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st: -ksmirnov- for uniform distribution?


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: -ksmirnov- for uniform distribution?
Date   Thu, 27 Mar 2008 14:08:27 -0500

I've done some simulations on performance of certain tests, and I want
to relate the p-values that come out of a test to the uniform
distribution. Looking at the syntax of -ksmirnov-, it appears that I
need to put something like the straight line for the RHS expression,
so I am trying:

sort p
ksmirnov p = (_n-1/2)/(_N+1)
One-sample Kolmogorov-Smirnov test against theoretical distribution
           (_n-0.5)/2001

 Smaller group       D       P-value  Corrected
 ----------------------------------------------
  p:                  0.0007    0.998
 Cumulative:        -0.0002    1.000
 Combined K-S:       0.0007    1.000      1.000



and it happily gives me the p-value of 1. Well, I know that the test
is biased, I do the histogram -- and it produces an almost triangular
distribution of p-values heavily loaded on small p-values, and when I
do the distance between p and the right-hand side by hand, I find that
the difference between the distribution functions is like 0.33, not
0.0007 reported in -ksmirnov-. What am I doing wrong here?

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I don't check this account regularly
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