lazarus-ccr/applications/lazstats/source/forms/analysis/comparisons/onecaseanovaunit.pas

unit OneCaseANOVAUnit;

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

interface

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

type

  { TOneCaseAnovaForm }

  TOneCaseAnovaForm = class(TBasicStatsReportAndChartForm)
    ShowPlotsChk: TCheckBox;
    Plot3DChk: TCheckBox;
    DepIn: TBitBtn;
    DepOut: TBitBtn;
    DepVarEdit: TEdit;
    Fact1In: TBitBtn;
    Fact1Out: TBitBtn;
    Fact2In: TBitBtn;
    Fact2Out: TBitBtn;
    Fact3In: TBitBtn;
    Fact3Out: TBitBtn;
    Factor1Edit: TEdit;
    Factor2Edit: TEdit;
    Factor3Edit: TEdit;
    PlotGroup: TGroupBox;
    PostHocGroup: TGroupBox;
    InteractChk: TCheckBox;
    Label1: TLabel;
    Label3: TLabel;
    Label4: TLabel;
    NewmanKeulsChk: TCheckBox;
    OverallAlphaEdit: TEdit;
    PostAlphaEdit: TEdit;
    ScheffeChk: TCheckBox;
    StaticText1: TStaticText;
    StaticText2: TStaticText;
    StaticText3: TStaticText;
    StaticText4: TStaticText;
    PostHocPage: TTabSheet;
    TukeyBChk: TCheckBox;
    TukeyHSDChk: TCheckBox;
    TukeyKramerChk: TCheckBox;
    VarList: TListBox;
    procedure DepInClick(Sender: TObject);
    procedure DepOutClick(Sender: TObject);
    procedure Fact1InClick(Sender: TObject);
    procedure Fact1OutClick(Sender: TObject);
    procedure Fact2InClick(Sender: TObject);
    procedure Fact2OutClick(Sender: TObject);
    procedure Fact3InClick(Sender: TObject);
    procedure Fact3OutClick(Sender: TObject);
    procedure Plot3DChkChange(Sender: TObject);
    procedure ShowPlotsChkChange(Sender: TObject);
    procedure VarListDblClick(Sender: TObject);
    procedure VarListSelectionChange(Sender: TObject; {%H-}User: boolean);

  private
    { private declarations }
    N: integer;
    ColNoSelected: IntDyneVec;
    Nf1cells, Nf2cells, Nf3cells: Integer;
    minf1, maxf1, minf2, maxf2, minf3, maxf3, nofactors: integer;
    NoGrpsA, NoGrpsB, NoGrpsC: integer;
    SSDep, SSErr, SSF1, SSF2, SSF3, SSF1F2, SSF1F3, SSF2F3: double;
    MSDep, MSErr, MSF1, MSF2, MSF3, MSF1F2, MSF1F3, MSF2F3: double;
    DFTot, DFErr, DFF1, DFF2, DFF3, DFF1F2, DFF1F3, DFF2F3: double;
    Omega, OmegaF1, OmegaF2, OmegaF3, OmegaF1F2: double;
    OmegaF1F3, OmegaF2F3: double;
    FF1, FF2, FF1F2, ProbF1, ProbF2, ProbF3, ProbF1F2, ProbF1F3: double;
    FF3, FF2F3, FF1F3, ProbF2F3: double;
    MeanDep: Double;
    SSNonAdd, SSBalance,MSNonAdd, MSBalance, GrandMean, DFBalance: double;
    FNonAdd, ProbNonAdd: double;
    counts : IntDyneMat;      // matrix for 2-way containing cell sizes
    sums : DblDyneMat;        // matrix for 2-way containing cell sums
    vars : DblDyneMat;        // matrix for 2-way containing sums of squares
    RowSums : DblDyneVec;     // 2 way row sums
    ColSums : DblDyneVec;     // 2 way col sums
    RowCount : IntDyneVec;    // 2 way row count
    ColCount : IntDyneVec;    // 2 way col count
    SlcSums : DblDyneVec;     // 3 way slice sums
    SlcCount : IntDyneVec;    // 3 way slice counts
//    DepValues: DblDyneVec;
    wsum, wx2: DblDyneCube;
    ncnt : IntDyneCube;
    equal_grp : boolean;   // check for equal groups for post-hoc tests

    procedure Init;
    procedure GetLevels(out DepValues, F1Values, F2Values, F3Values: DblDyneVec);
    procedure Init2Way;
    function Calc2Way(const DepValues, F1Values, F2Values: DblDyneVec): Boolean;
    procedure TwoWayTable;
    procedure TwoWayContrasts;
    procedure TwoWayPlot;
    procedure Init3Way;
    function Calc3Way(const DepValues, F1Values, F2Values, F3Values: DblDyneVec): Boolean;
    procedure ThreeWayTable;
    procedure ThreeWayContrasts;
    procedure ThreeWayPlot;

  private
    FPosthocReportFrame: TReportFrame;
    FSeries: TChartSeries;
    FChartCombobox: TCombobox;
    FStyles: TChartStyles;
    procedure GetDataIndices(out ix, iy, iz: Integer);
    procedure PopulateChartCombobox(ThreeWay: Boolean);
    procedure SelectTwoWayPlot(Sender: TObject);
    procedure SelectThreeWayPlot(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
  OneCaseAnovaForm: TOneCaseAnovaForm;

implementation

{$R *.lfm}

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

{ TOneCaseAnovaForm }

constructor TOneCaseAnovaForm.Create(AOwner: TComponent);
var
  panel: TPanel;
  lbl: TLabel;
begin
  inherited;

  OverallAlphaEdit.Text := FormatFloat('0.00', DEFAULT_ALPHA_LEVEL);
  PostAlphaEdit.Text := FormatFloat('0.00', DEFAULT_ALPHA_LEVEL);

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

  FStyles := TChartStyles.Create(FChartFrame);

  panel := TPanel.Create(FChartFrame.ChartToolbar);
  lbl := TLabel.Create(panel);
  lbl.Parent := panel;
  lbl.Caption := 'Plots:';
  FChartCombobox := TCombobox.Create(panel);
  FChartCombobox.Parent := panel;
  FChartCombobox.Style := csDropdownList;
  FChartCombobox.DropdownCount := 24;
  FChartCombobox.Items.Clear;
  FChartCombobox.Constraints.MinWidth := 300;
  lbl.AnchorSideLeft.Side := asrTop;
  lbl.AnchorSideLeft.Control := panel;
  lbl.AnchorSideTop.Side := asrCenter;
  lbl.AnchorSideTop.Control := FChartCombobox;
  FChartCombobox.AnchorSideLeft.Control := lbl;
  FChartCombobox.AnchorSideLeft.Side := asrBottom;
  FChartCombobox.BorderSpacing.Left := 6;
  FChartCombobox.BorderSpacing.Around := 2;
  panel.Parent := FChartFrame.ChartToolbar;
  panel.AutoSize := true;
  panel.BevelInner := bvNone;
  panel.BevelOuter := bvNone;

  FChartFrame.Chart.Margins.Bottom := 0;

  PageControl.ActivePageIndex := 0;
end;


procedure TOneCaseAnovaForm.AdjustConstraints;
begin
  inherited;

  ParamsPanel.Constraints.MinHeight := InteractChk.Top + InteractChk.Height +
    PostHocGroup.BorderSpacing.Top + PostHocGroup.Height + PostHocGroup.BorderSpacing.Bottom +
    PostAlphaEdit.Height + ButtonBevel.Height + CloseBtn.BorderSpacing.Top + CloseBtn.Height;
  ParamsPanel.Constraints.MinWidth := Max(
    4*CloseBtn.Width + 3*CloseBtn.BorderSpacing.Left,
    PostHocGroup.Width +  PlotGroup.BorderSpacing.Left + PlotGroup.Width
  );

  FChartFrame.ChartToolbar.ButtonHeight := Max(
    FChartFrame.ChartToolbar.ButtonHeight,
    FChartCombobox.Height + 2*FChartCombobox.BorderSpacing.Around
  );
end;


procedure TOneCaseAnovaForm.Reset;
var
  i: integer;
begin
  inherited;
	
  VarList.Clear;
  DepVarEdit.Text := '';
  Factor1Edit.Text := '';
  Factor2Edit.Text := '';
  Factor3Edit.Text := '';
  //PlotMeans.Checked := false;
  ScheffeChk.Checked := false;
  TukeyHSDChk.Checked := false;
  TukeyBChk.Checked := false;
  TukeyKramerChk.Checked := false;
  NewmanKeulsChk.Checked := false;
//  BonferroniChk.Checked := false;
  for i := 1 to NoVariables do
    VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
  UpdateBtnStates;
end;


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


procedure TOneCaseAnovaForm.DepOutClick(Sender: TObject);
begin
  if DepVarEdit.Text <> '' then
  begin
    VarList.Items.Add(DepVarEdit.Text);
    DepVarEdit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact1InClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (Factor1Edit.Text = '') then
  begin
    Factor1Edit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact1OutClick(Sender: TObject);
begin
  if Factor1Edit.Text <> '' then
  begin
    VarList.Items.Add(Factor1Edit.Text);
    Factor1Edit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact2InClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (Factor2Edit.Text = '') then
  begin
    Factor2Edit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact2OutClick(Sender: TObject);
begin
  if Factor2Edit.Text <> '' then
  begin
    VarList.Items.Add(Factor2Edit.Text);
    Factor2Edit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact3InClick(Sender: TObject);
var
  index: integer;
begin
  index := VarList.ItemIndex;
  if (index > -1) and (Factor3Edit.Text = '') then
  begin
    Factor3Edit.Text := VarList.Items[index];
    VarList.Items.Delete(index);
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Fact3OutClick(Sender: TObject);
begin
  if Factor3Edit.Text <> '' then
  begin
    VarList.Items.Add(Factor3Edit.Text);
    Factor3Edit.Text := '';
  end;
  UpdateBtnStates;
end;


procedure TOneCaseAnovaForm.Compute;
var
  DepValues, F1Values, F2Values, F3Values: DblDyneVec;
begin
  // Initialize variables
  Init;

