From: Jan CONRAD <jconrad_at_mail.cern.ch>

Date: Sat, 13 Aug 2005 17:36:54 +0200 (CEST)

Date: Sat, 13 Aug 2005 17:36:54 +0200 (CEST)

Dear Rene,

I would agree that you leave the KS test if you add the following discussion to the KS test documentation (with apropiate change of the routine names)

This is coming directly from the HDIFF documentation:

"The value of PROB returned by HDIFF is calculated such that it will be uniformly distributed between zero and one for compatible histograms, provided the data are not binned (or the number of bins is very large compared with the number of events). Users who have access to unbinned data and wish exact confidence levels should therefore not put their data into histograms, but should save them in ordinary Fortran arrays and call the routine TKOLMO which is being introduced into the Program Library. On the other hand, since HBOOK is a convenient way of collecting data and saving space, the routine HDIFF has been provided, and we believe it is the best test for comparison even on binned data. However, the values of PROB for binned data will be shifted slightly higher than expected, depending on the effects of the binning. For example, when comparing two uniform distributions of 500 events in 100 bins, the values of PROB, instead of being exactly uniformly distributed between zero and one, have a mean value of about 0.56. Since we are physicists, we can apply a useful rule: As long as the bin width is small compared with any significant physical effect (for example the experimental resolution) then the binning cannot have an important effect. Therefore, we believe that for all practical purposes, the probability value PROB is calculated correctly provided the user is aware that:

- The value of PROB should not be expected to have exactly the correct distribution for binned data.
- The user is responsible for seeing to it that the bin widths are small compared with any physical phenomena of interest.
- The effect of binning (if any) is always to make the value of PROB slightly too big. That is, setting an acceptance criterion of (PROB>0.05 will assure that at most 5% of truly compatible histograms are rejected, and usually somewhat less."

It is maybe a little pedantic, but I think users should be aware of the fact that the quoted confidence levels might be wrong.

Also, the KS test for unbinned data might be a nice addition to ROOT. In fact it seems much more suitable for TGraph !

Best,

Jan

*> *

*> Hi,*

*> I am just back from holidays: the Kolmogorov Smirnov test does not work *

*> for histograms. You can test it yourself, the test statistics will not be *

*> uniformly distributed. Therefore I suggested to remove it for histograms.*

*> *

*> Best,*

*> Jan*

*> *

*> *

*> *

*> > Hi Gero,*

*> > *

*> > Thanks for your comments.*

*> > It would be nice if an expert in statistics (if possible with*

*> > experience with KolmogorovTest and Chi2Test) could write some lines*

*> > on the virtues/problems of the two methods. I will add these comments*

*> > in the documentation of the two functions.*

*> > *

*> > Rene Brun*

*> > *

*> > On *

*> > Thu, *

*> > 11 *

*> > Aug 2005, Gero Flucke wrote:*

*> > *

*> > > On Thu, 11 Aug 2005, Rene Brun wrote:*

*> > >*

*> > >> On Wed, 3 Aug 2005, Jan Conrad wrote:*

*> > >>*

*> > >>> Dear Root-developers,*

*> > >>>*

*> > >>> two suggestions:*

*> > >*

*> > > <snip>*

*> > >*

*> > >>> 2) having Chi2Test in place, maybe it is time to get rid of the*

*> > >>> Kolmogorov-Smirnov Test for*

*> > >>> histograms ?*

*> > >>*

*> > >> I dont't think that users will appreciate this proposal.*

*> > >> Could you comment on the relative merits/drawbacks of the two approaches.*

*> > >> I will add your comment in the KolmogorovTest functions.*

*> > >*

*> > > Hi Jan and Rene,*

*> > > so far I neither used the chi2Test nor the KolmogorovTest, but as far as I*

*> > > know from statistics, Kolmogorov is superior to chi2 in that sense that it*

*> > > is sensitive to differences in shape while chi2 is better in taking into*

*> > > account the histogram errors. So both tests have their own validity.*

*> > >*

*> > > Cheers*

*> > >*

*> > > Gero*

*> > >*

*> > *

*> *

*> *

-- ------------------------------------------------------------ Jan CONRAD, PH/EP Dpt., CERN, CH-1211 Geneva 23, Switzerland +41 22 767 0182 (9480) (fax), Office 160-1-0012, Swiss mobile: +41796073622, Swedish mobile:+46707875229 ------------------------------------------------------------Received on Sat Aug 13 2005 - 17:37:00 MEST

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