{ Test file: ABCNested.laz (imported from OpenStat sample data zip file)
    Dependent: Dep
    Factor A : A
    Factor B : B
    Factor C : C
}

unit ABCNestedUnit;

{$mode objfpc}{$H+}
{$WARN 6058 off : Call to subroutine "$1" marked as inline is not inlined}

interface

uses
  Classes, SysUtils, FileUtil, TAStyles, Forms, Controls, Graphics, Dialogs,
  StdCtrls, Buttons, ExtCtrls, ComCtrls, LCLVersion,
  TACustomSeries,
  MainUnit, Globals, ReportFrameUnit, BasicStatsReportAndChartFormUnit;

type

  { TABCNestedForm }

  TABCNestedForm = class(TBasicStatsReportAndChartForm)
    ChartStyles: TChartStyles;
    ShowPlotsChk: TCheckBox;
    Plot3DChk: TCheckBox;
    FactorCEdit: TEdit;
    FactorAEdit: TEdit;
    AInBtn: TBitBtn;
    AOutBtn: TBitBtn;
    FactorBEdit: TEdit;
    BInBtn: TBitBtn;
    BOutBtn: TBitBtn;
    DepEdit: TEdit;
    DepInBtn: TBitBtn;
    CInBtn: TBitBtn;
    DepOutBtn: TBitBtn;
    COutBtn: TBitBtn;
    PlotOptionsGroup: TGroupBox;
    Label1: TLabel;
    Label2: TLabel;
    Label3: TLabel;
    Label4: TLabel;
    Label5: TLabel;
    Memo1: TLabel;
    Panel1: TPanel;
    MeansPage: TTabSheet;
    VarList: TListBox;
    procedure AInBtnClick(Sender: TObject);
    procedure AOutBtnClick(Sender: TObject);
    procedure BInBtnClick(Sender: TObject);
    procedure BOutBtnClick(Sender: TObject);
    procedure CInBtnClick(Sender: TObject);
    procedure COutBtnClick(Sender: TObject);
    procedure DepInBtnClick(Sender: TObject);
    procedure DepOutBtnClick(Sender: TObject);
    procedure Plot3DChkChange(Sender: TObject);
    procedure ShowPlotsChkChange(Sender: TObject);
    procedure VarListDblClick(Sender: TObject);
    procedure VarListSelectionChange(Sender: TObject; {%H-}User: boolean);

  private
    CellCount: IntDyneCube;
    ASS, BSS, CSS, ASumSqr, BSumSqr, CSumSqr, ASDs, BSDs, CSDs : DblDyneVec;
    ACSS,ACSumSqr, ACSDs, ABSS, ABSumSqr, ABSDs : DblDyneMat;
    ACount, BCount, CCount : IntDyneVec;
    ACCount, ABCount : IntDyneMat;
    CellSDs, SS, SumSqr, CellMeans : DblDyneCube;
    MinA, MaxA, NoALevels: Integer;
    MinB, MaxB, NoBLevels: Integer;
    MinC, MaxC, NoCLevels: integer;
    SSTot, SumSqrTot, TotMean, MSTot, SSA, MSA, SSB, MSB, SSW, MSW : double;
    SSC, MSC, SSAC, MSAC, SSBwAC, SSAB, MSBwAC : double;
    TotN, dfA, dfBwA, dfwcell, dftotal, dfC, dfAC, dfBwAC : integer;

    AMeans, BMeans, CMeans: DblDyneVec;
    ABMeans, ACMeans: DblDyneMat;

    function GetVariables(out AValues, BValues, CValues, DepValues: DblDyneVec): Boolean;
    procedure GetMemory;
    procedure GetSums(const AValues, BValues, CValues, DepValues: DblDyneVec);
    procedure ShowMeans;
    procedure GetResults;
    procedure ShowResults;
    procedure ReleaseMemory;
    procedure TwoWayPlot;

  private
    FMeansReportFrame: TReportFrame;
    FChartCombobox: TCombobox;
    FSeries: TChartSeries;
    procedure PopulateChartCombobox;
    procedure SelectPlot(Sender: TObject);

  protected
    procedure AdjustConstraints; override;
    procedure Compute; override;
    procedure UpdateBtnStates; override;
    function Validate(out AMsg: String; out AControl: TWinControl): Boolean; override;
		
  public
    constructor Create(AOwner: TComponent); override;
    procedure Reset; override;
  end; 

var
  ABCNestedForm: TABCNestedForm;


implementation

{$R *.lfm}

uses
  Math,
  TAChartUtils, TACustomSource, TALegend, TASeries,
  Utils, MathUnit, MatrixUnit, GridProcs, ChartFrameUnit;


