// Use file "itemdata2.laz" for testing

unit WithinANOVAUnit;

{$mode objfpc}{$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, Math,
  MainUnit, FunctionsLib, MatrixLib, Globals,
  ReportFrameUnit, BasicStatsReportAndChartFormUnit;

type

  { TWithinANOVAFrm }

  TWithinANOVAResults = record
    // Sum of squares
    SSRows, SScols, SSwithinRows, SStotal, SSresidual: Double;
    // Mean square errors
    MSRows, MScols, MSwithinRows, MStotal, MSresidual: Double;
    // Degrees of freedom
    DFRows, DFcols, DFWithinRows, DFtotal, DFresidual: Integer;
    // Grand mean
    GrandMean: Double;
    // F value
    F: Double;
    // Probability for > F
    Probability: Double;
  end;

  TWithinANOVAFrm = class(TBasicStatsReportAndChartForm)
    AssumpChk: TCheckBox;
    PlotChk: TCheckBox;
    RelChk: TCheckBox;
    GroupBox1: TGroupBox;
    InBtn: TBitBtn;
    Label2: TLabel;
    SelList: TListBox;
    OutBtn: TBitBtn;
    Label1: TLabel;
    ReliabilityPage: TTabSheet;
    TestAssumptionsPage: TTabSheet;
    VarList: TListBox;
    procedure InBtnClick(Sender: TObject);
    procedure OutBtnClick(Sender: TObject);
    procedure SelListDblClick(Sender: TObject);
    procedure VarListDblClick(Sender: TObject);
    procedure VarListSelectionChange(Sender: TObject; {%H-}User: boolean);

  private
    FReliabilityReportFrame: TReportFrame;
    FTestAssumptionsReportFrame: TReportFrame;

    procedure CalcANOVA(
      const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
      const AGrandSum, AGrandSumOfSquares: Double;
      out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
      out AResults: TWithinANOVAResults);

    procedure CalcReliability(const AResults: TWithinANOVAResults;
      ANumSelected: Integer; out R1, R2, R3, R4: Double);

    procedure GetData(
      out ASelected: IntDyneVec; out AColLabels: StrDyneVec;
      out ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
      out AGrandSum, AGrandSumOfSquares: Double);

    procedure Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec);

    procedure TestAssumptions(const ASelected: IntDyneVec;
      out ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
      out ADeterminant1, ADeterminant2, Chi2, AProbability: Double;
      out DF: Integer; out ErrorFound: Boolean);

    procedure WriteANOVAReport(const AColLabels: StrDyneVec;
      const AColMeans, AColVariances: DblDyneVec; const AResults: TWithinANOVAResults);

    procedure WriteReliabilityReport(const R1, R2, R3, R4: Double);

    procedure WriteTestAssumptionsReport(
      const ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
      const AColLabels: StrDyneVec;
      ADeterminant1, ADeterminant2, Chi2, AProbability: Double; DF: Integer;
      ErrorFound: Boolean);

  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
  WithinANOVAFrm: TWithinANOVAFrm;


implementation

{$R *.lfm}

uses
  TAChartUtils, TACustomSeries,
  GridProcs,
  Utils, MathUnit, ChartFrameUnit;


{ TWithinANOVAFrm }

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

  FReliabilityReportFrame := TReportFrame.Create(self);
  FReliabilityReportFrame.Name := '';
  FReliabilityReportFrame.Parent := ReliabilityPage;
  FReliabilityReportFrame.Align := alClient;
  FReliabilityReportFrame.BorderSpacing.Left := 0;
  FReliabilityReportFrame.BorderSpacing.Top := 0;
  FReliabilityReportFrame.BorderSpacing.Bottom := 0;
  FReliabilityReportFrame.BorderSpacing.Right := 0;

  FTestAssumptionsReportFrame := TReportFrame.Create(self);
  FTestAssumptionsReportFrame.Name := '';
  FTestAssumptionsReportFrame.Parent := TestAssumptionsPage;
  FTestAssumptionsReportFrame.Align := alClient;
  FTestAssumptionsReportFrame.BorderSpacing.Left := 0;
  FTestAssumptionsReportFrame.BorderSpacing.Top := 0;
  FTestAssumptionsReportFrame.BorderSpacing.Bottom := 0;
  FTestAssumptionsReportFrame.BorderSpacing.Right := 0;

