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From |
"JVerkuilen (Gmail)" <jvverkuilen@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Using Wilcoxon rank-sum (Mann-Whitney) test to compare an emipirical and a uniform distribution |

Date |
Sat, 9 Mar 2013 18:35:57 -0500 |

On Sat, Mar 9, 2013 at 8:49 AM, Tsankova, Teodora <TsankovT@ebrd.com> wrote: > Dear David, > > Thank you for the suggestion. > > What I mean is that I create a uniform distribution between 0 and 1 with > 15 observation. Given that every value should have the same probability > under a uniform distribution I divide 1 by 14 and create those equally > spaces 15 values. Plotting the CDF of those values would result in a > straight diagonal line which is ultimately what the ksmirnov test would > test against as well. > So it looks from ksmirnov that you reject the null of uniformity but, naturally enough, want some measure of directionality. That's why I think many of us were dubious of ksmirnov in the first place. However, you can invert it to generate a confidence interval by working out what the rejection region of the relevant test is and plotting it using quantile. I don't have access to a book on nonparametric statistics (such as Gibbons & Chakraborti) at the moment, but I've done this to generate a confidence interval for the ECDF. However, the resulting confidence interval is usually very wide. In the past when I had this problem I seem to recall bootstrapping worked out better. (It was a long time ago, I'm not sure I recall how.) 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) * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Using Wilcoxon rank-sum (Mann-Whitney) test to compare an emipirical and a uniform distribution***From:*"Tsankova, Teodora" <TsankovT@ebrd.com>

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