{ TABCNestedForm }

constructor TABCNestedForm.Create(AOwner: TComponent);
begin
  inherited;

  FMeansReportFrame := TReportFrame.Create(MeansPage);
  FMeansReportFrame.Parent := MeansPage;
  FMeansReportFrame.Align := alClient;
  InitToolbar(FMeansReportFrame.ReportToolbar, tpTop);
  MeansPage.PageIndex := 1;

  FChartFrame.Chart.Margins.Bottom := 0;
  FChartFrame.Chart.BottomAxis.AxisPen.Visible := true;
  FChartFrame.Chart.BottomAxis.ZPosition := 1;
  FChartFrame.Chart.BottomAxis.Grid.Visible := false;
  AddComboboxToToolbar(FChartFrame.ChartToolbar, 'Plots:', FChartCombobox);
  FChartCombobox.OnSelect := @SelectPlot;

  PageControl.ActivePageIndex := 0;
end;


procedure TABCNestedForm.AdjustConstraints;
begin
  inherited;

  ParamsPanel.Constraints.MinWidth := Max(
    4*CloseBtn.Width + 3*CloseBtn.BorderSpacing.Left,
    MaxValue([Label2.Width, Label3.Width, Label4.Width, Label5.Width])*2 + AInBtn.Width + VarList.BorderSpacing.Right*2
  );
  ParamsPanel.Constraints.MinHeight := COutBtn.Top + COutBtn.Height +
    ButtonBevel.Height + CloseBtn.Height + CloseBtn.BorderSpacing.Top;
end;


procedure TABCNestedForm.AInBtnClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (FactorAEdit.Text = '') then
  begin
    FactorAEdit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.AOutBtnClick(Sender: TObject);
begin
  if FactorAEdit.Text <> '' then
  begin
    VarList.Items.Add(FactorAEdit.Text);
    FactorAEdit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.BInBtnClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (FactorBEdit.Text = '') then
  begin
    FactorBEdit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.BOutBtnClick(Sender: TObject);
begin
  if FactorBEdit.Text <> '' then
  begin
    VarList.Items.Add(FactorBEdit.Text);
    FactorBEdit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.CInBtnClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (FactorCEdit.Text = '') then
  begin
    FactorCEdit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.COutBtnClick(Sender: TObject);
begin
  if FactorCEdit.Text <> '' then
  begin
    VarList.Items.Add(FactorCEdit.Text);
    FactorCEdit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.Compute;
var
  dataA: DblDyneVec = nil;
  dataB: DblDyneVec = nil;
  dataC: DblDyneVec = nil;
  dataDep: DblDyneVec = nil;
begin
  if GetVariables(dataA, dataB, dataC, dataDep) then
  begin
    GetMemory;
    GetSums(dataA, dataB, dataC, dataDep);
    ShowMeans;
    GetResults;
    ShowResults;
    TwoWayPlot;
    ReleaseMemory;
  end;
end;


procedure TABCNestedForm.DepInBtnClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (DepEdit.Text = '') then
  begin
    DepEdit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.DepOutBtnClick(Sender: TObject);
begin
  if DepEdit.Text <> '' then
  begin
    VarList.Items.Add(DepEdit.Text);
    DepEdit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TABCNestedForm.Plot3DChkChange(Sender: TObject);
begin
  if FSeries is TBarSeries then
  begin
    if Plot3dChk.Checked then
      TBarSeries(FSeries).Depth := 20
    else
      TBarSeries(FSeries).Depth := 0;
  end;
end;


procedure TABCNestedForm.ShowPlotsChkChange(Sender: TObject);
begin
  ChartPage.TabVisible := ShowPlotsChk.Checked;
  Plot3DChk.Enabled := ShowPlotsChk.Checked;
end;


procedure TABCNestedForm.PopulateChartCombobox;
var
  a, b, c: String;
  idx: Integer;
begin
  idx := FChartCombobox.ItemIndex;

  a := FactorAEdit.Text;
  b := FactorBEdit.Text;
  c := FactorCEdit.Text;

  FChartCombobox.Items.Clear;
  FChartCombobox.Items.Add(a);
  FChartCombobox.Items.Add(b);
  FChartCombobox.Items.Add(c);
  FChartCombobox.Items.Add(Format('%s x %s', [a, b]));
  FChartCombobox.Items.Add(Format('%s x %s', [a, c]));

  FChartCombobox.ItemIndex := EnsureRange(idx, 0, FChartCombobox.Items.Count-1);
end;


function TABCNestedForm.GetVariables(
  out AValues, BValues, CValues, DepValues: DblDyneVec): Boolean;
var
  ColNoSelected: IntDyneVec = nil;
  mn, mx: Double;
  msg: String;
begin
  Result := false;