  FChartFrame.Chart.Margins.Bottom := 0;

  PageControl.ActivePageIndex := 0;
end;


procedure TWithinANOVAFrm.AdjustConstraints;
begin
  inherited;

  ParamsPanel.Constraints.MinWidth := Max(
    4*CloseBtn.Width + 3*CloseBtn.BorderSpacing.Left,
    GroupBox1.Width
  );
  ParamsPanel.Constraints.MinHeight := OutBtn.Top + 6*OutBtn.Height +
    VarList.BorderSpacing.Bottom + GroupBox1.Height + ButtonBevel.Height +
    CloseBtn.BorderSpacing.Top + CloseBtn.Height;
end;


procedure TWithinANOVAFrm.CalcANOVA(
  const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
  const AGrandSum, AGrandSumOfSquares: Double;
  out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
  out AResults: TWithinANOVAResults);
var
  SS: Double = 0;
  term1, term2, term3, term4: Double;
  noSelected: Integer;
  i, count: Integer;

begin
  ARowMeans := nil;
  ARowVariances := nil;
  AColMeans := nil;
  AColVariances := nil;

  noSelected := SelList.Items.Count;
  count := Length(ARowSums);

  term1 := sqr(AGrandSum) / (count * noSelected);

  term2 := AGrandSumOfSquares;

  SS := 0;
  for i := 0 to count-1 do
    SS := SS + sqr(ARowSums[i]);
  term4 := SS / noSelected;

  SS := 0;
  for i := 0 to noSelected-1 do
    SS := SS + sqr(AColSums[i]);
  term3 := SS / count;

  AResults.SSrows := term4 - term1;
  AResults.SScols := term3 - term1;
  AResults.SSwithinRows := term2 - term4;
  AResults.SSresidual := term2 - term3 - term4 + term1;
  AResults.SStotal := term2 - term1;

  AResults.DFrows := count - 1;
  AResults.DFcols := noSelected - 1;
  AResults.DFwithinRows := count * (noSelected - 1);
  AResults.DFresidual := (count - 1) * (noSelected - 1);
  AResults.DFtotal := count * noSelected - 1;

  AResults.MSrows := AResults.SSrows / AResults.DFRows;
  AResults.MScols := AResults.SScols / AResults.DFcols;
  AResults.MSwithinRows := AResults.SSwithinRows / AResults.DFwithinRows;
  AResults.MSresidual := AResults.SSresidual / AResults.DFresidual;
  AResults.MStotal := AResults.SStotal / AResults.DFtotal;  // variance of all scores

  AResults.GrandMean := AGrandSum / (count * noSelected);
                               (*
  AResults.SSRows := VecSum(ARowMeans);

  term1 := sqr(AGrandSum) / (count * noSelected);
  term2 := AGrandSumOfSquares);


  Term1 := sqr(GrandMean) / (count * NoSelected);
  Term2 := SStot;
  for i := 0 to count-1 do
    SSrows := SSrows + sqr(RowMeans[i]);
  Term4 := SSrows / NoSelected;
  for i := 0 to NoSelected-1 do
    SScols := SScols + sqr(ColMeans[i]);
  Term3 := SScols / count;
  SSrows := Term4 - Term1;
  SScols := Term3 - Term1;
  SSwrows := Term2 - Term4;
  SSerr := Term2 - Term3 - Term4 + Term1;
  SStot := Term2 - Term1;
  dfrows := count - 1;
  dfcols := NoSelected - 1;
  dfwrows := count * (NoSelected - 1);
  dferr := (count - 1) * (NoSelected - 1);
  dftot := (count * NoSelected) - 1;
  MSrows := SSrows / dfrows;
  MScols := SScols / dfcols;
  MSwrows := SSwrows / dfwrows;
  MSerr := SSerr / dferr;
  MStot := SStot / dftot; // variance of all scores
  GrandMean := GrandMean / (count * NoSelected);
  for i := 0 to count-1 do
  begin
    RowVar[i] := RowVar[i] - (RowMeans[i] * RowMeans[i] / NoSelected);
    RowVar[i] := RowVar[i] / (NoSelected - 1);
    RowMeans[i] := RowMeans[i] / NoSelected;
  end;
  for i := 0 to NoSelected-1 do
  begin
    ColVar[i] := ColVar[i] - (ColMeans[i] * ColMeans[i] / count);
    ColVar[i] := ColVar[i] / (count - 1);
    ColMeans[i] := ColMeans[i] / count;
  end;
  f1 := MScols / MSerr; // treatment F statistic
  probf1 := ProbF(f1, dfcols, dferr);
  *)

