chi2test.C: Example to use chi2 test for comparing two histograms

// 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. 
//
//Authors: 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);

  // error is automatically the sqrt of the bin content
//   h1->SetBinError(1, 0);
//   h1->SetBinError(2, 1);
//   h1->SetBinError(3, 0);
//   h1->SetBinError(4, 1);
//   h1->SetBinError(5, 1);
//   h1->SetBinError(6, 2.44948983);
//   h1->SetBinError(7, 2.64575124 );
//   h1->SetBinError(8, 1.41421354);
//   h1->SetBinError(9, 4.69041586);
//   h1->SetBinError(10, 5.47722578);
//   h1->SetBinError(11, 5.19615221);
//   h1->SetBinError(12, 4.47213602);
//   h1->SetBinError(13, 3.60555124);
//   h1->SetBinError(14, 3.);
//   h1->SetBinError(15, 5.38516474);
//   h1->SetBinError(16, 3.60555124);
//   h1->SetBinError(17, 4.35889912);
//   h1->SetBinError(18, 3.31662488);
//   h1->SetBinError(19, 3.);
//   h1->SetBinError(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->SetFillColor(33);
  c1->Divide(2,2);

// Draw Histogramms and Graphs
  c1->cd(1);
  gPad->SetFrameFillColor(21);
  h1->SetMarkerColor(4);
  h1->SetMarkerStyle(20);

  h1->Draw("E");

  c1->cd(2);
  gPad->SetFrameFillColor(21);
  h2->Draw("");
  h2->SetMarkerColor(4);
  h2->SetMarkerStyle(20);

  c1->cd(3);
  gPad->SetFrameFillColor(21);
  gPad->SetGridy();
  resgr->Draw("APL");

  c1->cd(4);
  gPad->SetFrameFillColor(21);
  qqplot->Draw("AP");

  c1->cd(0);
  
  c1->Update();
   return c1;
}