  SetLength(ColNoSelected, 4);
  ColNoSelected[0] := GetVariableIndex(OS3MainFrm.DataGrid, FactorAEdit.Text);  // A
  ColNoSelected[1] := GetVariableIndex(OS3MainFrm.DataGrid, FactorBEdit.Text);  // B
  ColNoSelected[2] := GetVariableIndex(OS3MainFrm.DataGrid, FactorCEdit.Text);  // C
  ColNoSelected[3] := GetVariableindex(OS3MainFrm.DataGrid, DepEdit.Text);      // Dependent

  AValues := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[0], ColNoSelected);
  if not CheckFactorCodes(FactorAEdit.Text, AValues, msg) then
  begin
    ErrorMsg(msg);
    exit;
  end;

  BValues := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[1], ColNoSelected);
  if not CheckFactorCodes(FactorBEdit.Text, BValues, msg) then
  begin
    ErrorMsg(msg);
    exit;
  end;

  CValues := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[2], ColNoSelected);
  if not CheckFactorCodes(FactorCEdit.Text, CValues, msg) then
  begin
    ErrorMsg(msg);
    exit;
  end;

  DepValues := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[3], ColNoSelected);

  if (Length(DepValues) <> Length(AValues)) or
     (Length(DepValues) <> Length(BValues)) or
     (Length(DepValues) <> Length(CValues)) then
  begin
    ErrorMsg('All variables must contain equal amounts of cases.');
    exit;
  end;

  VecMaxMin(AValues, mx, mn);
  MaxA := round(mx);
  MinA := round(mn);

  VecMaxMin(BValues, mx, mn);
  MaxB := round(mx);
  MinB := round(mn);

  VecMaxMin(CValues, mx, mn);
  MaxC := round(mx);
  MinC := round(mn);

  NoALevels := MaxA - MinA + 1;
  NoBLevels := MaxB - MinB + 1;
  NoCLevels := MaxC - MinC + 1;

  Result := true;
end;


procedure TABCNestedForm.GetMemory;
begin
  SS := CubeCreate(NoBLevels, NoALevels, NoCLevels);
  SumSqr := CubeCreate(NoBLevels, NoALevels, NoCLevels);
  CellCount := IntCubeCreate(NoBLevels, NoALevels, NoCLevels);
  CellMeans := CubeCreate(NoBLevels, NoALevels, NoCLevels);
  CellSDs := CubeCreate(NoBLevels, NoALevels, NoCLevels);
  ASS := VecCreate(NoALevels);
  BSS := VecCreate(NoBLevels);
  CSS := VecCreate(NoCLevels);
  ASumSqr := VecCreate(NoALevels);
  BSumSqr := VecCreate(NoBLevels);
  CSumSqr := VecCreate(NoCLevels);
  AMeans := VecCreate(NoALevels);
  BMeans := VecCreate(NoBLevels);
  CMeans := VecCreate(NoCLevels);
  ACount := IntVecCreate(NoALevels);
  BCount := IntVecCreate(NoBLevels);
  CCount := IntVecCreate(NoCLevels);
  ASDs := VecCreate(NoALevels);
  BSDs := VecCreate(NoBLevels);
  CSDs := VecCreate(NoCLevels);
  ACSS := MatCreate(NoALevels, NoCLevels);
  ACSumSqr := MatCreate(NoALevels, NoCLevels);
  ACCount := IntMatCreate(NoALevels, NoCLevels);
  ACMeans := MatCreate(NoALevels, NoCLevels);
  ACSDs := MatCreate(NoALevels, NoCLevels);
  ABSS := MatCreate(NoALevels, NoBLevels);
  ABSumSqr := MatCreate(NoALevels, NoBLevels);
  ABMeans := MatCreate(NoALevels, NoBLevels);
  ABCount := IntMatCreate(NoALevels, NoBLevels);
  ABSDs := MatCreate(NoALevels,NoBLevels);
end;


procedure TABCNestedForm.GetSums(const AValues, BValues, CValues, DepValues: DblDyneVec);
VAR
  Aindex, Bindex, Cindex, i, j, k: integer;
  YValue, YValueSqr: double;
begin
  // Accumulate sums and sums of squared values
  SSTot := 0.0;
  SumSqrTot := 0.0;
  TotN := 0;
  for i := 0 to High(DepValues) do
  begin
    AIndex := round(AValues[i]) - MinA;
    BIndex := round(BValues[i]) - MinB;
    CIndex := round(CValues[i]) - MinC;
    YValue := DepValues[i];
    YValueSqr := YValue * YValue;