  SetLength(ARowMeans, count);
  SetLength(ARowVariances, count);
  for i := 0 to count-1 do
  begin
    ARowVariances[i] := (ARowSumsOfSquares[i] - (ARowSums[i] * ARowSums[i]) / noSelected) / (noSelected - 1);
    ARowMeans[i] := ARowSums[i] / noSelected;
  end;

  SetLength(AColMeans, noSelected);
  SetLength(AColVariances, noSelected);
  for i := 0 to noSelected-1 do
  begin
    AColVariances[i] := (AColSumsOfSquares[i] - (AColSums[i] * AColSums[i]) / count) / (count - 1);
    AColMeans[i] := AColSums[i] / count;
  end;

  with AResults do
  begin
    F := MScols / MSresidual;  // treatment F statistic
    Probability := ProbF(F, DFcols, DFresidual);
  end;
 end;


procedure TWithinANOVAFrm.CalcReliability(const AResults: TWithinANOVAResults;
  ANumSelected: Integer; out R1, R2, R3, R4: Double);
begin
  with AResults do
  begin
    // unadjusted reliability of test
    R1 := 1.0 - (MSwithinRows / MSrows);

    // R2 is unadjusted reliability of a single item
    R2 := (MSrows - MSwithinRows) / (MSrows + (ANumSelected - 1) * MSwithinRows);

    // Cronbach alpha for test
    R3 := (MSrows - MSresidual) / MSrows;

    // R4 is adjusted reliability of a single item
    R4 := (MSrows - MSresidual) / (MSrows + (ANumSelected - 1) * MSresidual);
  end;
end;


procedure TWithinANOVAFrm.Compute;
var
  noSelected, DF: integer;
  r1, r2, r3, r4: double;
  grandSum, grandSS: Double;
  determ1, determ2, chi2, prob: Double;
  errorfound: boolean;
  selected: IntDyneVec = nil;
  colLabels: StrDyneVec = nil;
  colSums: DblDyneVec = nil;
  colMeans: DblDyneVec = nil;
  colSS: DblDyneVec = nil;
  colVars: DblDyneVec = nil;
  rowSums: DblDyneVec = nil;
  rowMeans: DblDyneVec = nil;
  rowSS: DblDyneVec = nil;
  rowVars: DblDyneVec = nil;
  sampleVarCovarMat: DblDyneMat = nil;
  assumedVarCovarMat: DblDyneMat = nil;
  res: TWithinANOVAResults;
begin
  noSelected := SelList.Items.Count;

  // Read data and compute sums while reading
  GetData(selected, colLabels, rowSums, rowSS, colSums, colSS, grandSum, grandSS);

  // Calculate ANOVA
  CalcANOVA(rowSums, rowSS, colSums, colSS, grandSum, grandSS, rowMeans, rowVars, colMeans, colVars, res);
  WriteANOVAReport(colLabels, colMeans, colVars, res);

  // Do reliability terms if requested
  if RelChk.Checked then
  begin
    CalcReliability(res, noSelected, r1, r2, r3, r4);
    WriteReliabilityReport(r1, r2, r3, r4);
    ReliabilityPage.TabVisible := RelChk.Checked;
  end;

