at the SciPy docs for kstwobign but
I'm still totally confuzzled by that piece.

Thanks for your time!

Moy

1: https://github.com/scipy/scipy/blob/master/scipy/stats/stats.py#L4298
2:
http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture14.pdf


I don't think I ever looked at the details for that, or don't remember. For similar one-sample test Stephens had several articles with similar small sample corrections as a function of the number of observations.

I don't find anything related in a brief google search. My guess would be that this is from an old (older than 30 or 40 years) study that found that the fractional polynomial provides a good approximation.

has this form of the polynomial with 0.11 and 0.12 coefficients, but AFAICS from a quick browse and from what I remember of his other articles it's for one-sample tests, but maybe he has somewhere a section on two-sample tests.
The best reference for Stephens is a chapter in a book that summarizes his earlier articles, but I don't remember where I have a copy of it.

Josef
 

Some of the nonparametric tests in scipy.stats also referred to older (maybe 1980s) books on nonparametric testing where I never had access to.

Sometimes another statistics package, R, SAS, Stata, has a relevant original reference in the documentation.


Josef
 



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Moy
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Re: KS 2-sample p-value

Moy

> Stephens 1970 http://www.jstor.org/stable/2984408
> has this form of the polynomial with 0.11 and 0.12 coefficients, but
> AFAICS from a quick browse and from what I remember of his other
> articles it's for one-sample tests, but maybe he has somewhere a
> section on two-sample tests.
> The best reference for Stephens is a chapter in a book that summarizes
> his earlier articles, but I don't remember where I have a copy of it.

Thanks, Josef, this is very helpful.

Best,
Moy

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