    SS[Bindex,Aindex,Cindex] := SS[Bindex,Aindex,Cindex] + YValueSqr;
    SumSqr[Bindex,Aindex,Cindex] := SumSqr[Bindex,Aindex,Cindex] + YValue;    // wp: why no square?
    CellCount[Bindex,Aindex,Cindex] := CellCount[Bindex,Aindex,Cindex] + 1;
    ACount[Aindex] := ACount[Aindex] + 1;
    BCount[Bindex] := BCount[Bindex] + 1;
    CCount[Cindex] := CCount[Cindex] + 1;
    ASS[Aindex] := ASS[Aindex] + YValueSqr;
    BSS[Bindex] := BSS[Bindex] + YValueSqr;
    CSS[Cindex] := CSS[Cindex] + YValueSqr;
    ASumSqr[Aindex] := ASumSqr[Aindex] + YValue;
    BSumSqr[Bindex] := BSumSqr[Bindex] + YValue;
    CSumSqr[Cindex] := CSumSqr[Cindex] + YValue;
    ACSS[Aindex,Cindex] := ACSS[Aindex,Cindex] + YValueSqr;
    ACSumSqr[Aindex,Cindex] := ACSumSqr[Aindex,Cindex] + YValue;
    ACCount[Aindex,Cindex] := ACCount[Aindex,Cindex] + 1;
    ABSS[Aindex,Bindex] := ABSS[Aindex,Bindex] + YValueSqr;
    ABSumSqr[Aindex,Bindex] := ABSumSqr[Aindex,Bindex] + YValue;
    ABCount[Aindex,Bindex] := ABCount[Aindex,Bindex] + 1;
    SSTot := SSTot + YValueSqr;
    SumSqrTot := SumSqrTot + YValue;
    TotN := TotN + 1;
  end;

  // Get cell means and marginal means plus square of sums
   for i := 0 to NoBLevels-1 do
   begin
     for j := 0 to NoALevels-1 do
     begin
       for k := 0 to NoCLevels-1 do
       begin
         if CellCount[i,j,k] > 0 then
         begin
           CellMeans[i,j,k] := SumSqr[i,j,k] / CellCount[i,j,k];
           SumSqr[i,j,k] := SumSqr[i,j,k] * SumSqr[i,j,k];
           CellSDs[i,j,k] := SS[i,j,k] - (SumSqr[i,j,k] / CellCount[i,j,k]);
           CellSDs[i,j,k] := CellSDs[i,j,k] / (CellCount[i,j,k] - 1);
           CellSDs[i,j,k] := sqrt(CellSDs[i,j,k]);
         end;
       end;
     end;
   end;

   for i := 0 to NoBLevels-1 do
   begin
     if BCount[i] > 0 then
     begin
       BMeans[i] := BSumSqr[i] / BCount[i];
       BSumSqr[i] := BSumSqr[i] * BSumSqr[i];
       BSDs[i] := BSS[i] - (BSumSqr[i] / BCount[i]);
       BSDs[i] := BSDs[i] / (BCount[i] - 1);
       BSDs[i] := sqrt(BSDs[i]);
     end;
   end;

   for i := 0 to NoALevels-1 do
   begin
     AMeans[i] := ASumSqr[i] / ACount[i];
     ASumSqr[i] := ASumSqr[i] * ASumSqr[i];
     ASDs[i] := ASS[i] - (ASumSqr[i] / ACount[i]);
     ASDs[i] := ASDs[i] / (ACount[i] - 1);
     ASDs[i] := Sqrt(ASDs[i]);
   end;

   for i := 0 to NoCLevels-1 do
   begin
     CMeans[i] := CSumSqr[i] / CCount[i];
     CSumSqr[i] := CSumSqr[i] * CSumSqr[i];
     CSDs[i] := CSS[i] - (CSumSqr[i] / CCount[i]);
     CSDs[i] := CSDs[i] / (CCount[i] - 1);
     CSDs[i] := sqrt(CSDs[i]);
   end;

   for i := 0 to NoALevels-1 do
   begin
     for k := 0 to NoCLevels-1 do
     begin
       ACMeans[i,k] := ACMeans[i,k] / ACCount[i,k];
       ACSumSqr[i,k] := ACSumSqr[i,k] * ACSumSqr[i,k];
       ACSDs[i,k] := ACSS[i,k] - (ACSumSqr[i,k] / ACCount[i,k]);
       ACSDs[i,k] := ACSDs[i,k] / (ACCount[i,k] - 1);
       ACSDs[i,k] := sqrt(ACSDs[i,k]);
     end;
   end;

   for i := 0 to NoALevels-1 do
   begin
   for j := 0 to NoBLevels-1 do
   begin
     if ABCount[i,j] > 0 then
     begin
       ABMeans[i,j] := ABSumSqr[i,j] / ABCount[i,j];
       ABSumSqr[i,j] := ABSumSqr[i,j] * ABSumSqr[i,j];
       ABSDs[i,j] := ABSS[i,j] - (ABSumSqr[i,j] / ABCount[i,j]);
       ABSDs[i,j] := ABSDs[i,j] / (ABCount[i,j] - 1);
       ABSDs[i,j] := sqrt(ABSDs[i,j]);
     end;
   end;
  end;

