unit LatinSqrsUnit; {$mode objfpc}{$H+} interface uses Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs, StdCtrls, ExtCtrls, LatinSpecsUnit, MainUnit, Globals, FunctionsLib, OutputUnit, GraphLib, MatrixLib, ContextHelpUnit; type { TLatinSqrsFrm } TLatinSqrsFrm = class(TForm) ComputeBtn: TButton; HelpBtn: TButton; CloseBtn: TButton; Plan: TRadioGroup; procedure ComputeBtnClick(Sender: TObject); procedure FormActivate(Sender: TObject); procedure FormCreate(Sender: TObject); procedure HelpBtnClick(Sender: TObject); private { private declarations } function CheckDataCol(ACol: Integer): boolean; function GetRange(ACol: Integer; out ARange, AMin, AMax: Integer): boolean; procedure Plan1; procedure Plan2; procedure Plan3; procedure Plan4; procedure Plan5; procedure Plan6; procedure Plan7; // procedure Plan8; procedure Plan9; public { public declarations } end; var LatinSqrsFrm: TLatinSqrsFrm; implementation uses Math, Utils; const NO_VALID_NUMBER_ERROR = 'No valid number in row %d of variable "%s"'; { TLatinSqrsFrm } function TLatinSqrsFrm.CheckDataCol(ACol: Integer): Boolean; var i: Integer; value: Double; begin Result := false; for i := 1 to NoCases do if not TryStrToFloat(OS3MainFrm.DataGrid.Cells[ACol, i], value) then begin ErrorMsg(NO_VALID_NUMBER_ERROR, [i, OS3MainFrm.DataGrid.Cells[ACol, 0]]); exit; end; Result := true; end; procedure TLatinSqrsFrm.ComputeBtnClick(Sender: TObject); var btn: Integer; begin btn := Plan.ItemIndex + 1; case btn of 1: Plan1; 2: Plan2; 3: Plan3; 4: Plan4; 5: Plan5; 6: Plan6; 7: Plan7; 8: Plan9; end; end; procedure TLatinSqrsFrm.FormActivate(Sender: TObject); var w: Integer; begin w := MaxValue([HelpBtn.Width, ComputeBtn.Width, CloseBtn.Width]); HelpBtn.Constraints.MinWidth := w; ComputeBtn.Constraints.MinWidth := w; CloseBtn.Constraints.MinWidth := w; end; procedure TLatinSqrsFrm.FormCreate(Sender: TObject); begin Assert(OS3MainFrm <> nil); if LatinSpecsFrm = nil then Application.CreateForm(TLatinSpecsFrm, LatinSpecsFrm); end; function TLatinSqrsFrm.GetRange(ACol: Integer; out ARange, AMin, AMax: Integer): boolean; var i: Integer; mn, mx, value: Double; begin Result := true; mn := MaxInt; mx := -MaxInt; for i := 1 to NoCases do begin if TryStrToFloat(OS3MainFrm.DataGrid.Cells[ACol, i], value) then begin if value < mn then mn := value; if value > mx then mx := value; end else begin ErrorMsg(NO_VALID_NUMBER_ERROR, [i, OS3MainFrm.DataGrid.Cells[ACol, 0]]); Result := false; exit; end; end; AMin := round(mn); AMax := round(mx); ARange := AMax - AMin + 1; end; procedure TLatinSqrsFrm.HelpBtnClick(Sender: TObject); begin if ContextHelpForm = nil then Application.CreateForm(TContextHelpForm, ContextHelpForm); ContextHelpForm.HelpMessage((Sender as TButton).tag); end; procedure TLatinSqrsFrm.Plan1; var n: integer; // no. of subjects per cell Acol, Bcol, Ccol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; FactorC: string; DataVar: string; cellstring: string; i, j, rangeA, rangeB, rangeC, mn, mx: integer; cellcnts: IntDyneMat; celltotals: DblDyneMat; Ctotals: DblDyneVec; design: StrDyneMat; G, term1, term2, term3, term4, term5, term6, sumxsqr: double; sumAsqr, sumBsqr, sumCsqr, sumABCsqr, SSA, SSB, SSC: double; SSwithin, SSres, SStotal: double; MSa, MSb, MSc, MSres, MSwithin: double; data, GrandMean: double; p, row, col, slice: integer; dfa, dfb, dfc, dfres, dfwithin, dftotal, fa, fb, fc, fpartial: double; proba, probb, probc, probpartial: double; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(1); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and C if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not CheckDataCol(Datacol) then exit; // check for squareness if (rangeA <> rangeB) or (rangeA <> rangeC) or (rangeB <> rangeC) then begin ErrorMsg('In a Latin square the range of values should all be equal.'); exit; end; p := rangeA; // set up an array for cell counts and for cell sums and marginal sums SetLength(cellcnts, rangeA+1, rangeB+1); SetLength(celltotals, rangeA+1, rangeB+1); SetLength(Ctotals, rangeC+1); SetLength(Design, rangeA, rangeB); // initialize arrays and values for i := 0 to rangeA do for j := 0 to rangeB do begin cellcnts[i,j] := 0; celltotals[i,j] := 0.0; end; for i := 0 to rangeC-1 do Ctotals[i] := 0; G := 0.0; sumxsqr := 0.0; sumAsqr := 0.0; sumBsqr := 0.0; sumCsqr := 0.0; sumABCsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; GrandMean := 0.0; // Read in the data for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrTofloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[row-1,col-1] := cellcnts[row-1,col-1] + 1; celltotals[row-1,col-1] := celltotals[row-1,col-1] + data; Ctotals[slice-1] := Ctotals[slice-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do begin if cellcnts[i,j] <> n then begin ErrorMsg('Cell sizes are not equal.'); exit; end; end; // calculate values for i := 0 to p - 1 do // get row and column sums begin for j := 0 to p-1 do begin celltotals[i,p] := celltotals[i,p] + celltotals[i,j]; celltotals[p,j] := celltotals[p,j] + celltotals[i,j]; sumABCsqr := sumABCsqr + (celltotals[i,j] * celltotals[i,j]); end; end; for i := 0 to p-1 do G := G + Ctotals[i]; term1 := (G * G) / (n * p * p); term2 := sumxsqr; for i := 0 to p-1 do // sum of squared A's sumAsqr := sumAsqr + (celltotals[i,p] * celltotals[i,p]); for i := 0 to p-1 do // sum of squared B's sumBsqr := sumBsqr + (celltotals[p,i] * celltotals[p,i]); for i := 0 to p-1 do // sum of squared C's sumCsqr := sumCsqr + (Ctotals[i] * Ctotals[i]); term3 := sumAsqr / (n * p); term4 := sumBsqr / (n * p); term5 := sumCsqr / (n * p); term6 := sumABCsqr / n; SSA := term3 - term1; SSB := term4 - term1; SSC := term5 - term1; SSwithin := term2 - term6; SSres := term6 - term3 - term4 - term5 + 2 * term1; SStotal := SSA + SSB + SSC + SSres + SSwithin; dfa := p-1; dfb := p-1; dfc := p-1; dfres := (p-1) * (p-2); dfwithin := (p * p) * (n - 1); dftotal := n * p * p - 1; MSa := SSA / dfa; MSb := SSB / dfb; MSc := SSC / dfc; MSres := SSres / dfres; MSwithin := SSwithin / dfwithin; fa := MSa / MSwithin; fb := MSb / MSwithin; fc := MSc / MSwithin; fpartial := MSres / MSwithin; proba := probf(fa,dfa,dfwithin); probb := probf(fb,dfb,dfwithin); probc := probf(fc,dfc,dfwithin); probpartial := probf(fpartial,dfres,dfwithin); // show ANOVA table results lReport := TStringList.Create; try lReport.Add('LATIN SQUARE ANALYSIS Plan 1 Results'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSA, dfa, MSa, fa, proba]); lReport.Add('Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSB, dfb, MSb, fb, probb]); lReport.Add('Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSC, dfc, MSc, fc, probc]); lReport.Add('Residual %9.3f %9.0f %9.3f %9.3f %9.3f',[SSres, dfres, MSres, fpartial, probpartial]); lReport.Add('Within %9.3f %9.0f %9.3f', [SSwithin, dfwithin, MSwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design lReport.Add(''); lReport.Add('Experimental Design'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ',[i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add('%10s', [FactorA]); for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); Design[row-1, col-1] := 'C' + IntToStr(slice); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ',[i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); // show table cell means for i := 0 to p-1 do for j := 0 to p-1 do celltotals[i,j] := celltotals[i,j] / n; for i := 0 to p-1 do begin celltotals[i,p] := celltotals[i,p] / (p * n); celltotals[p,i] := celltotals[p,i] / (p * n); end; GrandMean := GrandMean / (p * p * n); for i := 0 to p-1 do Ctotals[i] := Ctotals[i] / (p * n); lReport.Add(''); lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [celltotals[i,j]]); cellstring := cellstring + Format(' %8.3f ', [celltotals[i,p]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [celltotals[p,j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // show category means lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorC]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Ctotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellString); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; Design := nil; Ctotals := nil; celltotals := nil; cellcnts := nil; end; end; procedure TLatinSqrsFrm.Plan2; var n: integer; // no. of subjects per cell Acol, Bcol, Ccol, Dcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; FactorC: string; FactorD: string; DataVar: string; cellstring: string; i, j, k: integer; rangeA, rangeB, rangeC, rangeD: integer; mn, mx, minD: Integer; cellcnts: IntDyneCube; celltotals: DblDyneCube; Ctotals: DblDyneVec; design: StrDyneMat; G, term1, term2, term3, term4, term5, term6, term7, term8: double; term9, sumxsqr: double; sumAsqr, sumBsqr, sumCsqr, sumDsqr, SSA, SSB, SSC, SSD: double; sumADsqr, sumBDsqr, sumCDsqr: double; ADmat, BDmat, CDmat: DblDyneMat; SSAD, SSBD, SSCD, SSwithin, SSres, SStotal: double; MSa, MSb, MSc, MSd, MSAD, MSBD, MSCD, MSres, MSwithin: double; data, GrandMean: double; p, row, col, slice, block: integer; dfa, dfb, dfc, dfres, dfwithin, dftotal, fa, fb, fc, fpartial: double; dfd, fd, fad, fbd, fcd, dfad, dfbd, dfcd: double; proba, probb, probc, probd, probpartial: double; probad, probbd, probcd: double; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(2); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; FactorD := LatinSpecsFrm.DCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = FactorD) then Dcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and C if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not GetRange(DCol, rangeD, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; minD := mn; p := rangeA; // check for squareness if (rangeA <> rangeB) or (rangeA <> rangeC) or (rangeB <> rangeC) then begin ErrorMsg('In a Latin square the range of values should all be equal.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(cellcnts, rangeA+1, rangeB+1, rangeD+1); SetLength(celltotals, rangeA+1, rangeB+1, rangeD+1); SetLength(ADmat, rangeA+1, rangeD+1); SetLength(BDmat, rangeB+1, rangeD+1); SetLength(CDmat, rangeC+1, rangeD+1); SetLength(Ctotals, rangeC+1); SetLength(Design, rangeA, rangeB); // initialize arrays and values for i := 0 to rangeA do for j := 0 to rangeB do for k := 0 to rangeD do begin cellcnts[i, j, k] := 0; celltotals[i, j, k] := 0.0; end; for i := 0 to rangeA do for j := 0 to rangeD do ADmat[i,j] := 0.0; for i := 0 to rangeB do for j := 0 to rangeD do BDmat[i,j] := 0.0; for i := 0 to rangeC do for j := 0 to rangeD do CDmat[i,j] := 0.0; for i := 0 to rangeC-1 do Ctotals[i] := 0; G := 0.0; sumxsqr := 0.0; sumAsqr := 0.0; sumBsqr := 0.0; sumCsqr := 0.0; sumDsqr := 0.0; sumADsqr := 0.0; sumBDsqr := 0.0; sumCDsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; term8 := 0.0; term9 := 0.0; GrandMean := 0.0; SSwithin := 0.0; // Read in the data for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); block := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Dcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[row-1,col-1,block-1] := cellcnts[row-1,col-1,block-1] + 