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From |
"Tsankova, Teodora" <TsankovT@ebrd.com> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Thu, 7 Mar 2013 20:11:58 -0000 |

Some time ago I posted on statlist with a question regarding the use of a one-sided KS test and I was advised that for my purpose I can use the Wilcoxon-Mann-Whitney test (ranksum command in Stata). I basically have 15 observations that go from 0 to 1 and constitute my empirical distribution and I want to prove that those take higher values than a uniform distribution would suggest. I have three questions related to the test: 1) I generate myself 15 more observation which take values from 0 to 1 with a constant markup of 1/14 (I simulate a uniform distribution of 15 variables in the same interval). Has anyone else used this method for creating uniform distribution and do you see any problems with it? 2) I use the ponder option to compute the p-value for the one sided test and I get the following output: Two-sample Wilcoxon rank-sum (Mann-Whitney) test ObservedOr~m | obs rank sum expected -------------+--------------------------------- Observed | 15 236 232.5 Uniform | 15 229 232.5 -------------+--------------------------------- combined | 30 465 465 unadjusted variance 581.25 adjustment for ties 0.00 ---------- adjusted variance 581.25 Ho: ktaub_~m(Observ~m==Observed) = ktaub_~m(Observ~m==Uniform) z = 0.145 Prob > |z| = 0.8846 P{ktaub_~m(Observ~m==Observed) > ktaub_~m(Observ~m==Uniform)} = 0.516 999996 (15 real changes made) (0 real changes made) (0 real changes made) I would interpret it in the following way: In 51.6% of the cases you would draw a random number from Observed that would be higher than a random draw from Uniform. Is this the correct interpretation? 3) My last question is related to the fact that Wilcoxon Mann-Whitney test is used to analyse ordinal data. My data has an ordinal meaning in the sense higher values represent more homogenous group lending villages in my case. However, the values the variable takes are not interval but continuous ones. Can I still use this test? Thank you, Teodora ______________________________________________________________ This message may contain privileged information. If you have received this message by mistake, please keep it confidential and return it to the sender. Although we have taken steps to minimise the risk of transmitting software viruses, the EBRD accepts no liability for any loss or damage caused by computer viruses and would advise you to carry out your own virus checks. The contents of this e-mail do not necessarily represent the views of the EBRD. * * 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/

**Follow-Ups**:**Re: st: Using Wilcoxon rank-sum (Mann-Whitney) test to compare an emipirical and a uniform distribution***From:*David Hoaglin <dchoaglin@gmail.com>

**Re: st: Using Wilcoxon rank-sum (Mann-Whitney) test to compare an emipirical and a uniform distribution***From:*Nick Cox <njcoxstata@gmail.com>

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