  // Test assumptions of variance - covariance homogeneity if requested
  if AssumpChk.Checked then
  begin
    TestAssumptions(selected, sampleVarCovarMat, assumedVarCovarMat, determ1, determ2, chi2, prob, DF, errorFound);
    WriteTestAssumptionsReport(sampleVarCovarMat, assumedVarCovarMat, colLabels, determ1, determ2, chi2, prob, DF, errorFound);
  end;
  TestAssumptionsPage.TabVisible := AssumpChk.Checked;

  // Finally, plot values if indicated in options list
  if PlotChk.Checked then
    Plot(ColMeans, ColLabels);
  ChartPage.TabVisible := PlotChk.Checked;

  // Make sure that the chart tab is at the end of the pagecontrol.
  ChartPage.PageIndex := PageControl.PageCount-1;
end;


procedure TWithinANOVAFrm.GetData(
  out ASelected: IntDyneVec; out AColLabels: StrDyneVec;
  out ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
  out AGrandSum, AGrandSumOfSquares: Double);
var
  i, j, row, count, noSelected: Integer;
  k: Integer;
  X, Xsq: Double;
begin
  ARowSums := nil;    // to silence FPC 3.2
  ARowSumsOfSquares := nil;
  AColSums := nil;
  AColSumsOfSquares := nil;
  AColLabels := nil;
  ASelected := nil;

  noSelected := SelList.Items.Count;
  SetLength(ASelected, noSelected);
  SetLength(AColLabels, noSelected);
  SetLength(AColSums, noSelected);
  SetLength(AColSumsOfSquares, noSelected);
  SetLength(ARowSums, NoCases);
  SetLength(ARowSumsOfSquares, NoCases);

  for i := 0 to noSelected-1 do
  begin
    ASelected[i] := GetVariableIndex(OS3MainFrm.DataGrid, SelList.Items[i]);
    AColLabels[i] := SelList.Items[i];
  end;

  for i := 0 to noSelected-1 do
  begin
    AColSums[i] := 0.0;
    AColSumsOfSquares[i] := 0.0;
  end;
  for j := 0 to NoCases-1 do
  begin
    ARowSums[j] := 0.0;
    ARowSumsOfSquares[j] := 0.0;
  end;

  AGrandSum := 0;
  AGrandSumOfSquares := 0;
  count := 0;
  row := 0;

  for i := 1 to NoCases do
  begin
    if not GoodRecord(OS3MainFrm.DataGrid, i, ASelected) then continue;
    count := count + 1;
    for j := 0 to High(ASelected) do
    begin
      k := ASelected[j];
      X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[k, i]));
      Xsq := X*X;
      ARowSums[row] := ARowSums[row] + X;
      ARowSumsOfSquares[row] := ARowSumsOfSquares[row] + Xsq;
      AColSums[j] := AColSums[j] + X;
      AColSumsOfSquares[j] := AColSumsOfSquares[j] + Xsq;
      AGrandSum := AGrandSum + X;
      AGrandSumOfSquares := AGrandSumOfSquares + XSq;
    end;
    row := row + 1;
  end;

  SetLength(ARowSums, count);
  SetLength(ARowSumsOfSquares, count);
  // Lengths of AColSums etc already correct.
end;

procedure TWithinANOVAFrm.InBtnClick(Sender: TObject);
var
  i: integer;
begin
  i := 0;
  while i < VarList.Items.Count do
  begin
    if VarList.Selected[i] then
    begin
      SelList.Items.Add(VarList.Items[i]);
      VarList.Items.Delete(i);
      i := 0;
    end else
      inc(i);
  end;
  UpdateBtnStates;
end;


procedure TWithinANOVAFrm.OutBtnClick(Sender: TObject);
var
  i: integer;
begin
  i := 0;
  while i < SelList.Items.Count do
  begin
    if SelList.Selected[i] then
    begin
      VarList.Items.Add(SelList.Items[i]);
      SelList.Items.Delete(i);
      i := 0;
    end else
      inc(i);
  end;
  VarList.ItemIndex := -1;
  SelList.ItemIndex := -1;
  UpdateBtnStates;
end;


procedure TWithinANOVAFrm.Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec);
var
  ser: TChartSeries;
begin
  FChartFrame.Clear;