  // Get min and max of each factor code
  GetLevels(DepValues, F1Values, F2Values, F3Values);

  // Analysis
  case NoFactors of
    2 : begin    // Two-way anova
          Init2Way;
          if Calc2Way(DepValues, F1Values, F2Values) then
          begin
            TwoWayTable;
            TwoWayContrasts;
            TwoWayPlot;
          end;
        end;

    3 : begin  // Three way anova
          Init3Way;
          if Calc3Way(DepValues, F1Values, F2Values, F3Values) then
          begin
            ThreeWayTable;
            ThreeWayContrasts;
            ThreeWayPlot;
          end;
        end;
  end;
end;


procedure TOneCaseAnovaForm.Init;
begin
  if Factor3Edit.Text = '' then
    NoFactors := 2
  else
    NoFactors := 3;

  //  Get column numbers of dependent variable and factors
  SetLength(ColNoSelected, NoFactors + 1);  // +1 because DepVar is at index 0
  ColNoSelected[0] := GetVariableIndex(OS3MainFrm.DataGrid, DepVarEdit.Text);
  ColNoSelected[1] := GetVariableIndex(OS3MainFrm.DataGrid, Factor1Edit.Text);
  ColNoSelected[2] := GetVariableIndex(OS3MainFrm.DataGrid, Factor2Edit.Text);
  if Factor3Edit.Text <> '' then
    ColNoSelected[3] := GetVariableIndex(OS3MainFrm.DataGrid, Factor3Edit.Text);
end;


procedure TOneCaseAnovaForm.GetLevels(out DepValues, F1Values, F2Values, F3Values: DblDyneVec);
var
  mn, mx: Double;
begin
  DepValues := nil;
  F1Values := nil;
  F2Values := nil;
  F3Values := nil;

  // Extract dependent variable values
  DepValues := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[0], ColNoSelected);

  // Extract factor 1 values
  F1Values := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[1], ColNoSelected);
  VecMaxMin(F1Values, mx, mn);
  MaxF1 := round(mx);
  MinF1 := round(mn);
  NF1Cells := MaxF1 - MinF1 + 1;   // this can be wrong when codes are with gaps.

  // Extract factor 2 values
  F2Values := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[2], ColNoSelected);
  VecMaxMin(F2Values, mx, mn);
  MaxF2 := round(mx);
  MinF2 := round(mn);
  NF2Cells := MaxF2 - MinF2 + 1;

  // Extract factor 3 values
  if NoFactors >= 3 then
  begin
    F3Values := CollectVecValues(OS3MainFrm.DataGrid, ColNoSelected[3], ColNoSelected);
    VecMaxMin(F3Values, mx, mn);
    MaxF3 := round(mx);
    MinF3 := round(mn);
    NF3Cells := MaxF3 - MinF2 + 1;
  end else
    NF3Cells := 0;
end;


procedure TOneCaseAnovaForm.Init2Way;
begin
  RowSums := nil;
  ColSums := nil;
  RowCount := nil;
  ColCount := nil;
  counts := nil;
  sums := nil;
  vars := nil;

  SetLength(RowSums, NF1Cells);   // 2-way row sums
  SetLength(ColSums, NF2Cells);   // 2-way column sums
  SetLength(RowCount, NF1Cells);  // 2-way row counts
  SetLength(ColCount, NF2Cells);  // 2-way column counts
  SetLength(counts, NF1Cells, NF2Cells); // matrix for 2-way containing cell sizes
  SetLength(sums, NF1Cells, NF2Cells);  // matrix for 2-way containing cell sums
  SetLength(vars, NF1Cells, NF2Cells);  // matrix for 2-way containing sums of squares
end;


function TOneCaseAnovaForm.Calc2Way(const DepValues, F1Values, F2Values: DblDyneVec): Boolean;
var
  i, j, grpA, grpB: integer;
  Constant, RowsTotCnt, ColsTotCnt: double;
  X, Xsq, rowMean, colmean: Double;
begin
  // initialize matrix values
  NoGrpsA := MaxF1 - MinF1 + 1;
  NoGrpsB := MaxF2 - MinF2 + 1;

  RowSums := Default(DblDyneVec);
  ColSums := Default(DblDyneVec);
  RowCount := Default(IntDyneVec);
  ColCount := Default(IntDyneVec);
  counts := Default(IntDyneMat);
  sums := Default(DblDyneMat);
  vars := Default(DblDyneMat);

  // Get working totals
  N := 0;
  MeanDep := 0;
  SSDep := 0;
  for i := 0 to High(DepValues) do
  begin
    grpA := round(F1Values[i]) - MinF1;
    grpB := round(F2Values[i]) - MinF2;
    X := DepValues[i];
    Xsq := X * X;
    Counts[grpA, grpB] := Counts[grpA, grpB] + 1;
    sums[grpA, grpB] := sums[grpA, grpB] + X;
    vars[grpA, grpB] := vars[grpA, grpB] + Xsq;
    RowSums[grpA] := RowSums[grpA] + X;
    ColSums[grpB] := ColSums[grpB] + X;
    RowCount[grpA] := RowCount[grpA] + 1;
    ColCount[grpB] := ColCount[grpB] + 1;
    MeanDep := MeanDep + X;
    SSDep := SSDep + Xsq;
    N := N + 1;
  end;

  // Calculate results
  SSF1 := 0;
  RowsTotCnt := 0;
  for i := 0 to NoGrpsA - 1 do
  begin
    SSF1 := SSF1 + sqr(RowSums[i]) / RowCount[i];
    RowsTotCnt := RowsTotCnt + RowCount[i];
  end;

  SSF2 := 0;
  ColsTotCnt := 0;
  for j := 0 to NoGrpsB - 1 do
  begin
    SSF2 := SSF2 + sqr(ColSums[j]) / ColCount[j];
    ColsTotCnt := ColsTotCnt + ColCount[j];
  end;

  GrandMean := MeanDep / N;

  SSNonAdd := 0;
  for i := 0 to NoGrpsA - 1 do
  begin
    rowmean := RowSums[i] / RowCount[i];
    for j := 0 to NoGrpsB - 1 do
    begin
      colmean := ColSums[j] / ColCount[j];
      SSNonAdd := SSNonAdd + (colmean - GrandMean) * (rowmean - GrandMean) * sums[i,j];
    end;
  end;

  if (N > 0) then
    Constant := sqr(MeanDep) / N
  else
    Constant := 0.0;

  SSDep := SSDep - Constant;
  SSF1 := SSF1 - Constant;
  SSF2 := SSF2 - Constant;
  SSErr := SSDep - (SSF1 + SSF2);
  SSNonAdd := (SSNonAdd * SSNonAdd) / ((SSF1 * SSF2) / (NoGrpsA * NoGrpsB)  );
  MSNonAdd := SSNonAdd;
  SSBalance := SSErr - SSNonAdd;
  if ((SSF1 < 0) or (SSF2 < 0)) then
  begin
    ErrorMsg('A negative SS found. Unbalanced design? Ending analysis.');
    Result := false;
    exit;
  end;

  DFTot := N - 1;
  DFF1 := NoGrpsA - 1;
  DFF2 := NoGrpsB - 1;
  DFErr := DFF1 * DFF2;
  DFBalance := DFErr - 1;

  MSF1 := SSF1 / DFF1;
  MSF2 := SSF2 / DFF2;
  MSErr := SSErr / DFErr;
  MSDep := SSDep / DFTot;
  MSBalance := SSBalance / DFBalance;

  OmegaF1 := (SSF1 - DFF1 * MSErr) / (SSDep + MSErr);
  OmegaF2 := (SSF2 - DFF2 * MSErr) / (SSDep + MSErr);
  Omega := OmegaF1 + OmegaF2;

  MeanDep := MeanDep / N;

  // F tests for fixed effects
  FF1 := abs(MSF1 / MSErr);
  FF2 := abs(MSF2 / MSErr);
  if (MSBalance > 0.0) then
    FNonAdd := MSNonAdd / MSBalance
  else
    FNonAdd := 0.0;
  ProbF1 := ProbF(FF1,DFF1,DFErr);
  ProbF2 := ProbF(FF2,DFF2,DFErr);
  ProbNonAdd := ProbF(FNonAdd,1.0,DFBalance);
  if (ProbF1 > 1.0) then ProbF1 := 1.0;
  if (ProbF2 > 1.0) then ProbF2 := 1.0;

  // Obtain omega squared (proportion of dependent variable explained)
  if (OmegaF1 < 0.0) then OmegaF1 := 0.0;
  if (OmegaF2 < 0.0) then OmegaF2 := 0.0;
  if (Omega < 0.0) then Omega := 0.0;

