// ----------------------------------------------------------------------------------- //
/*
  ROOT macro for illustrating the importance of VISUAL INSPECTION of a dataset.

  The example is called "Anscombe's Quartet" (F.J. Anscombe, "Graphs in Statistical
  Analysis," American Statistician, 27 [February 1973], 17-21) and consists of four
  datasets, which have the same:
   - Mean of each x variable                   9.0
   - Variance of each x variable              10.0
   - Mean of each y variable                   7.5
   - Variance of each y variable               3.75
   - Correlation between each x and y variable 0.816
   - Linear regression line                    y = 3 + 0.5x

  However, they are very different! For more information on Anscombe's Quartet, see:
    http://en.wikipedia.org/wiki/Anscombe's_quartet

  Author: Troels C. Petersen (NBI/CERN)
  Email:  Troels.Petersen@cern.ch
  Date:   26th of August 2010
*/
// ----------------------------------------------------------------------------------- //


//---------------------------------------------------------------------------------- 
// Run in ROOT by: .x AnscombesQuartet.c
// Output:         AnscombesQuartet.eps
//---------------------------------------------------------------------------------- 


// ----------------------------------------------------------------------------------- //
void AnscombesQuartet() {
// ----------------------------------------------------------------------------------- //
  gROOT->Reset();

  // Set the showing of statistics and fitting results (0 means off, 1111 means all on):
  gStyle->SetOptStat(1111);
  // gStyle->SetOptStat(0);
  gStyle->SetOptFit(1111);
  // gStyle->SetOptFit(0);

  // Statistics and fitting results replaced in:
  // gStyle->SetStatX(0.52);    // Top left corner.
  // gStyle->SetStatY(0.86);
  gStyle->SetStatX(0.89);       // Bottom right corner.
  gStyle->SetStatY(0.33);

  // Set the graphics:
  gStyle->SetStatBorderSize(1);
  gStyle->SetStatFontSize(0.055);
  gStyle->SetCanvasColor(4);
  gStyle->SetPalette(1);


  // ------------------------------------------------------------------ //
  // Get data in arrays:
  // ------------------------------------------------------------------ //

  const int Ndatasets = 4;
  const int Npoints = 11;
  double x[Ndatasets][Npoints] =
	{{10.0,  8.0, 13.0,  9.0, 11.0, 14.0,  6.0,  4.0, 12.0,  7.0,  5.0},
	 {10.0,  8.0, 13.0,  9.0, 11.0, 14.0,  6.0,  4.0, 12.0,  7.0,  5.0},
	 {10.0,  8.0, 13.0,  9.0, 11.0, 14.0,  6.0,  4.0, 12.0,  7.0,  5.0},
	 { 8.0,  8.0,  8.0,  8.0,  8.0,  8.0,  8.0, 19.0,  8.0,  8.0,  8.0}};
  double y[Ndatasets][Npoints] =
    {{ 8.04,  6.95,  7.58,  8.81,  8.33,  9.96,  7.24,  4.26, 10.84,  4.82,  5.68},
     { 9.14,  8.14,  8.74,  8.77,  9.26,  8.10,  6.13,  3.10,  9.13,  7.26,  4.74},
     { 7.46,  6.77, 12.74,  7.11,  7.81,  8.84,  6.08,  5.39,  8.15,  6.42,  5.73},
     { 6.58,  5.76,  7.71,  8.84,  8.47,  7.04,  5.25, 12.50,  5.56,  7.91,  6.89}};


  // ------------------------------------------------------------------ //
  // Fit data:
  // ------------------------------------------------------------------ //

  // Make graphs:
  TGraph* graph[Ndatasets];                                        // Make 4 graphs
  for (int idataset=0; idataset < Ndatasets; idataset++) {         // Put data into them
    graph[idataset] = new TGraph(Npoints, x[idataset], y[idataset]);
  }
  TF1 *fit_p1 = new TF1("fit_p1", "[0]*x + [1]", 3.5, 20.0);       // Make a linear function
  fit_p1->SetParameters(1.0, 1.0);                                 // Set its parameters

  // Make canvas:
  canvas = new TCanvas("canvas","",650,20,600,450);                // Make a new window
  canvas->SetFillColor(0);                                         // Make it white
  canvas->Divide(2,2);                                             // Divide it into a 2x2 window

  // Fit and plot graphs:
  for (int idataset=0; idataset < Ndatasets; idataset++) {         // Loop over data sets
    canvas->cd(idataset+1);                                        // Point at the relevant window

    fit_p1->SetLineColor(4);                                       // Set function line color!
    fit_p1->SetLineWidth(2);                                       // Set function line width!
    graph[idataset]->SetMarkerColor(2);                            // Set data marker color
    graph[idataset]->SetMarkerStyle(20);                           // Set data marker type
    graph[idataset]->SetMarkerSize(1.0);                           // Set data marker size
    graph[idataset]->Fit("fit_p1","r");                            // Fit data with function
    graph[idataset]->Draw("AP");                                   // Draw data in window
  }

  canvas->Update();                                                // Make sure everything is in!
  canvas->SaveAs("AnscombesQuartet.eps");                          // Print window to file
}

//---------------------------------------------------------------------------------- 
/*

First acquaint yourself with the program, and get yourself a "free" (possibly first)
look at how ROOT works. Understand that each of the four distributions are being fitted
with a linear function (here called "fit_p1") and the results plottet. There are comments
for most lines in the macro!

Run the macro, and then take a close look at each of the four results.


Questions:
----------
 1) Looking closely at each of the four fits, determine which points gives the largest
    contribution to the "mismatch" (which is chi-square) between the data and the fit.

 2) Consider how YOU would treat each of the four datasets and fit them!


Advanced questions:
-------------------
 1) How would you with (smarter) statistical techniques detect that something was
    not right?

*/
//----------------------------------------------------------------------------------