chi2test.C

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/// \file
/// \ingroup tutorial_math
/// \notebook
/// Example to use chi2 test for comparing two histograms
/// One unweighted histogram is compared with a weighted histogram.
/// The normalized residuals are retrieved and plotted in a simple graph.
/// The QQ plot of the normalized residual using the
/// normal distribution is also plotted.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Nikolai Gagunashvili, Daniel Haertl, Lorenzo Moneta

#include "TH1.h"
#include "TH1D.h"
#include "TF1.h"
#include "TGraph.h"
#include "TGraphQQ.h"
#include "TCanvas.h"
#include "TStyle.h"
#include "TMath.h"

TCanvas * chi2test(Float_t w=0)
{
   // Note: The parameter w is used to produce the 2 pictures in
   // the TH1::Chi2Test method. The 1st picture is produced with
   // w=0 and the 2nd with w=17 (see TH1::Chi2Test() help).

   // Define Histograms.
   const Int_t n = 20;

   TH1D *h1 = new TH1D("h1", "h1", n, 4, 16);
   TH1D *h2 = new TH1D("h2", "h2", n, 4, 16);

   h1->SetTitle("Unweighted Histogram");
   h2->SetTitle("Weighted Histogram");

   h1->SetBinContent(1, 0);
   h1->SetBinContent(2, 1);
   h1->SetBinContent(3, 0);
   h1->SetBinContent(4, 1);
   h1->SetBinContent(5, 1);
   h1->SetBinContent(6, 6);
   h1->SetBinContent(7, 7);
   h1->SetBinContent(8, 2);
   h1->SetBinContent(9, 22);
   h1->SetBinContent(10, 30);
   h1->SetBinContent(11, 27);
   h1->SetBinContent(12, 20);
   h1->SetBinContent(13, 13);
   h1->SetBinContent(14, 9);
   h1->SetBinContent(15, 9 + w);
   h1->SetBinContent(16, 13);
   h1->SetBinContent(17, 19);
   h1->SetBinContent(18, 11);
   h1->SetBinContent(19, 9);
   h1->SetBinContent(20, 0);

   h2->SetBinContent(1, 2.20173025 );
   h2->SetBinContent(2, 3.30143857);
   h2->SetBinContent(3, 2.5892849);
   h2->SetBinContent(4, 2.99990201);
   h2->SetBinContent(5, 4.92877054);
   h2->SetBinContent(6, 8.33036995);
   h2->SetBinContent(7, 6.95084763);
   h2->SetBinContent(8, 15.206357);
   h2->SetBinContent(9, 23.9236012);
   h2->SetBinContent(10, 44.3848114);
   h2->SetBinContent(11, 49.4465599);
   h2->SetBinContent(12, 25.1868858);
   h2->SetBinContent(13, 16.3129692);
   h2->SetBinContent(14, 13.0289612);
   h2->SetBinContent(15, 16.7857609);
   h2->SetBinContent(16, 22.9914703);
   h2->SetBinContent(17, 30.5279255);
   h2->SetBinContent(18, 12.5252123);
   h2->SetBinContent(19, 16.4104557);
   h2->SetBinContent(20, 7.86067867);
   h2->SetBinError(1, 0.38974303 );
   h2->SetBinError(2, 0.536510944);
   h2->SetBinError(3, 0.529702604);
   h2->SetBinError(4, 0.642001867);
   h2->SetBinError(5, 0.969341516);
   h2->SetBinError(6, 1.47611344);
   h2->SetBinError(7, 1.69797957);
   h2->SetBinError(8, 3.28577447);
   h2->SetBinError(9, 5.40784931);
   h2->SetBinError(10, 9.10106468);
   h2->SetBinError(11, 9.73541737);
   h2->SetBinError(12, 5.55019951);
   h2->SetBinError(13, 3.57914758);
   h2->SetBinError(14, 2.77877331);
   h2->SetBinError(15, 3.23697519);
   h2->SetBinError(16, 4.3608489);
   h2->SetBinError(17, 5.77172089);
   h2->SetBinError(18, 3.38666105);
   h2->SetBinError(19, 2.98861837);
   h2->SetBinError(20, 1.58402085);

   h1->SetEntries(217);
   h2->SetEntries(500);

   //apply the chi2 test and retrieve the residuals
   Double_t res[n], x[20];
   h1->Chi2Test(h2,"UW P",res);

   //Graph for Residuals
   for (Int_t i=0; i<n; i++) x[i]= 4.+i*12./20.+12./40.;
   TGraph *resgr = new TGraph(n,x,res);
   resgr->GetXaxis()->SetRangeUser(4,16);
   resgr->GetYaxis()->SetRangeUser(-3.5,3.5);
   resgr->GetYaxis()->SetTitle("Normalized Residuals");
   resgr->SetMarkerStyle(21);
   resgr->SetMarkerColor(2);
   resgr->SetMarkerSize(.9);
   resgr->SetTitle("Normalized Residuals");

   //Quantile-Quantile plot
   TF1 *f = new TF1("f","TMath::Gaus(x,0,1)",-10,10);
   TGraphQQ *qqplot = new TGraphQQ(n,res,f);
   qqplot->SetMarkerStyle(20);
   qqplot->SetMarkerColor(2);
   qqplot->SetMarkerSize(.9);
   qqplot->SetTitle("Q-Q plot of Normalized Residuals");

   //create Canvas
   TCanvas *c1 = new TCanvas("c1","Chistat Plot",10,10,700,600);
   c1->Divide(2,2);

   // Draw Histogramms and Graphs
   c1->cd(1);
   h1->SetMarkerColor(4);
   h1->SetMarkerStyle(20);

   h1->Draw("E");

   c1->cd(2);
   h2->Draw("");
   h2->SetMarkerColor(4);
   h2->SetMarkerStyle(20);

   c1->cd(3);
   gPad->SetGridy();
   resgr->Draw("APL");

   c1->cd(4);
   qqplot->Draw("AP");

   c1->cd(0);

   c1->Update();
   return c1;
}