  FChartFrame.SetTitle('WITHIN SUBJECTS ANOVA');
  FChartFrame.SetXTitle('Repeated Measure Variables');
  FChartFrame.SetYTitle('Mean');

  ser := FChartFrame.PlotXY(ptBars, nil, ColMeans, ColLabels, nil, '', DATA_COLORS[0]);
  FChartFrame.Chart.BottomAxis.Marks.Source := ser.Source;
  FChartFrame.Chart.BottomAxis.Marks.Style := smsLabel;
  FChartFrame.Chart.Legend.Visible := false;
end;


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

  if FReliabilityReportFrame <> nil then
    FReliabilityReportFrame.Clear;
  if FTestAssumptionsReportFrame <> nil then
    FTestAssumptionsReportFrame.Clear;

  VarList.Clear;
  SelList.Clear;
  PlotChk.Checked := false;
  RelChk.Checked := false;
  AssumpChk.Checked := false;
  for i := 1 to NoVariables do
    VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);

  ReliabilityPage.TabVisible := false;
  TestAssumptionsPage.TabVisible := false;
  ChartPage.TabVisible := false;

  UpdateBtnStates;
end;


procedure TWithinANOVAFrm.SelListDblClick(Sender: TObject);
var
  index: Integer;
begin
  index := SelList.ItemIndex;
  if index > -1 then
  begin
    VarList.Items.Add(SelList.Items[index]);
    SelList.Items.Delete(index);
    UpdateBtnStates;
  end;
end;


procedure TWithinANOVAFrm.TestAssumptions(const ASelected: IntDyneVec;
  out ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
  out ADeterminant1, ADeterminant2, Chi2, AProbability: Double;
  out DF: Integer; out ErrorFound: Boolean);
var
  vcMat: DblDyneMat = nil;
  workMat: DblDyneMat = nil;
  colMeans: DblDyneVec = nil;
  colVars: DblDyneVec = nil;
  colStdDevs: DblDyneVec = nil;
  avgVar, avgCov, C2, M2: Double;
  i, j, noSelected, count: Integer;
begin
  ASampleVarCovarMat := nil;
  AssumedVarCovarMat := nil;

  ErrorFound := false;
  noSelected := Length(ASelected);
  count := NoCases;

  DF := 0;
  Chi2 := NaN;
  AProbability := NaN;

  SetLength(ASampleVarCovarMat, noSelected+1, noSelected+1);  // +1 due to augmentation in GridCovar
  SetLength(AssumedVarCovarMat, noSelected+1, noSelected+1);
  SetLength(vcMat, noSelected+1, noSelected+1);
  SetLength(workMat, noSelected+1, noSelected+1);
  SetLength(colMeans, noSelected+1);
  SetLength(colVars, noSelected+1);
  SetLength(colStdDevs, noSelected+1);

  GridCovar(noSelected, ASelected, ASampleVarCovarMat, colMeans, colVars, colStdDevs, ErrorFound, count);
  if Errorfound then
  begin
    ErrorMsg('Zero variance found for a variable.');
    exit;
  end;

  // get average of variances into workmat diagonal and average of
  // covariances into workmat off-diagonals (See Winer, pg 371)
  avgVar := 0.0;
  avgCov := 0.0;
  for i := 0 to noSelected-1 do
    vcMat[i, i] := ASampleVarCovarMat[i,i];

  for i := 0 to noSelected-2 do
  begin
    for j := i+1 to noSelected-1 do
    begin
      vcMat[i, j] := ASampleVarCovarMat[i, j];
      vcMat[j, i] := vcMat[i, j];
    end;
  end;

  for i := 0 to noSelected-1 do
    avgVar := avgVar + ASampleVarCovarMat[i, i];

  for i := 0 to NoSelected-2 do
    for j := i+1 to NoSelected-1 do
      avgCov := avgCov + ASampleVarCovarMat[i, j];

  avgVar := avgVar / noSelected;
  avgCov := avgCov / (noSelected * noSelected - 1) / 2.0;

  for i := 0 to noSelected-1 do
    workMat[i, i] := avgVar;

  for i := 0 to noSelected-2 do
  begin
    for j := i+1 to noSelected-1 do
    begin
      workMat[i, j] := avgCov;
      workMat[j, i] := workMat[i, j];
    end;
  end;

