[ROOT] wrong error calculation in TGraphAsymmErrors::GetErrorY(int point)

From: Miroslav Helbich (helbich@mail.desy.de)
Date: Wed Dec 11 2002 - 20:41:42 MET 

 Hi Rene, Fons and other rooters,

  I think this behaviour of the 
TGraphAsymmErrors::GetErrorY(int point) and TGraphAsymmErrors::GetErrorY(int point)
is not as expected.

root [6] gr1 = TGraphErrors(1)
(class TGraphErrors)146016688
root [7] gr1->SetPoint(0,1.,1.)
root [8] gr1->SetPointError(0.,0.,0.5)
root [11] gr1->GetErrorY(0)
(const Double_t)5.00000000000000000e-01     <----- correct

root [12] gr2 = new TGraphAsymmErrors(1)
(class TGraphAsymmErrors*)0x8ebe288
root [13] gr2->SetPoint(0,1.,1.)
root [14] gr2->SetPointError(0,0.,0.,0.5,0.5)
root [15] gr2->GetErrorY(0)
(const Double_t)7.07106781186547573e-01    <------ sqrt(2)*0.5

I would expect the errors to be the same since the graphs are the same.

This formula is used to calculate the chi2 which then leads to a
factor of 2 lower chi2 for the same data set defined with different class.

I understand it is difficult to fit data with assymetric error bars
and no simple prescription can be given. 

 So far the error is calculated as
 return TMath::Sqrt(elow*elow + ehigh*ehigh);

I would suggest something of the following 
 (elow+ehigh)/2.
 sqrt((elow*elow+ehigh*ehigh)/2.) 
 max(elow,ehigh)

I am not sure which one is the best - it depends on the problem. Probably #3 or #1 would do.

						    Miro



Double_t TGraphAsymmErrors::GetErrorY(Int_t i) const
{
//    This function is called by GraphFitChisquare.
//    It returns the quadratic error along Y at point i.

   if (i < 0 || i >= fNpoints) return -1;
   if (!fEYlow && !fEYhigh) return -1;
   Double_t elow=0, ehigh=0;
   if (fEYlow)  elow  = fEYlow[i];
   if (fEYhigh) ehigh = fEYhigh[i];
   return TMath::Sqrt(elow*elow + ehigh*ehigh);
}

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