  TotMean := SumSqrTot / TotN;
  SumSqrTot := SumSqrTot * SumSqrTot;
end;


procedure TABCNestedForm.ShowMeans;
var
  lReport: TStrings;
  i, j, k : integer;
begin
  lReport := TStringList.Create;
  try
    lReport.Add('Nested ANOVA by Bill Miller');
    lReport.Add('');
    lReport.Add('File analyzed: %s', [OS3MainFrm.FileNameEdit.Text]);
    lReport.Add('Factor A:      %s', [FactorAEdit.Text]);
    lReport.Add('Factor B:      %s', [FactorBEdit.Text]);
    lReport.Add('Factor C:      %s', [FactorCEdit.Text]);
    lReport.Add('');

    lReport.Add('CELL MEANS');
    lReport.Add('-----------------------------------------------------');
    lReport.Add('A LEVEL   B LEVEL   C LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   -------   -------   ----------   ----------');
    for i := 0 to NoALevels-1 do
      for j := 0 to NoBLevels-1 do
        for k := 0 to NoCLevels-1 do
          if CellCount[j,i,k] > 0 then
            lReport.Add('%5d     %5d     %5d     %10.3f   %10.3f', [i+MinA, j+MinB, k+MinC, CellMeans[j,i,k], CellSDs[j,i,k]]);
    lReport.Add('-----------------------------------------------------');
    lReport.Add('');

    lReport.Add('A MARGIN MEANS');
    lReport.Add('---------------------------------');
    lReport.Add('A LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   ----------   ----------');
    for i := 0 to NoALevels-1 do
      lReport.Add('%5d     %10.3f   %10.3f', [i+MinA, AMeans[i], ASDs[i]]);
    lReport.Add('---------------------------------');
    lReport.Add('');

    lReport.Add('B MARGIN MEANS');
    lReport.Add('---------------------------------');
    lReport.Add('B LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   ----------   ----------');
    for i := 0 to NoBLevels-1 do
      if BCount[i] > 0 then
        lReport.Add('%5d     %10.3f   %10.3f', [i+MinB, BMeans[i], BSDs[i]]);
    lReport.Add('---------------------------------');
    lReport.Add('');

    lReport.Add('C MARGIN MEANS');
    lReport.Add('---------------------------------');
    lReport.Add('C LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   ----------   ----------');
    for i := 0 to NoCLevels-1 do
      if CCount[i] > 0 then
        lReport.Add('%5d     %10.3f   %10.3f', [i+MinC, CMeans[i], CSDs[i]]);
    lReport.Add('---------------------------------');
    lReport.Add('');

    lReport.Add('AB MARGIN MEANS');
    lReport.Add('-------------------------------------------');
    lReport.Add('A LEVEL   B LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   -------   ----------   ----------');
    for i := 0 to NoALevels-1 do
      for j := 0 to NoBLevels-1 do
        if ABCount[i,j] > 0 then
          lReport.Add('%5d     %5d     %10.3f   %10.3f', [i+MinA, j+MinB, ABMeans[i,j], ABSDs[i,j]]);
    lReport.Add('-------------------------------------------');
    lReport.Add('');

    lReport.Add('AC MARGIN MEANS');
    lReport.Add('-------------------------------------------');
    lReport.Add('A LEVEL   C LEVEL      MEAN       STD.DEV. ');
    lReport.Add('-------   -------   ----------   ----------');
    for i := 0 to NoALevels-1 do
      for j := 0 to NoCLevels-1 do
        if ACCount[i,j] > 0 then
          lReport.Add('%5d     %5d     %10.3f   %10.3f',[i+MinA, j+MinC, ACMeans[i,j], ACSDs[i,j]]);
    lReport.Add('-------------------------------------------');
    lReport.Add('');

    lReport.Add('GRAND MEAN: %10.3f', [TotMean]);
    lReport.Add('');

    FMeansReportFrame.DisplayReport(lReport);

  finally
    lReport.Free;
  end;
end;


procedure TABCNestedForm.GetResults;
VAR
  temp, temp2, temp3, temp4, constant : double;
  NoBLevelsInA, BLevCount, i, j, k, celln : integer;
begin
  celln := 0;
  for i := 0 to NoALevels-1 do
      begin
         for j := 0 to NoBLevels-1 do
             begin
               for k := 0 to NoCLevels-1 do
                   begin
                        if CellCount[j,i,k] > celln then celln := CellCount[j,i,k];
                   end;
             end;
      end;