  Result := True;
end;


procedure TOneCaseAnovaForm.TwoWayTable;
var
  lReport: TStrings;
  i, j, groupsize: integer;
  MinVar, MaxVar, sumvars, sumDFrecip, XBar, V, S, RowSS, ColSS: double;
  sumfreqlogvar: double;
begin
  lReport := TStringList.Create;
  try
    lReport.Add('TWO-WAY ANALYSIS OF VARIANCE');
    lReport.Add('');
    lReport.Add('Variable analyzed:           %s', [DepVarEdit.Text]);
    lReport.Add('');
    lReport.Add('Factor A (rows) variable:    %s', [Factor1Edit.Text]);
    lReport.Add('Factor B (columns) variable: %s', [Factor2Edit.Text]);
    lReport.Add('');
    lReport.Add('SOURCE         D.F.       SS            MS           F       PROB.> F  Omega Squared');
    lReport.Add('-------------- ----  ------------  ------------  ----------  --------  -------------');
    lReport.Add('Among Rows     %4.0f  %12.3f  %12.3f  %10.3f  %8.3f  %10.3f', [DFF1, SSF1, MSF1, FF1, ProbF1, OmegaF1]);
    lReport.Add('Among Columns  %4.0f  %12.3f  %12.3f  %10.3f  %8.3f  %10.3f', [DFF2, SSF2, MSF2, FF2, ProbF2, OmegaF2]);
    lReport.Add('Residual       %4.0f  %12.3f  %12.3f',                        [DFErr, SSErr, MSErr]);
    lReport.Add(' NonAdditivity %4.0f  %12.3f  %12.3f  %10.3f  %8.3f',         [1.0, SSNonAdd, MSNonAdd, FNonAdd, ProbNonAdd]);
    lReport.Add(' Balance       %4.0f  %12.3f  %12.3f',                        [DFBalance, SSBalance, MSBalance]);
    lReport.Add('Total          %4.0f  %12.3f  %12.3f',                        [DFTot, SSDep, MSDep]);
    lReport.Add('');
    lReport.Add('Omega squared for combined effects:  %10.3f',                 [Omega]);
    lReport.Add('');
    lReport.Add('DESCRIPTIVE STATISTICS');
    lReport.Add('');
    lReport.Add('GROUP Row Col.  N     MEAN   VARIANCE  STD.DEV.');
    lReport.Add('----- --- ---- ---- -------- -------- ---------');

    groupsize := ceil(counts[0,0]);
    equal_grp := true;
    MaxVar := -1e308;
    MinVar := 1e308;
    sumvars := 0.0;
    sumfreqlogvar := 0.0;
    sumDFrecip := 0.0;

    // Display cell means, variances, standard deviations
    for i := 0 to NoGrpsA - 1 do
    begin
      for j := 0 to NoGrpsB - 1 do
      begin
        if (counts[i,j] > 1) then
        begin
          XBar := sums[i, j] / counts[i, j];
          V := vars[i, j] - sqr(sums[i, j]) / counts[i, j];
          V := V / (counts[i, j] - 1.0);
          S := sqrt(V);
          sumvars  := sumvars + V;
          if (V > MaxVar) then MaxVar := V;
          if (V < MinVar) then MinVar := V;
          sumDFrecip := sumDFrecip + 1.0 / (counts[i, j] - 1.0);
          sumFreqLogVar := sumFreqLogVar + (counts[i,j] - 1.0) * ln(V);
          if (counts[i, j] <> groupsize) then equal_grp := false;
        end
        else
          XBar := sums[i, j];
        lReport.Add('Cell %3d %3d  %3d  %8.3f  %8.3f  %8.3f', [minf1+i, minf2+j, counts[i, j], XBar, V, S]);
      end;
    end;

    //Display Row means, variances, standard deviations
    for i := 0 to NoGrpsA - 1 do
    begin
      XBar := RowSums[i] / RowCount[i];
  //    OrdMeansA[i] := XBar;
      RowSS := 0.0;
      for j := 0 to NoGrpsB - 1 do RowSS := RowSS + vars[i,j];
      V := RowSS - sqr(RowSums[i]) / RowCount[i];
      V := V / (RowCount[i] - 1.0);
      S := sqrt(V);
      lReport.Add('Row  %3d      %3d  %8.3f  %8.3f  %8.3f', [minf1+i, RowCount[i], XBar, V, S]);
    end;

    //Display means, variances and standard deviations for columns
    for j := 0 to NoGrpsB - 1 do
    begin
      XBar := ColSums[j] / ColCount[j];
  //    OrdMeansB[j] := XBar;
      ColSS := 0.0;
      for i := 0 to NoGrpsA - 1 do ColSS := ColSS + vars[i,j];
      if (ColCount[j] > 0) then V := ColSS - sqr(ColSums[j]) / ColCount[j];
      if (ColCount[j] > 1) then V := V / (ColCount[j] - 1.0);
      if (V > 0.0) then S := sqrt(V);
      lReport.Add('Col  %3d      %3d  %8.3f  %8.3f  %8.3f', [minf2+j, ColCount[j], XBar, V, S]);
    end;

    lReport.Add('TOTAL         %3d  %8.3f  %8.3f  %8.3f', [N, MeanDep, MSDep, sqrt(MSDep)]);

    FReportFrame.DisplayReport(lReport);
  finally
    lReport.Free;
  end;
end;


procedure TOneCaseAnovaForm.PopulateChartCombobox(ThreeWay: Boolean);
var
  a, b, c: String;
  i, idx: Integer;
begin
  a := Factor1Edit.Text;
  b := Factor2Edit.Text;
  c := Factor3Edit.Text;

  idx := FChartCombobox.ItemIndex;

  FChartCombobox.Items.Clear;
  FChartCombobox.Items.Add(a);
  FChartCombobox.Items.Add(b);
  if ThreeWay then
    FChartCombobox.Items.Add(c);

  if InteractChk.Checked then
  begin
    if ThreeWay then
    begin
      for i := 0 to NF3Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [a, b, a, c, Round(MinF3) + i]));
      for i := 0 to NF3Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [a, b, b, c, Round(MinF3) + i]));
      for i := 0 to NF2Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [a, c, a, b, Round(MinF2) + i]));
      for i := 0 to NF2Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [a, c, c, b, Round(MinF2) + i]));
      for i := 0 to NF1Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [b, c, b, a, Round(MinF1) + i]));
      for i := 0 to NF1Cells-1 do
        FChartCombobox.Items.Add(Format('%s * %s vs %s with %s=%d', [b, c, c, a, Round(MinF1) + i]));
    end else
    begin
      FChartCombobox.Items.Add(Format('%s * %s vs %s', [a, b, a]));
      FChartCombobox.Items.Add(Format('%s * %s vs %s', [a, b, b]));
    end;
  end;

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


procedure TOneCaseAnovaForm.SelectTwoWayPlot(Sender: TObject);
var
  i, j, idx: Integer;
  item: PChartDataItem;
begin
  FStyles.Styles.Clear;
  FSeries.Clear;

  case FChartCombobox.ItemIndex of
    0: begin  // Plot means vs factor A
         FSeries.ListSource.YCount := 1;
         for i := 0 to NF1Cells-1 do
           FSeries.AddXY(minF1 + i, RowSums[i] / RowCount[i], IntToStr(MinF1 + i));
         FChartFrame.SetXTitle(Factor1Edit.Text + ' codes');
       end;
    1: begin // Plot means vs factor B
         FSeries.ListSource.YCount := 1;
         for j := 0 to NF2Cells-1 do
           FSeries.AddXY(minF2 + j, ColSums[j] / ColCount[j], IntToStr(MinF2 + j));
         FChartFrame.SetXTitle(Factor2Edit.Text + ' codes');
       end;
    2: begin  // Plot interaction A*B vs A
         FSeries.ListSource.YCount := NF2Cells;
         for i := 0 to NF1Cells-1 do
         begin
           idx := FSeries.AddXY(minF1 + i, NaN, IntToStr(minF1 + i));
           item := FSeries.Source.Item[idx];
           for j := 0 to NF2Cells-1 do
             item^.SetY(j, sums[i, j] / counts[i, j]);
         end;
         FChartFrame.SetXTitle(Factor1Edit.Text + ' codes');
         for j := 0 to NF2cells-1 do
           with TChartStyle(FStyles.Styles.Add) do
           begin
             Brush.Color := DATA_COLORS[j mod Length(DATA_COLORS)];
             UseBrush := true;
             Text := Format('%s %s', [Factor2Edit.Text, IntToStr(MinF2 + j)]);
           end;
       end;
    3: begin   // Plot means vs interaction A*B vs B
         FSeries.ListSource.YCount := NF1Cells;
         for j := 0 to NF2Cells-1 do
         begin
           idx := FSeries.AddXY(minF2 + j, NaN, IntToStr(minF2 + j));
           item := FSeries.Source.Item[idx];
           for i := 0 to NF1Cells-1 do
             item^.SetY(i, sums[i, j] / counts[i, j]);
         end;
         FChartFrame.SetXTitle(Factor2Edit.Text + ' codes');
         for i := 0 to NF1Cells-1 do
           with TChartStyle(FStyles.styles.Add) do
           begin
             Brush.Color := DATA_COLORS[i mod Length(DATA_COLORS)];
             UseBrush := True;
             Text := Format('%s %s', [Factor1Edit.Text, IntToStr(MinF1 + i)]);
           end;
       end;
  end;  // case

  if (FSeries is TBarSeries) then
  begin
    if FStyles.Styles.Count > 0 then
    begin
      TBarSeries(FSeries).Styles := FStyles;
      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 TOneCaseAnovaForm.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;
  PopulateChartCombobox(false);
  FChartCombobox.OnChange := @SelectTwoWayPlot;
  SelectTwoWayPlot(nil);

