Re: Strange behaviour in TH1::Chi2Test

From: Lorenzo Moneta <Lorenzo.Moneta_at_cern.ch>
Date: Fri, 20 Apr 2007 18:06:01 +0200


Dear Tobias,

  thanks for sumbitting this. There was a bug in dealing with underflow and overflows entries (options OF or UF) It should be fixed now in the latest CVS

  Cheers

  Lorenzo
On Apr 20, 2007, at 11:38 AM, Tobias Raufer wrote:

> Dear Roottalk,
>
> I am using root version 5.15/05 on SL 3.
>
> I am seeing some strange behaviour in the function TH1::Chi2Test.
> Please
> consider the following macro:
>
> void debugChi2(){
>
> gStyle->SetOptStat(111111);
> TH1F* h2 = new TH1F("h2","h2",10,-3,3);
> TH1F* h1 = new TH1F("h1","h1",10,-3,3);
> h1->FillRandom("gaus");
> h2->FillRandom("gaus");
> h1->Draw();
> h2->Draw("sames");
>
> h1->Chi2Test(h2,"UUP");
> h1->Chi2Test(h2,"UUPOF"); // use overflow bin
> h1->Chi2Test(h2,"UUPUF"); // use underflow bin
> h1->Chi2Test(h2,"UUPOFUF"); // use both over- and underflow
>
> }
>
> As you can see I am testing two randomly filled gaussian
> histograms. In
> both cases, the overflow and underflow bins are empty. The difference
> between the four calls to TH1::Chi2Test is whether or not these
> overflow
> and underflow bins should be included in the test. The output of the
> macro looks like this:
>
> Processing debugChi2.C...
> <TCanvas::MakeDefCanvas>: created default TCanvas with name c1
> Chi2 = 8.935781, Prob = 0.443223, NDF = 9, igood = 0
> Chi2 = 35.743124, Prob = 0.0164853, NDF = 20, igood = 0
> Chi2 = 35.743124, Prob = 0.00496242, NDF = 17, igood = 0
> Chi2 = 80.422029, Prob = 6.86344e-09, NDF = 21, igood = 0
>
> As you can see, both the chi2 values and the ndf numbers are different
> in the four cases. Looking at the documentation, I thought empty bins
> (such as the overflow) will be automatically removed from the
> calculation of chi2 and ndf. How can the options "OF" and "UF" change
> the result then?
>
> You will also notice that, in the second and third case, the chi2
> value
> is exactly 4 times that of the first one and in the last case, it's 9
> times that.
>
> Am I misunderstanding the way the function works? I suspect, this has
> something to do with the handling of the y- and z-axis of the TH1.
>
> Thanks for your help.
>
> Tobi
>
> ---
> Tobias Raufer
> Denys Wilkinson Building
> Keble Road, Oxford OX1 3RH, UK
>
> Tel. +44 (0)1865 273409
> Fax. +44 (0)1865 273418
> tobias.raufer_at_physics.ox.ac.uk
>
>
Received on Fri Apr 20 2007 - 18:06:23 CEST

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