  // Assume all cells have same n size
  // Get number of levels in A
  BLevCount := 0;
  for i := 0 to NoALevels-1 do
      begin
         NoBLevelsInA := 0;
         for j := 0 to NoBLevels-1 do
             begin
                if CellCount[j,i,0] > 0 then NoBLevelsInA := NoBLevelsInA + 1;
             end;
         if NoBLevelsInA > BLevCount then BLevCount := NoBLevelsInA;
      end;
  dfA := NoALevels - 1;
  dfBwA := NoALevels * (BLevCount - 1);
  dfC := NoCLevels - 1;
  dfAC := (NoALevels-1) * (NoCLevels-1);
  dfBwAC := NoALevels * (BLevCount-1) * (NoCLevels -1);
  dfwcell := NoALevels * BLevCount * NoCLevels * (celln - 1);
  dftotal := TotN - 1;

  constant := SumSqrTot / TotN;
  SSTot := SSTot - constant;
  MSTot := SSTot / dftotal;

  // Get A Effects
  SSA := 0.0;
  for i := 0 to NoALevels-1 do SSA := SSA + (ASumSqr[i] / ACount[i]);
  temp := SSA;
  SSA := SSA - constant;
  MSA := SSA / dfA;

  // Get C Effects
  SSC := 0.0;
  for i := 0 to NoCLevels-1 do SSC := SSC + (CSumSqr[i] / CCount[i]);
  temp2 := SSC;
  SSC := SSC - constant;
  MSC := SSC / dfC;

  // Get B within A
  SSB := 0.0;
  for i := 0 to NoALevels - 1 do
      begin
         for j := 0 to NoBLevels-1 do
             begin
                if ABCount[i,j] > 0 then SSB := SSB + (ABSumSqr[i,j] / ABCount[i,j]);
             end;
      end;
  temp3 := SSB;
  SSB := SSB - temp;
  MSB := SSB / dfBwA;

  // Get AC interaction
  SSAC := 0.0;
  for i := 0 to NoALevels-1 do
      begin
         for j := 0 to NoCLevels-1 do SSAC := SSAC + ACSumSqr[i,j] / ACCount[i,j]
      end;
  temp4 := SSAC;
  SSAC := SSAC - temp - temp2 + constant;
  MSAC := SSAC / dfAC;

  // get B within A x C interaction
  SSBwAC := 0.0;
  for i := 0 to NoALevels-1 do
      begin
         for j := 0 to NoBLevels-1 do
             begin
                for k := 0 to NoCLevels-1 do
                    begin
                       if CellCount[j,i,k] > 0 then SSBwAC := SSBwAC +
                         (SumSqr[j,i,k] / CellCount[j,i,k]);
                    end;
             end;
      end;
  SSBwAC := SSBwAC - temp3 - temp4 + temp;
  MSBwAC := SSBwAC / dfBwAC;

  SSW := SSTot - SSA - SSB - SSAB - SSAC - SSBwAC;
  MSW := SSW / dfwcell;
end;


procedure TABCNestedForm.ShowResults;
var
  lReport: TStrings;
  F, PF : double;
begin
  lReport := TStringList.Create;
  try
    lReport.Add('Nested ANOVA by Bill Miller');
    lReport.Add('');
    lReport.Add('File analyzed: %s', [OS3MainFrm.FileNameEdit.Text]);
    lReport.Add('Factor A:      %s', [FactorAEdit.Text]);
    lReport.Add('Factor B:      %s', [FactorBEdit.Text]);
    lReport.Add('Factor C:      %s', [FactorCEdit.Text]);
    lReport.Add('');
    lReport.Add('ANOVA TABLE');
    lReport.Add('-------------------------------------------------------------');
    lReport.Add('SOURCE     D.F.      SS          MS          F        PROB.  ');
    lReport.Add('---------  ----  ----------  ----------  ---------  ---------');

    F := MSA / MSW;
    PF := ProbF(F,dfA,dfwcell);
    lReport.Add('A          %4d  %10.3f  %10.3f  %9.3f  %9.3f', [dfA, SSA, MSA, F, PF]);

    F := MSB / MSW;
    PF := ProbF(F,dfBwA,dfwcell);
    lReport.Add('B(A)       %4d  %10.3f  %10.3f  %9.3f  %9.3f', [dfBwA, SSB, MSB, F, PF]);

    F := MSC / MSW;
    PF := ProbF(F,dfC,dfwcell);
    lReport.Add('C          %4d  %10.3f  %10.3f  %9.3f  %9.3f', [dfC, SSC, MSC, F, PF]);