  ChartPage.TabVisible := true;
end;


procedure TOneCaseAnovaForm.Init3Way;
begin
  RowSums := nil;
  ColSums := nil;
  RowCount := nil;
  ColCount := nil;
  SlcSums := nil;
  SlcCount := nil;
  wsum := nil;
  wx2 := nil;
  ncnt := nil;

  SetLength(RowSums, NF1Cells);   // 2-way row sums
  SetLength(ColSums, NF2Cells);   // 2-way column sums
  SetLength(RowCount, NF1Cells);  // 2-way row counts
  SetLength(ColCount, NF2Cells);  // 2-way column counts
  SetLength(SlcSums, Nf3cells);   // 3 way slice sums
  SetLength(SlcCount, Nf3cells);  // 3 way slice counts
  SetLength(wsum, Nf1cells, Nf2cells, Nf3cells);
  SetLength(wx2, Nf1cells, Nf2cells, Nf3cells);
  SetLength(ncnt, Nf1cells, Nf2cells, Nf3cells);
end;


function TOneCaseAnovaForm.Calc3Way(const DepValues,
  F1Values, F2Values, F3Values: DblDyneVec): Boolean;
var
  i, j, k, grpA, grpB, grpC: integer;
  Constant, RowsTotCnt, ColsTotCnt, SlcsTotCnt, p, n2: double;
  X, Xsq, rowMean, colMean, sliceMean: Double;
begin
  // initialize matrix values
  NoGrpsA := maxf1 - minf1 + 1;
  NoGrpsB := maxf2 - minf2 + 1;
  NoGrpsC := maxf3 - minf3 + 1;

  // Get working totals
  N := 0;
  MeanDep := 0;
  SSDep := 0;
  for i := 0 to High(DepValues) do
  begin
    grpA := round(F1Values[i]) - MinF1;
    grpB := round(F2Values[i]) - MinF2;
    grpC := round(F3Values[i]) - MinF3;
    X := DepValues[i];
    Xsq := X * X;
    ncnt[grpA, grpB, grpC] := ncnt[grpA, grpB, grpC] + 1;
    wsum[grpA, grpB, grpC] := wsum[grpA, grpB, grpC] + X;
    wx2[grpA, grpB, grpC] := wx2[grpA, grpB, grpC] + Xsq;
    RowSums[grpA] := RowSums[grpA] + X;
    ColSums[grpB] := ColSums[grpB] + X;
    SlcSums[grpC] := SlcSums[grpC] + X;
    RowCount[grpA] := RowCount[grpA] + 1;
    Colcount[grpB] := ColCount[grpB] + 1;
    SlcCount[grpC] := SlcCount[grpC] + 1;
    MeanDep := MeanDep + X;
    SSDep := SSDep + Xsq;
    N := N + 1;
  end;

  // Calculate results
  Constant := sqr(MeanDep) / N;
  GrandMean := MeanDep /  N;

  // Get SS for rows
  SSF1 := 0;
  RowsTotCnt := 0;
  for i := 0 to NoGrpsA - 1 do
  begin
    SSF1 := SSF1 + sqr(RowSums[i]) / RowCount[i];
    RowsTotCnt := RowsTotCnt + RowCount[i];
  end;
  SSF1 := SSF1 - Constant;

  // Get SS for columns
  SSF2 := 0;
  ColsTotCnt := 0;
  for j := 0 to NoGrpsB - 1 do
  begin
    SSF2 := SSF2 + sqr(ColSums[j]) / ColCount[j];
    ColsTotCnt := ColsTotCnt + ColCount[j];
  end;
  SSF2 := SSF2 - Constant;

  // Get SS for slices
  SSF3 := 0;
  SlcsTotCnt := 0;
  for k := 0 to NoGrpsC - 1 do
  begin
    SSF3 := SSF3 + SlcSums[k] * SlcSums[k] / SlcCount[k];
    SlcsTotCnt := SlcsTotCnt + SlcCount[k];
  end;
  SSF3 := SSF3 - Constant;

  // Get ss for row x col interaction
  p := 0.0;
  n2 := 0.0;
  SSF1F2 := 0;
  for i := 0 to NoGrpsA - 1 do
  begin
    for j := 0 to NoGrpsB - 1 do
    begin
      for k := 0 to NoGrpsC - 1 do
      begin
        p := p + wsum[i,j,k];
        n2 := n2 + ncnt[i,j,k];
      end;
      SSF1F2 := SSF1F2 + p * p / n2;
    end;
  end;
  SSF1F2 := SSF1F2 - SSF1 - SSF2 - Constant;

  // Get ss for row x slice interaction
  SSF1F3 := 0;
  p := 0.0;
  n2 := 0.0;
  for i := 0 to NoGrpsA - 1 do
  begin
    for k := 0 to NoGrpsC - 1 do
    begin
      for j := 0 to NoGrpsB - 1 do
      begin
        p := p + wsum[i,j,k];
        n2 := n2 + ncnt[i,j,k];
      end;
      SSF1F3 := SSF1F3 + p * p / n2;
    end;
  end;
  SSF1F3 := SSF1F3 - SSF1 - SSF3 - Constant;

  // Get ss for columns x slices interaction
  SSF2F3 := 0;
  p := 0.0;
  n2 := 0.0;
  for j := 0 to NoGrpsB - 1 do
  begin
    for k := 0 to NoGrpsC - 1 do
    begin
      for i := 0 to NoGrpsA - 1 do
      begin
        p := p + wsum[i,j,k];
        n2 := n2 + ncnt[i,j,k];
      end;
      SSF2F3 := SSF2F3 + p * p / n2;
      p := 0.0;
      n2 := 0.0;
    end;
  end;
  SSF2F3 := SSF2F3 - SSF2 - SSF3 - Constant;

  SSNonAdd := 0;
  for i := 0 to NoGrpsA - 1 do
  begin
    rowmean := RowSums[i] / RowCount[i];
    for j := 0 to NoGrpsB - 1 do
    begin
      colmean := ColSums[j] / ColCount[j];
      for k := 0 to NoGrpsC - 1 do
      begin
        sliceMean := SlcSums[k] / SlcCount[k];
        SSNonAdd := SSNonAdd + (colmean-GrandMean) * (rowmean-GrandMean) * (sliceMean-GrandMean) * wsum[i,j,k];
      end;
    end;
  end;

  SSDep := SSDep - Constant;
  if InteractChk.Checked then
    SSErr := SSDep - (SSF1 + SSF2 + SSF3 + SSF1F2 + SSF1F3 + SSF2F3)
  else
    SSErr := SSDep - (SSF1 + SSF2 + SSF3);
  SSNonAdd := SSNonAdd * SSNonAdd / (SSF1 * SSF2 * SSF3);
  SSNonAdd := SSNonAdd * NoGrpsA * NoGrpsB * NoGrpsC * NoGrpsA * NoGrpsB * NoGrpsC;
  MSNonAdd := SSNonAdd;
  SSBalance := SSErr - SSNonAdd;

  if ((SSF1 < 0.0) or (SSF2 < 0.0) or (SSF3 < 0.0) or (SSF1F2 < 0.0) or (SSF1F3 < 0.0) or (SSF2F3 < 0.0)) then
  begin
    ErrorMsg('A negative SS found. Unbalanced design? Ending analysis.');
    Result := false;
    exit;
  end;

  DFTot := N - 1;
  DFF1 := NoGrpsA - 1;
  DFF2 := NoGrpsB - 1;
  DFF3 := NoGrpsC - 1;
  DFF1F2 := DFF1 * DFF2;
  DFF1F3 := DFF1 * DFF3;
  DFF2F3 := DFF2 * DFF3;
  if InteractChk.Checked then
    DFErr := DFTot - DFF1 - DFF2 - DFF3 - DFF1F2 - DFF1F3 - DFF2F3
  else
    DFErr := DFTot - DFF1 - DFF2 - DFF3;
  DFBalance := DFErr - 1;

  MSF1 := SSF1 / DFF1;
  MSF2 := SSF2 / DFF2;
  MSF3 := SSF3 / DFF3;
  MSF1F2 := SSF1F2 / DFF1F2;
  MSF1F3 := SSF1F3 / DFF1F3;
  MSF2F3 := SSF2F3 / DFF2F3;
  MSErr := SSErr / DFErr;
  MSDep := SSDep / DFTot;
  MSBalance := SSBalance / DFBalance;

  OmegaF1 := (SSF1 - DFF1 * MSErr) / (SSDep + MSErr);
  OmegaF2 := (SSF2 - DFF2 * MSErr) / (SSDep + MSErr);
  OmegaF3 := (SSF3 - DFF3 * MSErr) / (SSDep + MSErr);
  OmegaF1F2 := (SSF1F2 - DFF1F2 * MSErr) / (SSDep + MSErr);
  OmegaF1F3 := (SSF1F3 - DFF1F3 * MSErr) / (SSDep + MSErr);
  OmegaF2F3 := (SSF2F3 - DFF2F3 * MSErr) / (SSDep + MSErr);
  if InteractChk.Checked then
    Omega := OmegaF1 + OmegaF2 + OmegaF3 + OmegaF1F2 + OmegaF1F3 +  OmegaF2F3
  else
    Omega := OmegaF1 + OmegaF2 + OmegaF3;
  MeanDep := MeanDep / N;

