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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 12:22:39 -0500 |

On Sat, Mar 9, 2013 at 8:34 AM, David Hoaglin <dchoaglin@gmail.com> wrote: > It seems odd to use a two-sample test when you actually have only one > sample. 100% agreed, as the sampling variability in the second sample is illusory and costly. > 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. > Yeah that's the problem. It seems to me that the KS test isn't really reflecting the hypothesis because of its vague alternative. I think the Mann-Whitney came from the notion of using an ROC type approach to the problem, as per: Bamber, D. 1975. The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. J. Math. Psych., 12, 387-415. but I'm not sure. Bamber shows that the ordinal dominance plot test of the area under the curve is equivalent to the Mann-Whitney statistic, but that's for a two sample problem. The reason I thought -rocgold- might be tricked into giving the right answer is because in that sense the gold standard ROC curve is the uniform here, and Teodora wants to know if her data differ from it. ROC procedures also give confidence intervals, which will likely be very helpful. I'm guessing that it's time to consult a good text book (for which see the Stata documentation as a starting point as they usually have several good suggestions). > 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. That's certainly one method, as it would allow the use of qnorm. * * 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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