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From |
Nick Cox <njcoxstata@gmail.com> |

To |
"statalist@hsphsun2.harvard.edu" <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 17:31:49 +0000 |

Nick On 9 Mar 2013, at 13:34, David Hoaglin <dchoaglin@gmail.com> wrote:

Teodora, It seems odd to use a two-sample test when you actually have only one sample. What was the basis for the advice to use the Wilcoxon-Mann-Whitney test? A one-sided KS test would be all right. Some people might be more comfortable making the test two-sided, unless you would not have any interest in a situation where the data departed from the null hypothesis in the other direction. I don't know what the literature says about whether any other test has greater power for the type of alternative that you are interested in. With only 15 observations, the departure would have to be substantial to reject the uniform null hypothesis. I have an offbeat suggestion. Transform the sample to normal deviates by applying the inverse of the standard normal cumulative distribution function to each observation, and test whether the transformed sample departs from the standard normal distribution. You can also make a normal probability plot of the transformed sample. What do you mean by "a constant markup of 1/14"? David HoaglinOn Thu, Mar 7, 2013 at 3:11 PM, Tsankova, Teodora<TsankovT@ebrd.com> wrote:Some time ago I posted on statlist with a question regarding theuse of a one-sided KS test and I was advised that for my purpose Ican use the Wilcoxon-Mann-Whitney test (ranksum command in Stata).I basically have 15 observations that go from 0 to 1 and constitutemy empirical distribution and I want to prove that those takehigher values than a uniform distribution would suggest. I havethree questions related to the test:1) I generate myself 15 more observation which take values from 0to 1 with a constant markup of 1/14 (I simulate a uniformdistribution of 15 variables in the same interval). Has anyone elseused this method for creating uniform distribution and do you seeany problems with it?2) I use the ponder option to compute the p-value for the onesided 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 casesyou would draw a random number from Observed that would be higherthan 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 anordinal meaning in the sense higher values represent morehomogenous group lending villages in my case. However, the valuesthe variable takes are not interval but continuous ones. Can Istill use this test?Thank you, Teodora* * 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/

* * 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>

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

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