  FF1 := abs(MSF1 / MSErr);
  FF2 := abs(MSF2 / MSErr);
  FF3 := abs(MSF3 / MSErr);
  FF1F2 := abs(MSF1F2 / MSErr);
  FF1F3 := abs(MSF1F3 / MSErr);
  FF2F3 := abs(MSF2F3 / MSErr);
  if (MSBalance > 0.0) then
    FNonAdd := MSNonAdd / MSBalance
  else
    FNonAdd := 0.0;

  ProbF1 := probf(FF1,DFF1,DFErr);
  ProbF2 := probf(FF2,DFF2,DFErr);
  ProbF3 := probf(FF3,DFF3,DFErr);
  ProbF1F2 := probf(FF1F2,DFF1F2,DFErr);
  ProbF1F3 := probf(FF1F3,DFF1F3,DFErr);
  ProbF2F3 := probf(FF2F3,DFF2F3,DFErr);
  ProbNonAdd := probf(FNonAdd,1.0,DFBalance);

  if (ProbF1 > 1.0) then ProbF1 := 1.0;
  if (ProbF2 > 1.0) then ProbF2 := 1.0;
  if (ProbF3 > 1.0) then ProbF3 := 1.0;
  if (ProbF1F2 > 1.0) then ProbF1F2 := 1.0;
  if (ProbF1F3 > 1.0) then ProbF1F3 := 1.0;
  if (ProbF2F3 > 1.0) then ProbF2F3 := 1.0;

  // Obtain omega squared (proportion of dependent variable explained)
  if (OmegaF1 < 0.0) then OmegaF1 := 0.0;
  if (OmegaF2 < 0.0) then OmegaF2 := 0.0;
  if (OmegaF3 < 0.0) then OmegaF3 := 0.0;
  if (OmegaF1F2 < 0.0) then OmegaF1F2 := 0.0;
  if (OmegaF1F3 < 0.0) then OmegaF1F3 := 0.0;
  if (OmegaF2F3 < 0.0) then OmegaF2F3 := 0.0;
  if (Omega < 0.0) then Omega := 0.0;

  Result := true;
end;


procedure TOneCaseAnovaForm.ThreeWayTable;
var
  lReport: TStrings;
  i, j, k: integer;
  XBar, V, S, RowSS, ColSS, SlcSS: double;
begin
  lReport := TStringList.Create;
  try
    lReport.Add('THREE-WAY ANALYSIS OF VARIANCE');
    lReport.Add('');
    lReport.Add('Variable analyzed:           %s', [DepVarEdit.Text]);
    lReport.Add('');
    lReport.Add('Factor A (rows) variable:    %s', [Factor1Edit.Text]);
    lReport.Add('Factor B (columns) variable: %s', [Factor2Edit.Text]);
    lReport.Add('Factor C (slices) variable:  %s', [Factor3Edit.Text]);
    lReport.Add('');
    lReport.Add('SOURCE         D.F.        SS            MS             F      PROB.> F   Omega Squared');
    lReport.Add('');
    lReport.Add('Among Rows     %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF1, SSF1, MSF1, FF1, ProbF1, OmegaF1]);
    lReport.Add('Among Columns  %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF2, SSF2, MSF2, FF2, ProbF2, OmegaF2]);
    lReport.Add('Among Slices   %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF3, SSF3, MSF3, FF3, ProbF3, OmegaF3]);

    if InteractChk.Checked then
    begin
      lReport.Add('A x B Inter.   %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF1F2, SSF1F2, MSF1F2, FF1F2, ProbF1F2, OmegaF1F2]);
      lReport.Add('A x C Inter.   %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF1F3, SSF1F3, MSF1F3, FF1F3, ProbF1F3, OmegaF1F3]);
      lReport.Add('B x C Inter.   %4.0f  %12.4f  %12.4f  %12.4f  %6.3f     %6.3f', [DFF2F3, SSF2F3, MSF2F3, FF2F3, ProbF2F3, OmegaF2F3]);
    end;
    lReport.Add('Residual       %4.0f  %12.4f  %12.4f', [DFErr, SSErr, MSErr]);
    lReport.Add(' NonAdditivity %4.0f  %12.4f  %12.4f  %12.4f  %6.3f', [1.0, SSNonAdd, MSNonAdd, FNonAdd, ProbNonAdd]);
    lReport.Add(' Balance       %4.0f  %12.4f  %12.4f', [DFBalance, SSBalance, MSBalance]);
    lReport.Add('Total          %4.0f  %12.4f  %12.4f', [DFTot, SSDep, MSDep]);
    lReport.Add('');
    lReport.Add('Omega squared for combined effects := %8.4f', [Omega]);
    lReport.Add('');
    lReport.Add('');
    lReport.Add('DESCRIPTIVE STATISTICS');
    lReport.Add('');
    lReport.Add('GROUP              N     MEAN   VARIANCE  STD.DEV.');
    equal_grp := true;

    //Display Row means, variances, standard deviations
    for i := 0 to NoGrpsA - 1 do
    begin
      XBar := RowSums[i] / RowCount[i];
      RowSS := 0.0;
      for j := 0 to NoGrpsB - 1 do
        for k := 0 to NoGrpsC - 1 do
          RowSS := RowSS + wx2[i,j,k];
      V := (RowSS - sqr(RowSums[i]) / RowCount[i]) / (RowCount[i] - 1);;
      S := sqrt(V);
      lReport.Add('Row   %3d         %3d  %8.3f  %8.3f  %8.3f', [minf1+i, RowCount[i], XBar, V, S]);
    end;

    //Display means, variances and standard deviations for columns
    for j := 0 to NoGrpsB - 1 do
    begin
      XBar := ColSums[j] / ColCount[j];
      ColSS := 0.0;
      for i := 0 to NoGrpsA - 1 do
        for k := 0 to NoGrpsC - 1 do
          ColSS := ColSS + wx2[i,j,k];
      V := (ColSS - sqr(ColSums[j]) / ColCount[j]) / (ColCount[j] - 1);
      S := sqrt(V);
      lReport.Add('Col   %3d         %3d  %8.3f  %8.3f  %8.3f', [minf2+j, ColCount[j], XBar, V, S]);
    end;

    //Display means, variances and standard deviations for slices
    for k := 0 to NoGrpsC - 1 do
    begin
      XBar := SlcSums[k] / SlcCount[k];
      SlcSS := 0.0;
      for i := 0 to NoGrpsA - 1 do
        for j := 0 to NoGrpsB - 1 do
          SlcSS := SlcSS + wx2[i,j,k];
      V := (SlcSS - sqr(SlcSums[k]) / SlcCount[k]) / (SlcCount[k] - 1);
      S := sqrt(V);
      lReport.Add('Slice %3d         %3d  %8.3f  %8.3f  %8.3f', [minf3+k, SlcCount[k], XBar, V, S]);
    end;

    lReport.Add('TOTAL             %3d  %8.3f  %8.3f  %8.3f', [N, MeanDep, MSDep, sqrt(MSDep)]);

    FReportFrame.DisplayReport(lReport);

  finally
    lReport.Free;
  end;
end;


{ Determines from the ItemIndex of the FChartCombobox which factors will be
  plotted along x and as y index, and for which C index the interactions will
  be calculated. }
procedure TOneCaseAnovaform.GetDataIndices(out ix, iy, iz: Integer);
var
  index,  i1, i2, i3: Integer;
begin
  index := FChartComboBox.ItemIndex;
  i1 := 3;
  i2 := i1 + NF3Cells;
  i3 := i2 + NF3Cells;
  if (index >= i1) and (index < i3) then
  begin
    if index < i2 then
    begin
      ix := 1;
      iy := 2;
      iz := index - i1;
    end else
    begin
      ix := 2;
      iy := 1;
      iz := index - i2;
    end;
    exit;
  end;

  i1 := i3;
  i2 := i1 + NF2Cells;
  i3 := i2 + NF2Cells;
  if (index >= i1) and (index < i3) then
  begin
    if index < i2 then
    begin
      ix := 1;
      iy := 3;
      iz := index - i1;
    end else
    begin
      ix := 3;
      iy := 1;
      iz := index - i2;
    end;
    exit;
  end;

  i1 := i3;
  i2 := i1 + NF1Cells;
  i3 := i2 + NF1Cells;
  if (index >= i1) and (index < i3) then
  begin
    if index < i2 then
    begin
      ix := 2;
      iy := 3;
      iz := index - i1;
    end else
    begin
      ix := 3;
      iy := 2;
      iz := index - i2;
    end;
  end;
end;