1; celltotals[row-1,col-1,block-1] := celltotals[row-1,col-1,block-1] + data; ADmat[row-1,block-1] := ADmat[row-1,block-1] + data; BDmat[col-1,block-1] := BDmat[col-1,block-1] + data; CDmat[slice-1,block-1] := CDmat[slice-1,block-1] + data; Ctotals[slice-1] := Ctotals[slice-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to rangeD - 1 do if cellcnts[i,j,k] <> n then begin ErrorMsg('Cell sizes are not equal.'); exit; end; // calculate values for i := 0 to p - 1 do // get row, column and block sums for j := 0 to p-1 do for k := 0 to rangeD - 1 do begin celltotals[i,p,k] := celltotals[i,p,k] + celltotals[i,j,k]; celltotals[p,j,k] := celltotals[p,j,k] + celltotals[i,j,k]; celltotals[i,j,rangeD] :=celltotals[i,j,rangeD] + celltotals[i,j,k]; end; // get interaction AD for i := 0 to rangeA-1 do for j := 0 to rangeD-1 do begin sumADsqr := sumADsqr + (ADmat[i,j] * ADmat[i,j]); ADmat[i,rangeD] := ADmat[i,rangeD] + ADmat[i,j]; ADmat[rangeA,j] := ADmat[rangeA,j] + ADmat[i,j]; end; for i := 0 to rangeA-1 do sumAsqr := sumAsqr + (ADmat[i,rangeD] * ADmat[i,rangeD]); for i := 0 to rangeD-1 do sumDsqr := sumDsqr + (ADmat[rangeA,i] * ADmat[rangeA,i]); // get interaction BD for i := 0 to rangeB-1 do for j := 0 to rangeD-1 do begin sumBDsqr := sumBDsqr + (BDmat[i,j] * BDmat[i,j]); BDmat[i,rangeD] := BDmat[i,rangeD] + BDmat[i,j]; BDmat[rangeB,j] := BDmat[rangeB,j] + BDmat[i,j]; end; for i := 0 to rangeB-1 do sumBsqr := sumBsqr + (BDmat[i,rangeD] * BDmat[i,rangeD]); // get interaction CD for i := 0 to rangeC-1 do for j := 0 to rangeD-1 do begin sumCDsqr := sumCDsqr + (CDmat[i,j] * CDmat[i,j]); CDmat[i,rangeD] := CDmat[i,rangeD] + CDmat[i,j]; CDmat[rangeC,j] := CDmat[rangeC,j] + CDmat[i,j]; end; for i := 0 to rangeC-1 do sumCsqr := sumCsqr + (CDmat[i,rangeD] * CDmat[i,rangeD]); G := GrandMean; term1 := (G * G) / (n * p * p * rangeD); term2 := sumxsqr; term3 := sumAsqr / (n * p * rangeD); term4 := sumBsqr / (n * p * rangeD); term5 := sumCsqr / (n * p * rangeD); term6 := sumADsqr / (n * p); term7 := SumBDsqr / (n * p); term8 := SumCDsqr / (n * p); term9 := sumDsqr / (n * p * p); SSA := term3 - term1; SSD := term9 - term1; SSAD := term6 - term3 - term9 + term1; SSB := term4 - term1; SSBD := term7 - term4 - term9 + term1; SSC := term5 - term1; SSCD := term8 - term5 - term9 + term1; // get ss within for i := 0 to rangeA - 1 do for j := 0 to rangeB - 1 do for k := 0 to rangeD - 1 do SSwithin := SSwithin + (celltotals[i,j,k] * celltotals[i,j,k]); SSwithin := sumXsqr - (SSwithin / n); // get SS residual SStotal := sumXsqr - term1; SSres := SStotal - SSA - SSB - SSC - SSD - SSAD - SSBD - SSCD - SSwithin; dfa := p-1; dfb := p-1; dfc := p-1; dfd := rangeD - 1; dfad := (p-1) * (rangeD - 1); dfbd := dfad; dfcd := dfad; dfres := rangeD * (p-1) * (p-2); dfwithin := (p * p) * rangeD * (n - 1); dftotal := n * p * p * rangeD - 1; MSa := SSA / dfa; MSb := SSB / dfb; MSc := SSC / dfc; MSd := SSD / dfd; MSad := SSAD / dfad; MSbd := SSBD / dfbd; MScd := SSCD / dfcd; MSres := SSres / dfres; MSwithin := SSwithin / dfwithin; fa := MSa / MSwithin; fb := MSb / MSwithin; fc := MSc / MSwithin; fd := MSd / MSwithin; fad := MSad / MSwithin; fbd := MSbd / MSwithin; fcd := MScd / MSwithin; fpartial := MSres / MSwithin; proba := ProbF(fa, dfa, dfwithin); probb := ProbF(fb, dfb, dfwithin); probc := ProbF(fc, dfc, dfwithin); probd := ProbF(fd, dfd, dfwithin); probad := ProbF(fad, dfad, dfwithin); probbd := ProbF(fbd, dfbd, dfwithin); probcd := ProbF(fcd, dfcd, dfwithin); probpartial := ProbF(fpartial, dfres, dfwithin); // show ANOVA table results lReport := TStringList.Create; try lReport.Add(''); lReport.Add('LATIN SQUARE ANALYSIS Plan 2 