    F := MSAC / MSW;
    PF := ProbF(F,dfAC,dfwcell);
    lReport.Add('AxC        %4d  %10.3f  %10.3f  %9.3f  %9.3f', [dfAC, SSAC, MSAC, F, PF]);

    F := MSBwAC / MSW;
    PF := ProbF(F,dfBwAC,dfwcell);
    lReport.Add('B(A)xC     %4d  %10.3f  %10.3f  %9.3f  %9.3f', [dfBwAC, SSBwAC, MSBwAC, F, PF]);

    lReport.Add('w.cells    %4d  %10.3f  %10.3f',               [dfwcell, SSW, MSW]);
    lReport.Add('Total      %4d  %10.3f',                       [dftotal, SSTot]);
    lReport.Add('-------------------------------------------------------------');

    FReportFrame.DisplayReport(lReport);

  finally
    lReport.Free;
  end;
end;


procedure TABCNestedForm.ReleaseMemory;
begin
  ABSDs := nil;
  ABCount := nil;
//  ABMeans := nil;
  ABSumSqr := nil;
  ABSS := nil;
  ACSDs := nil;
//  ACMeans := nil;
  ACCount := nil;
  ACSumSqr := nil;
  ACSS := nil;
  CSDs := nil;
  BSDs := nil;
  ASDs := nil;
  CCount := nil;
  BCount := nil;
  ACount := nil;
//  CMeans := nil;
//  BMeans := nil;
//  AMeans := nil;
  CSumSqr := nil;
  BSumSqr := nil;
  ASumSqr := nil;
  CSS := nil;
  BSS := nil;
  ASS := nil;
  CellSDs := nil;
  CellMeans := nil;
  CellCount := nil;
  SumSqr := nil;
  SS := nil;
end;


procedure TABCNestedForm.Reset;
var
  i: integer;
begin
  inherited;

  if FMeansReportFrame <> nil then
    FMeansReportFrame.Clear;
  if FChartCombobox <> nil then
    FChartCombobox.Items.Clear;

  VarList.Items.Clear;
  for i := 1 to NoVariables do
    VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);

  FactorAEdit.Clear;
  FactorBEdit.Clear;
  FactorCEdit.Clear;
  DepEdit.Clear;

  UpdateBtnStates;
end;


procedure TABCNestedForm.SelectPlot(Sender: TObject);
var
  i, j, k, idx: Integer;
  item: PChartDataItem;
begin
  ChartStyles.Styles.Clear;
  FSeries.Clear;

  case FChartComboBox.ItemIndex of
    0: begin  // Plot means vs factor A
         FSeries.ListSource.YCount := 1;
         for i := 0 to NoALevels-1 do
           FSeries.AddXY(MinA + i, AMeans[i], IntToStr(MinA + i));
         FChartFrame.SetXTitle(FactorAEdit.Text + ' codes');
         FChartFrame.SetTitle('Factor ' + FactorAEdit.Text);
       end;
    1: begin // Plot means vs factor B
         FSeries.ListSource.YCount := 1;
         for i := 0 to NoBLevels-1 do
           FSeries.AddXY(MinB + i, BMeans[i], IntToStr(MinB + i));
         FChartFrame.SetXTitle(FactorBEdit.Text + ' codes');
         FChartFrame.SetTitle('Factor ' + FactorBEdit.Text);
       end;
    2: begin  // Plot means vs factor C
         FSeries.ListSource.YCount := 1;
         for i := 0 to NoCLevels-1 do
           FSeries.AddXY(MinC + i, CMeans[i], IntToStr(MinC + i));
         FChartFrame.SetXTitle(FactorCEdit.Text + ' codes');
         FChartFrame.SetTitle('Factor ' + FactorCEdit.Text);
       end;
    3: begin  // Plot interaction AxB
         FSeries.ListSource.YCount := NoALevels;
         for j := 0 to NoBLevels-1 do
         begin
           idx := FSeries.AddXY(MinB + j, NaN, IntToStr(MinB + j));
           item := FSeries.Source.Item[idx];
           for i := 0 to NoALevels-1 do
             item^.SetY(i, ABMeans[i, j]);
         end;
         FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"', [
           FactorAEdit.Text, FactorBEdit.Text]));
         FChartFrame.SetXTitle(FactorBEdit.Text + ' codes');
         for i := 0 to NoALevels-1 do
           with TChartStyle(ChartStyles.Styles.Add) do
           begin
             Brush.Color := DATA_COLORS[i mod Length(DATA_COLORS)];
             UseBrush := true;
             Text := Format('%s = %s', [FactorAEdit.Text, IntToStr(MinA+i)]);
           end;
       end;
    4: begin  // Plot interaction AxC
         FSeries.ListSource.YCount := NoALevels;
         for k := 0 to NoCLevels-1 do
         begin
            idx := FSeries.AddXY(MinC + k, NaN, IntToStr(MinC + k));
            item := FSeries.Source.Item[idx];
            for i := 0 to NoALevels-1 do
              item^.SetY(i, ACMeans[i, k]);
         end;
         FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"', [
           FactorAEdit.Text, FactorCEdit.Text]));
         FChartFrame.SetXTitle(FactorCEdit.Text + ' codes');
         for i := 0 to NoALevels-1 do
           with TChartStyle(ChartStyles.Styles.Add) do
           begin
             Brush.Color := DATA_COLORS[i mod Length(DATA_COLORS)];
             UseBrush := true;
             Text := Format('%s = %s', [FactorAEdit.Text, IntToStr(MinA+i)]);
           end;
       end;
  end;

