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Home Programming DataLab DLabPascal Statistics Tests PerformChi2DistComp
See also: FrequDistOfMatrix, PerformLillieforsTest 

PerformChi2DistComp

Declaration: PerformChi2DistComp (CountObserved, CountExpected: TIntArray; var Chi2, p: double; var df: integer; var nObs, nExp: integer): integer;
The function PerformChi2DistComp performs a chi2-test to compare two empirical distributions. The two datasets are specified by means of their frequency distributions stored in the arrays CountObserved and CountExpected. Please note that the bin limits of both frequency distributions must exactly match. The function returns the chi2-value in the variable parameter Chi2, its corresponding p-value in parameter p and the number of degrees of freedom in parameter df. The variable parameters nObs and nExp contain the number of obervations contained in CountObserved and CountExpected.

The function returns the following error codes:

 0 ... everything is OK
-1 ... the frequency distribution arrays do not have the same size
-2 ... one of the data arrays is not intialized
-3 ... one of the frequency distributions contain zero observations

Sample
program:		 The following sample code lets you select two variables of the currently loaded dataset. The frequency distributions of the two variables are then displayed and compared by means of a chi2-test. 

program FrequDistribution;

const
  PAGE = 1;       // chart page
  NBINS = 100;    // number of bins of the frequency distribution

(******************************************************************************)
procedure ListDistributions (Distri1, Distri2: TIntArray);
(******************************************************************************)

var
  i     : integer;

begin
with ChartBook.Tables[PAGE] do
  begin
  NrOfRows := length(Distri1);
  for i:=1 to length(Distri1) do  // lines
    Elem[1,i] := IntToStr(Distri1[i-1]);
  for i:=1 to length(Distri2) do  // lines
    Elem[2,i] := IntToStr(Distri1[i-1]);
  end;
end;

(******************************************************************************)
procedure DrawDistribution (Distri: TIntArray; Color: TColor; FirstBin,
                            Binwidth, Offset: double);
(******************************************************************************)

var
  i     : integer;

begin
with ChartBook.Charts[PAGE] do
  begin
  DataColor := Color;
  for i:=1 to length(Distri) do  // lines
    begin
    MoveTo (FirstBin+Binwidth*(i-1), 0+offset);
    DrawTo (FirstBin+Binwidth*(i-1), Distri[i-1]+offset);
    end;
  MoveTo (FirstBin, Distri[0]);  // envelope
  for i:=1 to length(Distri) do
    DrawTo (FirstBin+Binwidth*(i-1), Distri[i-1]+offset);
  AutoRange (1,4);
  Update;
  end;
end;

(******************************************************************************)
// main program
(******************************************************************************)

var
  Data           : TDouble2DArray;
  v1, v2         : integer;
  FrequDist1     : TIntArray;
  FrequDist2     : TIntArray;
  Underflow,
  Overflow,
  MaxCnt         : longint;
  Chi2, p        : double;
  df             : integer;
  nObs, nExp     : integer;
  min1, max1     : double;
  min2, max2     : double;
  minidx, maxidx : integer;
  offset         : double;
  Mask           : TBool2DArray;
  SelVars        : TIntArray;

begin
if SelectVariables (DStore, false, [], 'Please select the first variable',
                    SelVars) = 0 then
  begin
  v1 := SelVars[0];
  DStore.CopyDataToArray (Data);
  MinMaxMatrix (Data, v1-1, 0, v1-1, DStore.NrOfRows-1, min1, max1);
  if SelectVariables (DStore, false, [], 'Please select the second variable',
                      SelVars) = 0 then
    begin
    v2 := SelVars[0];
    MinMaxMatrix (Data, v2-1, 0, v2-1, DStore.NrOfRows-1, min2, max2);
    MinMaxVector ([Min1, min2, max1, max2], 0, 3, min1, max1, minidx, maxidx);
    if v1 = v2                // displace plots if the distributions
      then offset := 0.01     // come from the same variables
      else offset := 0.0;
    ResizeBool2DArray (Mask, DStore.NrOfColumns, DStore.NrOfRows);
    FillBoolMatrix (Mask, false);
    if FrequDistOfMatrix (Data, Mask,
                          v1-1,0,v1-1,DStore.NrOfRows-1, // LoX, LoY, HiX, HiY,
                          min1, max1,                    // FirstBin, LastBin,
                          (max1-min1)/NBINS,             // BinWidth,
                          FrequDist1,
                          Underflow, Overflow, MaxCnt) = 0 then
      begin
      ChartBook.Reset;
      ChartBook.Configure
         (PAGE,               // page 1
          true, true, false, // only the chart is visible
          250, 250);          // default width & height
      ChartBook.TabCaption[PAGE] := 'Frequency Distribution';
      with ChartBook.Charts[PAGE] do
        begin
        Reset;
        GridStyle := gsDotLines;
        GridColor := clSilver;
        ScalePropsY[1].ShortTicks := false;
        end;
      DrawDistribution (FrequDist1, clBlue, min1, (max1-min1)/NBINS, -offset);
      if FrequDistOfMatrix (Data, Mask,
                            v2-1,0,v2-1,DStore.NrOfRows-1, // LoX, LoY, HiX, HiY,
                            min1, max1,                    // FirstBin, LastBin
                            (max1-min1)/NBINS,             // BinWidth,
                            FrequDist2,
                            Underflow, Overflow, MaxCnt) = 0 then
        begin
        DrawDistribution (FrequDist2, clRed, min1, (max1-min1)/NBINS, +offset);
        PerformChi2DistComp (FrequDist1, FrequDist2, Chi2, p, df, nobs, nexp);
        ChartBook.Charts[PAGE].Caption := 'Frequency Distribution of Variable '+
                  IntToStr(v1)+': '+DStore.ColName[v1]+' (red) and Variable '+
                  IntToStr(v2)+': '+DStore.ColName[v2]+' (blue). p = '+
                  SigDigStr(p,12,4,true);
        ListDistributions (FrequDist1, FrequDist2);
        end;
      end;
    end;
  end;
end.