{ OnChange event handler for the ChartCombobox. Displays the chart associated
  with the current ItemIndex. }
procedure TOneCaseAnovaForm.SelectThreeWayPlot(Sender: TObject);
var
  i, j, k, idx, ix, iy, iz: Integer;
  item: PChartDataItem;
begin
  FStyles.Styles.Clear;
  FSeries.Clear;

  case FChartComboBox.ItemIndex of
    0: begin  // Plot means vs factor A
         FSeries.ListSource.YCount := 1;
         for i := 0 to NF1Cells-1 do
           FSeries.AddXY(minF1 + i, RowSums[i] / RowCount[i], IntToStr(MinF1 + i));
         FChartFrame.SetXTitle(Factor1Edit.Text + ' codes');
         FChartFrame.SetTitle(Factor1Edit.Text);
       end;
    1: begin // Plot means vs factor B
         FSeries.ListSource.YCount := 1;
         for j := 0 to NF2Cells-1 do
           FSeries.AddXY(minF2 + j, ColSums[j] / ColCount[j], IntToStr(MinF2 + j));
         FChartFrame.SetXTitle(Factor2Edit.Text + ' codes');
         FChartFrame.SetTitle(Factor2Edit.Text);
       end;
    2: begin  // Plot means vs factor C
         FSeries.ListSource.YCount := 1;
         for i := 0 to NF3Cells-1 do
           FSeries.AddXY(minF3 + i, SlcSums[i] / SlcCount[i], IntToStr(MinF3 + i));
         FChartFrame.SetXTitle(Factor3Edit.Text + ' codes');
         FChartFrame.SetTitle(Factor3Edit.Text);
       end;
  else
    GetDataIndices(ix, iy,iz);
    if (ix = 1) and (iy = 2) then
    begin
      FSeries.ListSource.YCount := NF2Cells;
      for i := 0 to NF1Cells-1 do
      begin
        idx := FSeries.AddXY(minF1 + i, NaN, IntToStr(minF1 + i));
        item := FSeries.Source.Item[idx];
        for j := 0 to NF2Cells-1 do
          item^.SetY(j, wsum[i,j,iz] / ncnt[i,j,iz]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor1Edit.Text, Factor2Edit.Text, Factor3Edit.Text, MinF3 + iz]));
      FChartFrame.SetXTitle(Factor1Edit.Text + ' codes');
      for j := 0 to NF2Cells-1 do
        with TChartStyle(FStyles.styles.Add) do
        begin
          Brush.Color := DATA_COLORS[j mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor2Edit.Text, IntToStr(MinF2 + j)]);
        end;
    end
    else
    if (ix = 2) and (iy = 1) then
    begin
      FSeries.ListSource.YCount := NF1Cells;
      for j := 0 to NF2Cells-1 do
      begin
        idx := FSeries.AddXY(minF2 + j, NaN, IntToStr(minF2 + j));
        item := FSeries.Source.Item[idx];
        for i := 0 to NF1Cells-1 do
          item^.SetY(i, wsum[i, j, iz] / ncnt[i, j, iz]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor1Edit.Text, Factor2Edit.Text, Factor3Edit.Text, MinF3 + iz]));
      FChartFrame.SetXTitle(Factor2Edit.Text + ' codes');
      for i := 0 to NF1Cells-1 do
        with TChartStyle(FStyles.styles.Add) do
        begin
          Brush.Color := DATA_COLORS[i mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor1Edit.Text, IntToStr(MinF1 + i)]);
        end;
    end
    else
    if (ix = 1) and (iy = 3) then
    begin
      FSeries.ListSource.YCount := NF3Cells;
      for i := 0 to NF1Cells-1 do
      begin
        idx := FSeries.AddXY(minF1 + i, NaN, IntToStr(minF1 + i));
        item := FSeries.Source.Item[idx];
        for k := 0 to NF3Cells-1 do
          item^.SetY(k, wsum[i, iz, k] / ncnt[i, iz, k]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor1Edit.Text, Factor3Edit.Text, Factor2Edit.Text, MinF2 + iz]));
      FChartFrame.SetXTitle(Factor1Edit.Text + ' codes');
      for k := 0 to NF3Cells-1 do
        with TChartStyle(FStyles.styles.Add) do
        begin
          Brush.Color := DATA_COLORS[k mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor3Edit.Text, IntToStr(MinF3 + k)]);
        end;
    end
    else
    if (ix = 3) and (iy = 1) then
    begin
      FSeries.ListSource.YCount := NF1Cells;
      for k := 0 to NF3Cells-1 do
      begin
        idx := FSeries.AddXY(minF3 + k, NaN, IntToStr(minF3 + k));
        item := FSeries.Source.Item[idx];
        for i := 0 to NF1Cells-1 do
          item^.SetY(i, wsum[i, iz, k] / ncnt[i, iz, k]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor1Edit.Text, Factor3Edit.Text, Factor2Edit.Text, MinF2 + iz]));
      FChartFrame.SetXTitle(Factor3Edit.Text + ' codes');
      for i := 0 to NF1Cells-1 do
        with TChartStyle(FStyles.styles.Add) do
        begin
          Brush.Color := DATA_COLORS[i mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor1Edit.Text, IntToStr(MinF1 + i)]);
        end;
    end
    else
    if (ix = 2) and (iy = 3) then
    begin
      FSeries.ListSource.YCount := NF3Cells;
      for j := 0 to NF2Cells-1 do
      begin
        idx := FSeries.AddXY(minF2 + j, NaN, IntToStr(minF2 + j));
        item := FSeries.Source.Item[idx];
        for k := 0 to NF3Cells-1 do
          item^.SetY(k, wsum[iz, j, k] / ncnt[iz, j, k]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor2Edit.Text, Factor3Edit.Text, Factor1Edit.Text, MinF1 + iz]));
      FChartFrame.SetXTitle(Factor2Edit.Text + ' codes');
      for k := 0 to NF3Cells-1 do
        with TChartStyle(FStyles.styles.Add) do
        begin
          Brush.Color := DATA_COLORS[k mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor3Edit.Text, IntToStr(MinF3 + k)]);
        end;
    end
    else
    if (ix = 3) and (iy = 2) then
    begin
      FSeries.ListSource.YCount := NF2Cells;
      for k := 0 to NF3Cells-1 do
      begin
        idx := FSeries.AddXY(minF3 + k, NaN, IntToStr(minF3 + k));
        item := FSeries.Source.Item[idx];
        for j := 0 to NF2Cells-1 do
          item^.SetY(j, wsum[iz, j, k] / ncnt[iz, j, k]);
      end;
      FChartFrame.SetTitle(Format('Factor "%s" x Factor "%s"' + LineEnding + '"%s" = %d', [
        Factor2Edit.Text, Factor3Edit.Text, Factor1Edit.Text, MinF1 + iz]));
      FChartFrame.SetXTitle(Factor3Edit.Text + ' codes');
      for j := 0 to NF2Cells-1 do
        with TChartStyle(FStyles.Styles.Add) do
        begin
          Brush.Color := DATA_COLORS[j mod Length(DATA_COLORS)];
          UseBrush := True;
          Text := Format('%s = %s', [Factor2Edit.Text, IntToStr(MinF2 + j)]);
        end;
    end else
      raise Exception.Create('Fatal error in SelectThreeWayPlot');
  end;

  if (FSeries is TBarSeries) then
  begin
    if FStyles.Styles.Count > 0 then
    begin
      TBarSeries(FSeries).Styles := FStyles;
      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 TOneCaseAnovaForm.ThreeWayPlot;
begin
  if not ShowPlotsChk.Checked then
  begin
    ChartPage.TabVisible := false;
    exit;
  end;

  FChartFrame.Clear;   // this destroys the series
  FChartFrame.SetYTitle('Means');
  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;
  PopulateChartCombobox(true);
  FChartCombobox.OnChange := @SelectThreeWayPlot;
  SelectThreeWayPlot(nil);

  ChartPage.TabVisible := true;
end;


procedure TOneCaseAnovaForm.TwoWayContrasts;
var
  lReport: TStrings;
  i, j, totalCells: integer;
  value, alpha, posthocAlpha: double;
  cellCnts: IntDyneVec = nil;
  cellVars: DblDyneVec = nil;
  cellSums: DblDyneVec = nil;
  RowSS, ColSS: double;
  variances: DblDyneVec = nil;
begin
  if not (ScheffeChk.Checked or TukeyHSDChk.Checked or TukeyBChk.Checked or
          TukeyKramerChk.Checked or NewmanKeulsChk.Checked) then
  begin
    PostHocPage.TabVisible := false;
    exit;
  end;

  totalCells := NF1Cells + NF2Cells + NF3Cells;

  // allocate space
  SetLength(CellCnts, totalCells);  // array of cell counts
  SetLength(CellVars, totalCells);  // arrray of cell sums of squares  variances
  SetLength(CellSums, totalCells);  // array of cell sums  means
  SetLength(Variances, totalCells);

  alpha := StrToFloat(OverallAlphaEdit.Text);
  postHocAlpha := StrToFloat(PostAlphaEdit.Text);

  lReport := TStringList.Create;
  try
    //  row comparisons
    if (Nf1cells > 2) and (ProbF1 < alpha) then
    begin
      for i := 0 to NoGrpsA - 1 do
      begin
        RowSS := 0.0;
        for j := 0 to NoGrpsB - 1 do RowSS := RowSS + vars[i,j];
        variances[i] := RowSS - sqr(RowSums[i]) / RowCount[i];
        variances[i] := variances[i] / (RowCount[i] - 1.0);
      end;

      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG ROWS');

      // get smallest group size
      value := 1e308;
      for i := 0 to Nf1cells - 1 do
        if (RowCount[i] < value) then value := RowCount[i];

      if ScheffeChk.Checked then
        ScheffeTest(MSErr, RowSums, RowCount, minf1, maxf1, N, posthocAlpha, lReport);
      if TukeyHSDChk.Checked and equal_grp then
        Tukey(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
      if TukeyBChk.Checked and equal_grp then
        TukeyBTest(MSErr, DFErr, RowSums, RowCount, minf1, maxf1, value, posthocAlpha, lReport);
      if TukeyKramerChk.Checked and equal_grp then
        Tukey_Kramer(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
  //       if (BonferroniChk.Checked) then
  //          Bonferroni(RowSums,RowCount,variances,minf1,maxf1, lReport);
  //       if (OrthogonalChk.Checked) then
  //           CONTRASTS(MSErr,DFErr,RowSums,RowCount,minf1,maxf1,Alpha, lReport);
      if NewmanKeulsChk.Checked and equal_grp then
        Newman_Keuls(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
    end;

