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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Ksmirnov one-sided test interpretation |

Date |
Fri, 1 Mar 2013 09:49:08 +0000 |

As a testing problem this seems closer to Mann-Whitney-Wilcoxon. Even better to recast it as a problem for -somersd- (Roger Newson, SSC etc.) Nick On Fri, Mar 1, 2013 at 9:30 AM, Tsankova, Teodora <TsankovT@ebrd.com> wrote: > Thank you Joerg, for your comment. I am using the test not as an > equality of distributions check but as an one-sided (inequality) check. > > In my case I want to check whether a parameter is higher than a random > uniform distribution would suggest. So, I basically need to prove that > its values are higher than if they were chosen at random in the range > observed. I am not using a simple ttest because I would like to prove > that not only the mean is higher but that also all the values tend to be > higher than the uniform distribution. Also, it is difficult to deduct > this information from the CDF graphs as I have a limited number of > observations which are sometime above and sometimes below the 45 degree > line which would represent the random uniform distribution. > > That being said, most of the interpretation of the KS test are for a > two-sided test and this is why I have trouble making conclusions. > > Thank you again, > > Teodora > > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Joerg > Luedicke > Sent: 28 February 2013 18:38 > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: Ksmirnov one-sided test interpretation > > Yes, why not just looking at your data? > > That aside, I am wondering what the point of such a test is? What does > it even mean that one distribution is "lower" than another? Or to quote > the Stata manual, version 11: "We wish to use the two-sample > Kolmogorov-Smirnov test to determine if there are any differences in the > distribution of x for these two groups..." "Any" differences seem to > pick up a mix of differences with regard to the location and shape of > distributions. What is the motivation behind this? If there are > differences in two distributions, why not just looking at what these > differences are? But even if there was a good reason for using this > test, I am wondering what it is telling us. I did not try hard to come > up with the following example: > > Let's generate some data for two groups where the distribution in group > one is normal with mean 10 and SD 5, while the distribution in the other > group is a gamma with shape 5 and scale 2: > > *--------------- > clear > set obs 200 > set seed 1234 > > gen u = runiform()>.5 > gen x = rnormal(10,5) if u==0 > replace x=rgamma(5,2) if u==1 > *--------------- > > and have a look at the empirical distribution for this data realization: > > *--------------- > tw kdensity x if u==0 || kdensity x if u==1 > *--------------- > > As expected, these distributions surely look different to me. We can > also have a look at the true functions: > > *--------------- > tw function y = gammaden(5,2,0,x) , range(0 25) || /// > function y = normalden(x,10,5) , range(-5 25) /// > legend(order(1 "Gamma" 2 "Gauss")) > *--------------- > > Yet, if we run the K-S test: > > *--------------- > ksmirnov x, by(u) exact > *--------------- > > we would conclude that we cannot reject the hypothesis that the > distributions are "different"? That does not sound right to me. > > So, my bottom line is: a) that I wonder why one would use this test in > the first place, and b) even if there was a good reason, I probably > would not trust it. I may very well be missing something here as I have > never used or studied this test before, so others, please correct me if > I am wrong here with something. > > Joerg > > > > On Thu, Feb 28, 2013 at 1:06 PM, Nick Cox <njcoxstata@gmail.com> wrote: >> Why not plot the data to show what is going on? >> >> Nick >> >> On Thu, Feb 28, 2013 at 5:23 PM, Tsankova, Teodora <TsankovT@ebrd.com> > wrote: >> >>> I have a question related to a previous post: >>> >>> http://www.stata.com/statalist/archive/2009-01/msg00525.html >>> >>> The Stata output from this message is as follows: >>> >>> Two-sample Kolmogorov-Smirnov test for equality of distribution > functions: >>> >>> Smaller group D P-value Corrected >>> ---------------------------------------------- >>> male: 0.2468 0.002 >>> female: 0.0000 1.000 >>> Combined K-S: 0.2468 0.005 0.003 >>> >>> >>> From the one sided tests (first two lines) on can say which > distribution tends to be lower - for males or for females. However, I am > not sure how to interpret it. >>> >>> Given that the pvalue from the first line is low and that D in the > second line is 0, can we say that this is a proof that the distribution > of male is lower than that of female? To rephrase it - can we claim that > the distribution of male stochastically dominates the one of female > which would imply that the values of the underlying variable tend to be > larger for male than for female? Or, do we interpret it in the exactly > opposite way - that the values for male tend to be lower than the values > for female? > * * 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: Ksmirnov one-sided test interpretation***From:*"Tsankova, Teodora" <TsankovT@ebrd.com>

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