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

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

Subject |
st: Ksmirnov one-sided test interpretation |

Date |
Fri, 1 Mar 2013 09:30:46 -0000 |

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/ * * 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/ EBRD SECURITY NOTICE This email has been virus scanned ______________________________________________________________ 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. 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**Follow-Ups**:**Re: st: Ksmirnov one-sided test interpretation***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**Re: st: Ksmirnov one-sided test interpretation***From:*Nick Cox <njcoxstata@gmail.com>

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