  // get determinants of SampleVarCovarMat and workMat
  Determ(vcMat, noSelected, noSelected, ADeterminant1, ErrorFound);
  if ADeterminant1 < 0.0 then ADeterminant1 := 0.0;

  Determ(workMat, noSelected, noSelected, ADeterminant2, ErrorFound);
  if ADeterminant2 < 0.0 then ADeterminant2 := 0.0;

  // Get assumed var-covariance matrix
  count := NoCases;
  GridCovar(noSelected, ASelected, AssumedVarCovarMat, colMeans, colVars, colStdDevs, ErrorFound, count);
  ErrorFound := false;
  if ((ADeterminant1 > 0.0) and (ADeterminant2 > 0.0)) then
    M2 := -(NoCases*noSelected - 1) * ln(ADeterminant1 / ADeterminant2)
  else
  begin
    M2 := 0.0;
    errorFound := true;
    ErrorMsg('A determinant <= zero was found.');
  end;

  if not ErrorFound then
  begin
    C2 := noSelected * (noSelected+1) * (noSelected + 1) * (2 * noSelected - 3);
    C2  := C2 / (6 * (count - 1) * (noSelected - 1) * (noSelected * noSelected + noSelected - 4));
    Chi2 := (1.0 - C2) * M2;
    DF := (noSelected * noSelected + noSelected - 4) div 2;
    if ((Chi2 > 0.01) and (Chi2 < 1000.0)) then
      AProbability := ChiSquaredProb(Chi2, DF)
    else
    begin
      if Chi2 <= 0.0 then AProbability := 1.0;
      if Chi2 >= 1000.0 then AProbability := 0.0;
    end;
  end;

  for i := 0 to NoSelected-1 do
    for j := 0 to NoSelected-1 do
      AssumedVarCovarMat[i,j] := workMat[i, j];
end;


procedure TWithinANOVAFrm.UpdateBtnStates;
var
  i: Integer;
  lEnabled: Boolean;
begin
  inherited;

  if FReliabilityReportFrame <> nil then
    FReliabilityReportFrame.UpdateBtnStates;
  if FTestAssumptionsReportFrame <> nil then
     FTestAssumptionsReportFrame.UpdateBtnStates;

  lEnabled := false;
  for i:=0 to VarList.Items.Count-1 do
    if VarList.Selected[i] then
    begin
      lEnabled := true;
      break;
    end;
  InBtn.Enabled := lEnabled;

  lEnabled := false;
  for i:=0 to SelList.Items.Count-1 do
    if SelList.Selected[i] then
    begin
      lEnabled := true;
      break;
    end;
  OutBtn.Enabled := lEnabled;
end;


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

  if SelList.Items.Count = 0 then
  begin
    AControl := VarList;
    AMsg := 'No variables selected.';
   exit;
  end;
  if SelList.Items.Count = 1 then
  begin
    AControl := VarList;
    AMsg := 'At least two variables must be selected.';
    exit;
  end;

  Result := true;
end;


procedure TWithinANOVAFrm.VarListDblClick(Sender: TObject);
var
  index: Integer;
begin
  index := VarList.ItemIndex;
  if index > -1 then
  begin
    SelList.Items.Add(VarList.Items[index]);
    VarList.Items.Delete(index);
    UpdateBtnStates;
  end;
end;