    //  column comparisons
    if (Nf2cells > 2) and (ProbF2 < alpha) then
    begin
      for j := 0 to NoGrpsB - 1 do
      begin
        ColSS := 0.0;
        for i := 0 to NoGrpsA - 1 do ColSS := ColSS + vars[i,j];
        variances[j] := ColSS - (ColSums[j] * ColSums[j] / ColCount[j]);
        variances[j] := variances[j] / (ColCount[j] - 1.0);
      end;
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG COLUMNS');
      value := 1e308;
      for i := 0 to Nf2cells - 1 do
        if (ColCount[i] < value) then value := ColCount[i];

      if ScheffeChk.Checked then
        ScheffeTest(MSErr, ColSums, ColCount, minf2, maxf2, N, posthocAlpha, lReport);
      if TukeyHSDChk.Checked and equal_grp then
        Tukey(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
      if TukeyBChk.Checked and equal_grp then
        TukeyBTest(MSErr, DFErr, ColSums, ColCount, minf2, maxf2, value, posthocAlpha, lReport);
      if TukeyKramerChk.Checked and equal_grp then
        Tukey_Kramer(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
  //       if (BonferroniChk.Checked) then
  //          Bonferroni(ColSums,ColCount,variances,minf2,maxf2, lReport);
  //       if (OrthogonalChk.Checked) then
  //           CONTRASTS(MSErr,DFErr,ColSums,ColCount,minf2,maxf2,Alpha, lReport);
      if NewmanKeulsChk.Checked and equal_grp then
        Newman_Keuls(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
    end;

    //  simple effects for columns within each row
    if (ProbF3 < alpha) then
    begin
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG COLUMNS WITHIN EACH ROW');
      for i := 0 to Nf1cells - 1 do
      begin
        lReport.Add('');
        lReport.Add('ROW %d COMPARISONS', [i+1]);
        // move cell sums and counts to cellsums and cellcnts
        for j := 0 to Nf2cells - 1 do
        begin
          cellsums[j] := sums[i,j];
          cellcnts[j] := counts[i,j];
          cellvars[j] := vars[i,j];
        end;
        value := 1e308;
        for j := 0 to Nf2cells - 1 do
          if (cellcnts[j] < value) then value := cellcnts[j];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf2, maxf2, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf2, maxf2, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums,cellcnts,cellvars,minf2,maxf2, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr,DFErr,cellsums,cellcnts,minf2,maxf2,0.05, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
      end;
    end;

    //  simple effects for rows within each column
    if (ProbF3 < alpha) then
    begin
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG ROWS WITHIN EACH COLUMN');
      for j := 0 to Nf2cells - 1 do
      begin
        lReport.Add('');
        lReport.Add('COLUMN %d COMPARISONS', [j+1]);
        // move cell sums and counts to cellsums and cellcnts
        for i := 0 to Nf1cells - 1 do
        begin
          cellsums[i] := sums[i,j];
          cellcnts[i] := counts[i,j];
          cellvars[i] := vars[i,j];
        end;
        value := 1e308;
        for i := 0 to Nf1cells - 1 do
          if (cellcnts[j] < value) then value := cellcnts[j];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf1, maxf1, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf1, maxf1, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums,cellcnts,cellvars,minf1,maxf1, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr,DFErr,cellsums,cellcnts,minf1,maxf1,0.05, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
      end;
    end;

    FPostHocReportFrame.DisplayReport(lReport);
    PosthocPage.TabVisible := true;

  finally
    lReport.Clear;
  end;
end;


procedure TOneCaseAnovaForm.ThreeWayContrasts;
var
  lReport: TStrings;
  i, j, k, totalCells: integer;
  value, alpha, posthocAlpha: double;
  RowSS, ColSS, SlcSS: double;
  cellCnts: IntDyneVec = nil;
  cellVars: DblDyneVec = nil;
  cellSums: DblDyneVec = nil;
  variances: DblDyneVec = nil;
begin
  if not (ScheffeChk.Checked or TukeyHSDChk.Checked or TukeyBChk.Checked or
          TukeyKramerChk.Checked or NewmanKeulsChk.Checked) then
  begin
    PosthocPage.TabVisible := false;
    exit;
  end;

  alpha := StrToFloat(OverallAlphaEdit.Text);
  posthocAlpha := StrToFloat(PostAlphaEdit.Text);
  totalCells := NF1Cells + NF2Cells + NF3Cells;

  // allocate space
  SetLength(cellCnts, totalCells);  // array of cell counts
  SetLength(cellVars, totalCells);  // arrray of cell sums of squares  variances
  SetLength(cellSums, totalCells);  // array of cell sums  means
  SetLength(variances, totalCells);

  lReport := TStringList.Create;
  try
    //  row comparisons
    if (NF1cells > 2) and (ProbF1 < alpha) then
    begin
      for i := 0 to NoGrpsA - 1 do
      begin
        RowSS := 0.0;
        for j := 0 to NoGrpsB - 1 do
          for k := 0 to NoGrpsC - 1 do
            RowSS := RowSS + wx2[i,j,k];
        variances[i] := RowSS - sqr(RowSums[i]) / RowCount[i];
        variances[i] := variances[i] / (RowCount[i] - 1);
      end;

      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG ROWS');

      // get smallest group size
      value := 1e308;
      for i := 0 to Nf1cells - 1 do
        if (RowCount[i] < value) then value := RowCount[i];

      if ScheffeChk.Checked then
        ScheffeTest(MSErr, RowSums, RowCount, minf1, maxf1, N, posthocAlpha, lReport);
      if TukeyHSDChk.Checked and equal_grp then
        Tukey(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
      if TukeyBChk.Checked and equal_grp then
        TukeyBTest(MSErr, DFErr, RowSums, RowCount, minf1, maxf1, value, posthocAlpha, lReport);
      if TukeyKramerChk.Checked and equal_grp then
        Tukey_Kramer(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
  //       if (BonferroniChk.Checked) then
  //          Bonferroni(RowSums,RowCount,variances,minf1,maxf1, lReport);
  //       if (OrthogonalChk.Checked) then
  //           CONTRASTS(MSErr,DFErr,RowSums,RowCount,minf1,maxf1,Alpha, lReport);
      if NewmanKeulsChk.Checked and equal_grp then
        Newman_Keuls(MSErr, DFErr, value, RowSums, RowCount, minf1, maxf1, posthocAlpha, lReport);
    end;

    //  column comparisons
    if (Nf2cells > 2) and (ProbF2 < alpha) then
    begin
      for j := 0 to NoGrpsB - 1 do
      begin
        ColSS := 0.0;
        for i := 0 to NoGrpsA - 1 do
          for k := 0 to NoGrpsC - 1 do
            ColSS := ColSS + wx2[i,j,k];
        variances[j] := ColSS - sqr(ColSums[j]) / ColCount[j];
        variances[j] := variances[j] / (ColCount[j] - 1.0);
      end;
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG COLUMNS');
      value := 1e308;
      for i := 0 to Nf2cells - 1 do
        if (ColCount[i] < value) then value := ColCount[i];

      if ScheffeChk.Checked then
        ScheffeTest(MSErr, ColSums, ColCount, minf2, maxf2, N, posthocAlpha, lReport);
      if TukeyHSDChk.Checked and equal_grp then
        Tukey(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
      if TukeyBChk.Checked and equal_grp then
        TukeyBTest(MSErr, DFErr, ColSums, ColCount, minf2, maxf2, value, posthocAlpha, lReport);
      if TukeyKramerChk.Checked and equal_grp then
        Tukey_Kramer(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
  //       if (BonferroniChk.Checked) then
  //          Bonferroni(ColSums,ColCount,variances,minf2,maxf2, lReport);
  //       if (OrthogonalChk.Checked) then
  //           CONTRASTS(MSErr,DFErr,ColSums,ColCount,minf2,maxf2,Alpha, lReport);
      if NewmanKeulsChk.Checked and equal_grp then
        Newman_Keuls(MSErr, DFErr, value, ColSums, ColCount, minf2, maxf2, posthocAlpha, lReport);
    end;

    //  slice comparisons
    if (Nf3cells > 2) and (ProbF3 < alpha) then
    begin
      for k := 0 to NoGrpsC - 1 do
      begin
        SlcSS := 0.0;
        for i := 0 to NoGrpsA - 1 do
          for j := 0  to NoGrpsB - 1 do SlcSS := SlcSS + wx2[i,j,k];
        variances[k] := SlcSS - sqr(SlcSums[k]) / SlcCount[k];
        variances[k] := variances[k] / (SlcCount[k] - 1.0);
      end;
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG SLICES');
      value := 1e308;
      for i := 0 to Nf3cells - 1 do
        if (SlcCount[i] < value) then value := SlcCount[i];

      if ScheffeChk.Checked then
        ScheffeTest(MSErr, SlcSums, SlcCount, minf3, maxf3, N, posthocAlpha, lReport);
      if TukeyHSDChk.Checked and equal_grp then
        Tukey(MSErr, DFErr, value, SlcSums, SlcCount, minf3, maxf3, posthocAlpha, lReport);
      if TukeyBChk.Checked and equal_grp then
        TukeyBTest(MSErr, DFErr, SlcSums, SlcCount, minf3, maxf3, value, posthocAlpha, lReport);
      if TukeyKramerChk.Checked and equal_grp then
        Tukey_Kramer(MSErr, DFErr, value, SlcSums, SlcCount, minf3, maxf3, posthocAlpha, lReport);
  //       if (BonferroniChk.Checked) then
  //          Bonferroni(SlcSums,SlcCount,variances,minf3,maxf3, lReport);
  //       if (OrthogonalChk.Checked) then
  //           CONTRASTS(MSErr,DFErr,SlcSums,SlcCount,minf3,maxf3,Alpha, lReport);
      if NewmanKeulsChk.Checked and equal_grp then
        Newman_Keuls(MSErr, DFErr, value, SlcSums, SlcCount, minf3, maxf3, posthocAlpha, lReport);
    end;