  if (FSeries is TBarSeries) then
  begin
    if ChartStyles.Styles.Count > 0 then
    begin
      TBarSeries(FSeries).Styles := ChartStyles;
      FSeries.Legend.Multiplicity := lmStyle;
    end else
      FSeries.Legend.Multiplicity := lmSingle;
  end;

  FChartFrame.Chart.BottomAxis.Marks.Source := FSeries.Source;
  FChartFrame.Chart.BottomAxis.Marks.Style := smsLabel;
  FChartFrame.Chart.Legend.Visible := FSeries.Source.YCount > 1;

  FChartFrame.UpdateBtnStates;

end;


procedure TABCNestedForm.TwoWayPlot;
begin
  if not ShowPlotsChk.Checked then
  begin
    ChartPage.TabVisible := false;
    exit;
  end;
  FChartFrame.Clear;   // this destroys the series
  FChartFrame.SetYTitle('Mean');

  FSeries := FChartFrame.PlotXY(ptBars, nil, nil, nil, nil, '', DATA_Colors[0]);
  with TBarSeries(FSeries) do
  begin
    Stacked := false;
    {$IF LCL_FullVersion >= 2010000}
    DepthBrightnessDelta := -30;
    {$IFEND}
  end;
  if Plot3DChk.Checked then
    FSeries.Depth := 20;

  FChartCombobox.Parent.Left := 0;
  PopulateChartCombobox;
  SelectPlot(nil);

  ChartPage.TabVisible := true;
end;


procedure TABCNestedForm.UpdateBtnStates;
begin
  inherited;

  if FMeansReportFrame <> nil then
    FMeansReportFrame.UpdateBtnStates;

  AInBtn.Enabled := (VarList.ItemIndex > -1) and (FactorAEdit.Text = '');
  BInBtn.Enabled := (VarList.ItemIndex > -1) and (FactorBEdit.Text = '');
  CInBtn.Enabled := (VarList.ItemIndex > -1) and (FactorCEdit.Text = '');
  DepInBtn.Enabled := (VarList.ItemIndex > -1) and (DepEdit.Text = '');
  AOutBtn.Enabled := (FactorAEdit.Text <> '');
  BOutBtn.Enabled := (FactorBEdit.Text <> '');
  COutBtn.Enabled := (FactorCEdit.Text <> '');
  DepOutBtn.Enabled := (DepEdit.Text <> '');
end;


function TABCNestedForm.Validate(out AMsg: String;
  out AControl: TWinControl): Boolean;
begin
  Result := false;

  if DepEdit.Text = '' then
  begin
    AMsg := 'Dependent variable not specified.';
    AControl := VarList;
    exit;
  end;

  if FactorAEdit.Text = '' then
  begin
    AMsg := 'Factor A variable not specified.';
    AControl := VarList;
    exit;
  end;

  if FactorBEdit.Text = '' then
  begin
    AMsg := 'Factor B variable not specified.';
    AControl := VarList;
    exit;
  end;

  if FactorCEdit.Text = '' then
  begin
    AMsg := 'Factor C variable not specified.';
    AControl := VarList;
    exit;
  end;

  Result := true;
end;


procedure TABCNestedForm.VarListDblClick(Sender: TObject);
var
  index: Integer;
  s: String;
begin
  index := VarList.ItemIndex;
  if index > -1 then begin
    s := VarList.Items[index];
    if DepEdit.Text = '' then
      DepEdit.Text := s
    else if FactorAEdit.Text = '' then
      FactorAEdit.Text := s
    else if FactorBEdit.Text = '' then
      FactorBEdit.Text := s
    else if FactorCEdit.Text = '' then
      FactorCEdit.Text := s;
    VarList.Items.Delete(index);
    UpdateBtnStates;
  end;
end;


procedure TABCNestedForm.VarListSelectionChange(Sender: TObject; User: boolean);
begin
  UpdateBtnStates;
end;


end.