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


{ Write ANOVA results to ReportFrame }
procedure TWithinANOVAFrm.WriteANOVAReport(const AColLabels: StrDyneVec;
  const AColMeans, AColVariances: DblDyneVec; const AResults: TWithinANOVAResults);
var
  lReport: TStrings;
  noSelected: Integer;
  i: Integer;
begin
  noSelected := Length(AColMeans);

  lReport := TStringList.Create;
  try
    with AResults do
    begin
      lReport.Add('TREATMENTS BY SUBJECTS (AxS) ANOVA RESULTS');
      lReport.Add('');
      lReport.Add('Data File: ' + OS3MainFrm.FileNameEdit.Text);
      lReport.Add('');
      lReport.Add('-----------------------------------------------------------------');
      lReport.Add('SOURCE            DF         SS         MS         F    Prob. > F');
      lReport.Add('-----------------------------------------------------------------');
      lReport.Add('SUBJECTS        %4d %10.3f %10.3f', [DFrows, SSrows, MSrows]);
      lReport.Add('WITHIN SUBJECTS %4d %10.3f %10.3f', [DFwithinRows, SSwithinRows, MSwithinRows]);
      lReport.Add('   TREATMENTS   %4d %10.3f %10.3f %10.3f %10.3f', [DFcols, SScols, MScols, F, Probability]);
      lReport.Add('   RESIDUAL     %4d %10.3f %10.3f', [DFresidual, SSresidual, MSresidual]);
      lReport.Add('-----------------------------------------------------------------');
      lReport.Add('TOTAL           %4d %10.3f %10.3f', [DFtotal, SStotal, MStotal]);
      lReport.Add('-----------------------------------------------------------------');
      lReport.Add('');
      lReport.Add('');

      lReport.Add('TREATMENT (COLUMN) MEANS AND STANDARD DEVIATIONS');
      lReport.Add('');
      lReport.Add('VARIABLE    MEAN       STD.DEV. ');
      lReport.Add('--------  ----------  ----------');

      for i := 1 to NoSelected do
        lReport.Add('%-8s  %10.3f  %10.3f', [AColLabels[i-1], AColMeans[i-1], sqrt(AColVariances[i-1])]);

      lReport.Add('');
      lReport.Add('Mean of all scores:       %8.3f', [GrandMean]);
      lReport.Add(' with standard deviation: %8.3f', [sqrt(MStotal)]);
    end;

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


procedure TWithinANOVAFrm.WriteReliabilityReport(const R1, R2, R3, R4: double);
var
  lReport: TStrings;
begin
  lReport := TStringList.Create;
  try
    lReport.Add('RELIABILITY ESTIMATES');
    lReport.Add('');
    lReport.Add('TYPE OF ESTIMATE               VALUE ');
    lReport.Add('----------------------------  -------');
    lReport.Add('Unadjusted total reliability %7.3f', [R1]);
    lReport.Add('Unadjusted item reliability  %7.3f', [R2]);
    lReport.Add('Adjusted total (Cronbach)    %7.3f', [R3]);
    lReport.Add('Adjusted item reliability    %7.3f', [R4]);

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


procedure TWithinANOVAFrm.WriteTestAssumptionsReport(
  const ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
  const AColLabels: StrDyneVec;
  ADeterminant1, ADeterminant2, Chi2, AProbability: Double; DF: Integer;
  ErrorFound: Boolean);
var
  lReport: TStrings;
  title: String;
  noSelected: Integer;
begin
  noSelected := SelList.Items.Count;

  lReport := TStringList.Create;
  try
    lReport.Add('BOX TEST FOR HOMOGENEITY OF VARIANCE-COVARIANCE MATRIX');
    lReport.Add('');

    title := 'SAMPLE COVARIANCE MATRIX';
    MatPrint(ASampleVarCovarMat, noSelected, noSelected, title, AColLabels, AColLabels, NoCases, lReport);
    lReport.Add('');

    title := 'ASSUMED POPULATION COVARIANCE MATRIX';
    MatPrint(AssumedVarCovarMat, noSelected, noSelected, title, AColLabels, AColLabels, NoCases, lReport);
    lReport.Add('');

    lReport.Add('Determinant of variance-covariance matrix: %10.3g', [ADeterminant1]);
    lReport.Add('Determinant of homogeneity matrix:         %10.3g', [ADeterminant2]);
    if not errorfound then
    begin
      lReport.Add('ChiSquare:                                 %10.3f', [Chi2]);
      lReport.Add('  with %d degrees of freedom',                      [DF]);
      lReport.Add('Probability of larger chisquare:           %10.3f', [1.0 - AProbability]);
    end;

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

end.