    //  simple effects for columns within each row
    if (ProbF1F2 < alpha) then
    begin
      lReport.Add('');
      lReport.Add('COMPARISONS AMONG COLUMNS WITHIN EACH ROW');
      for i := 0 to Nf1cells - 1 do
      begin
        if lReport.Count > 0 then
          lReport.Add('');
        lReport.Add('ROW %d COMPARISONS', [i+1]);
        // move cell sums && counts to cellsums && cellcnts
        for j := 0 to Nf2cells - 1 do
        begin
          for k := 0 to Nf3cells - 1 do
          begin
            cellsums[j] := wsum[i,j,k];
            cellcnts[j] := ncnt[i,j,k];
            cellvars[j] := wx2[i,j,k];
          end;
        end;
        value := 1e308;
        for j := 0 to Nf2cells - 1 do
          if (cellcnts[j] < value) then value := cellcnts[j];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf2, maxf2, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf2, maxf2, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums,cellcnts,cellvars,minf2,maxf2, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr,DFErr,cellsums,cellcnts,minf2,maxf2,0.05, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
      end;
    end;

    //  simple effects for rows within each column
    if (ProbF1F2 < alpha) then
    begin
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG ROWS WITHIN EACH COLUMN');
      for j := 0 to Nf2cells - 1 do
      begin
        lReport.Add('');
        lReport.Add('COLUMN %d COMPARISONS', [j+1]);
        // move cell sums && counts to cellsums && cellcnts
        for i := 0 to Nf1cells - 1 do
        begin
          for k := 0 to Nf3cells - 1 do
          begin
            cellsums[i] := wsum[i,j,k];
            cellcnts[i] := ncnt[i,j,k];
            cellvars[i] := wx2[i,j,k];
          end;
        end;
        value := 1e308;
        for i := 0 to Nf1cells - 1 do
          if (cellcnts[j] < value) then value := cellcnts[j];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf1, maxf1, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf1, maxf1, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums,cellcnts,cellvars,minf1,maxf1, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr,DFErr,cellsums,cellcnts,minf1,maxf1,0.05, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
      end;
    end;

    //  simple effects for columns within each slice
    if (ProbF2F3 < alpha) then
    begin
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG COLUMNS WITHIN EACH SLICE');
      for k := 0 to Nf3cells - 1 do
      begin
        lReport.Add('');
        lReport.Add('SLICE %d COMPARISONS', [k+1]);
        // move cell sums && counts to cellsums && cellcnts
        for j := 0 to Nf2cells - 1 do
        begin
          for i := 0 to Nf1cells - 1 do
          begin
            cellsums[j] := wsum[i,j,k];
            cellcnts[j] := ncnt[i,j,k];
            cellvars[j] := wx2[i,j,k];
          end;
        end;
        value := 1e308;
        for j := 0 to Nf2cells-1 do
          if (cellcnts[j] < value) then value := cellcnts[j];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf2, maxf2, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf2, maxf2, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums, cellcnts, cellvars, minf2, maxf2, posthocAlpha, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr, DFErr, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf2, maxf2, posthocAlpha, lReport);
      end;
    end;

    //  simple effects for rows within each slice
    if (ProbF1F3 < alpha) then
    begin
      if lReport.Count > 0 then
        lReport.Add('');
      lReport.Add('COMPARISONS AMONG ROWS WITHIN EACH SLICE');
      for k := 0 to Nf3cells - 1 do
      begin
        lReport.Add('');
        lReport.Add('SLICE %d COMPARISONS', [k+1]);
        // move cell sums && counts to cellsums && cellcnts
        for i := 0 to Nf1cells - 1 do
        begin
          for j := 0 to Nf2cells - 1 do
          begin
            cellsums[j] := wsum[i,j,k];
            cellcnts[j] := ncnt[i,j,k];
            cellvars[j] := wx2[i,j,k];
          end;
        end;
        value := 1e308;
        for i := 0 to Nf1cells - 1 do
          if (cellcnts[i] < value) then value := cellcnts[i];

        if ScheffeChk.Checked then
          ScheffeTest(MSErr, cellsums, cellcnts, minf1, maxf1, N, posthocAlpha, lReport);
        if TukeyHSDChk.Checked and equal_grp then
          Tukey(MSErr,DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
        if TukeyBChk.Checked and equal_grp then
          TukeyBTest(MSErr, DFErr, cellsums, cellcnts, minf1, maxf1, value, posthocAlpha, lReport);
        if TukeyKramerChk.Checked and equal_grp then
          Tukey_Kramer(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
  //            if (BonferroniChk.Checked) then
  //               Bonferroni(cellsums,cellcnts,cellvars,minf1,maxf1, posthocAlpha, lReport);
  //            if (OrthogonalChk.Checked) then
  //               CONTRASTS(MSErr,DFErr,cellsums,cellcnts,minf1,maxf1,posthocAlpha, lReport);
        if NewmanKeulsChk.Checked and equal_grp then
          Newman_Keuls(MSErr, DFErr, value, cellsums, cellcnts, minf1, maxf1, posthocAlpha, lReport);
      end;
    end;

    FPosthocReportFrame.DisplayReport(lReport);
    PosthocPage.TabVisible := true;

  finally
    lReport.Free;
  end;
end;


procedure TOneCaseAnovaForm.Plot3DChkChange(Sender: TObject);
begin
  if FSeries <> nil then
  begin
    if Plot3DChk.Checked then
      FSeries.Depth := 20
    else
      FSeries.Depth := 0;
  end;
end;


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


procedure TOneCaseAnovaForm.UpdateBtnStates;
var
  i: Integer;
  lSelected: Boolean;
begin
  inherited;

  if FPosthocReportFrame <> nil then
    FPostHocReportFrame.UpdateBtnStates;

  lSelected := false;
  for i:=0 to VarList.Items.Count-1 do
    if VarList.Selected[i] then
    begin
      lSelected := true;
      break;
    end;
  DepIn.Enabled := lSelected and (DepVarEdit.Text = '');
  Fact1In.Enabled := lSelected and (Factor1Edit.Text = '');
  Fact2In.Enabled := lSelected and (Factor2Edit.Text = '');
  Fact3In.Enabled := lSelected and (Factor3Edit.Text = '');
  DepOut.Enabled := DepVarEdit.Text <> '';
  Fact1Out.Enabled := Factor1Edit.Text <> '';
  Fact2Out.Enabled := Factor2Edit.Text <> '';
  Fact3Out.Enabled := Factor3Edit.Text <> '';
end;


function TOneCaseAnovaForm.Validate(out AMsg: String; out AControl: TWinControl): Boolean;
var
  X: Double;
begin
  Result := false;
  if (DepVarEdit.Text = '') then
  begin
    AMsg := 'Dependent variable is not selected.';
    AControl := VarList;
    exit;
  end;

  if (Factor1Edit.Text = '') then
  begin
    AMsg := 'Factor 1 variable is not selected.';
    AControl := VarList;
    exit;
  end;

  if (Factor2Edit.Text = '') then
  begin
    AMsg := 'Factor 2 variable is not selected.';
    AControl := VarList;
    exit;
  end;

  // Factor 3 can be left empty to distinguish betwee two-way and three-way ANOVA.

  if (OverallAlphaEdit.Text = '') then
  begin
    AControl := OverallAlphaEdit;
    AMsg := 'No value specified for overall alpha.';
    exit;
  end;
  if not TryStrToFloat(OverallAlphaEdit.Text, X) then
  begin
    AControl := OverallAlphaEdit;
    AMsg := 'Overall alpha is not a valid number.';
    exit;
  end;

  if (PostAlphaEdit.Text = '') then
  begin
    AControl := PostAlphaEdit;
    AMsg := 'No value specified for post-hoc alpha.';
    exit;
  end;
  if not TryStrToFloat(PostAlphaEdit.Text, x) then
  begin
    AControl := PostAlphaEdit;
    AMsg := 'Post-hoc alpha is not a valid number.';
    exit;
  end;

  Result := true;
end;


procedure TOneCaseAnovaForm.VarListDblClick(Sender: TObject);
var
  index: Integer;
  s: String;
begin
  index := VarList.ItemIndex;
  if index > -1 then
  begin
    s := VarList.Items[index];
    if DepVarEdit.Text = '' then
      DepVarEdit.Text := s
    else
    if Factor1Edit.Text = '' then
      Factor1Edit.Text := s
    else
    if Factor2Edit.Text = '' then
      Factor2Edit.Text := s
    else
    if Factor3Edit.Text = '' then
      Factor3Edit.Text := s;
    VarList.Items.Delete(index);

    UpdateBtnStates;
  end;
end;


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


end.