Results'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSA, dfa, MSa, fa, proba]); lReport.Add('Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSB, dfb, MSb, fb, probb]); lReport.Add('Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSC, dfc, MSc, fc, probc]); lReport.Add('Factor D %9.3f %9.0f %9.3f %9.3f %9.3f', [SSD, dfd, MSd, fd, probd]); lReport.Add('A x D %9.3f %9.0f %9.3f %9.3f %9.3f', [SSAD, dfad, MSad, fad, probad]); lReport.Add('B x D %9.3f %9.0f %9.3f %9.3f %9.3f', [SSBD, dfbd, MSbd, fbd, probbd]); lReport.Add('C x D %9.3f %9.0f %9.3f %9.3f %9.3f', [SSCD, dfcd, MScd, fcd, probcd]); lReport.Add('Residual %9.3f %9.0f %9.3f %9.3f %9.3f', [SSres, dfres, MSres, fpartial, probpartial]); lReport.Add('Within %9.3f %9.0f %9.3f', [SSwithin, dfwithin, MSwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for each block for k := 0 to rangeD - 1 do begin lReport.Add(''); lReport.Add('Experimental Design for block %d', [k+1]); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ',[i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add('%10s', [FactorA]); for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol, i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol, i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol, i])); block := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Dcol, i])); if block = minD + k then Design[row-1, col-1] := 'C' + IntToStr(slice); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); end; // get cell means for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to rangeD - 1 do celltotals[i,j,k] := celltotals[i,j,k] / n; for i := 0 to p-1 do for k := 0 to rangeD - 1 do begin celltotals[i,p,k] := celltotals[i,p,k] / (p * n); celltotals[p,i,k] := celltotals[p,i,k] / (p * n); end; GrandMean := GrandMean / (p * p * n * rangeD); for i := 0 to p-1 do Ctotals[i] := Ctotals[i] / (p * n * rangeD); // show table of means for each block for k := 0 to rangeD-1 do begin lReport.Add(''); lReport.Add('BLOCK %d', [k+1]); lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ',[i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [celltotals[i, j, k]]); cellstring := cellstring + Format(' %8.3f ', [celltotals[i, p, k]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [celltotals[p, j, k]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); end; // show category means lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorC]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Ctotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; Design := nil; Ctotals := nil; CDmat := nil; BDmat := nil; ADmat := nil; celltotals := nil; cellcnts := nil; end; end; procedure TLatinSqrsFrm.Plan3; var n : integer; // no. of subjects per cell Acol, Bcol, Ccol, Dcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; FactorC: string; FactorD: string; DataVar: string; cellstring: string; i, j, k, m: integer; rangeA, rangeB, rangeC, rangeD: integer; minD, mn, mx: Integer; cellcnts: IntDyneCube; celltotals: DblDyneQuad; ABmat, ACmat, BCmat: DblDyneMat; ABCmat: DblDyneCube; Atotals: DblDyneVec; Btotals: DblDyneVec; Ctotals: DblDyneVec; Dtotals: DblDyneVec; design: StrDyneMat; G, term1, term2, term3, term4, term5, term6, term7, term8: double; term9, term10, sumxsqr: double; sumAsqr, sumBsqr, sumCsqr, sumDsqr, SSA, SSB, SSC, SSD: double; sumABsqr, sumACsqr, sumBCsqr, sumABCsqr: double; SSAB, SSAC, SSBC, SSABC, SSwithin, SStotal: double; MSa, MSb, MSc, MSd, MSAB, MSAC, MSBC, MSABC, MSwithin: double; data, GrandMean: double; p, row, col, slice, block: integer; dfa, dfb, dfc, dfwithin, dftotal, fa, fb, fc: double; dfd, fd, fab, fac, fbc, fabc, dfab, dfac, dfbc, dfabc: double; proba, probb, probc, probd: double; probab, probac, probbc, probabc: double; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(3); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; FactorD := LatinSpecsFrm.DCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = FactorD) then Dcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and C if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not GetRange(DCol, rangeD, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; minD := mn; p := rangeA; // check for squareness if (rangeA <> rangeB) or (rangeA <> rangeC) or (rangeB <> rangeC) or (rangeA <> rangeD) then begin ErrorMsg('In a Latin square the range of values should all be equal.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(cellcnts, p+1, p+1, p+1); SetLength(celltotals, p+1, p+1, p+1, p+1); SetLength(ABmat, p+1, p+1); SetLength(ACmat, p+1, p+1); SetLength(BCmat, p+1, p+1); SetLength(ABCmat, p+1, p+1, p+1); SetLength(Atotals, p); SetLength(Btotals, p); SetLength(Ctotals, p); SetLength(Dtotals, p); SetLength(Design,p, p); // initialize arrays and values for i := 0 to p do for j := 0 to p do for k := 0 to p do for m := 0 to p do celltotals[i,j,k,m] := 0.0; for i := 0 to p do for j := 0 to p do begin ABmat[i,j] := 0.0; ACmat[i,j] := 0.0; BCmat[i,j] := 0.0; end; for i := 0 to p do for j := 0 to p do for k := 0 to p do begin ABCmat[i,j,k] := 0.0; cellcnts[i,j,k] := 0; end; for i := 0 to p-1 do begin Atotals[i] := 0.0; Btotals[i] := 0.0; Ctotals[i] := 0.0; Dtotals[i] := 0.0; end; G := 0.0; sumxsqr := 0.0; sumAsqr := 0.0; sumBsqr := 0.0; sumCsqr := 0.0; sumDsqr := 0.0; sumABsqr := 0.0; sumACsqr := 0.0; sumBCsqr := 0.0; sumABCsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; term8 := 0.0; term9 := 0.0; term10 := 0.0; GrandMean := 0.0; SSwithin := 0.0; // Read in the data for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); block := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Dcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[row-1,col-1,slice-1] := cellcnts[row-1,col-1,slice-1] + 1; celltotals[row-1,col-1,slice-1,block-1] := celltotals[row-1,col-1,slice-1,block-1] + data; ABmat[row-1,col-1] := ABmat[row-1,col-1] + data; ACmat[row-1,slice-1] := ACmat[row-1,slice-1] + data; BCmat[col-1,slice-1] := BCmat[col-1,slice-1] + data; ABCmat[row-1,col-1,slice-1] := ABCmat[row-1,col-1,slice-1] + data; Atotals[row-1] := Atotals[row-1] + data; Btotals[col-1] := Btotals[col-1] + data; Ctotals[slice-1] := Ctotals[slice-1] + data; Dtotals[block-1] := Dtotals[block-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts in ABCmat for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to p - 1 do if cellcnts[i,j,k] <> n then begin ErrorMsg('Cell sizes are not equal.'); exit; end; // calculate values for i := 0 to p - 1 do // get row, column, slice and block sums for j := 0 to p-1 do for k := 0 to p - 1 do for m := 0 to p - 1 do begin celltotals[p,j,k,m] := celltotals[p,j,k,m] + celltotals[i,j,k,m]; celltotals[i,p,k,m] := celltotals[i,p,k,m] + celltotals[i,j,k,m]; celltotals[i,j,p,m] := celltotals[i,j,p,m] + celltotals[i,j,k,m]; celltotals[i,j,k,p] := celltotals[i,j,k,p] + celltotals[i,j,k,m]; end; for i := 0 to p - 1 do // get row, column and slice sums in ABC matrix for j := 0 to p-1 do for k := 0 to p-1 do begin ABCmat[p,j,k] := ABCmat[p,j,k] + ABCmat[i,j,k]; ABCmat[i,p,k] := ABCmat[i,p,k] + ABCmat[i,j,k]; ABCmat[i,j,p] := ABCmat[i,j,p] + ABCmat[i,j,k]; end; // get 2-way interactions for i := 0 to p-1 do for j := 0 to p-1 do begin sumABsqr := sumABsqr + (ABmat[i,j] * ABmat[i,j]); sumACsqr := sumACsqr + (ACmat[i,j] * ACmat[i,j]); sumBCsqr := SumBCsqr + (BCmat[i,j] * BCmat[i,j]); ABmat[i,p] := ABmat[i,p] + ABmat[i,j]; ABmat[p,j] := ABmat[p,j] + ABmat[i,j]; ACmat[i,p] := ACmat[i,p] + ACmat[i,j]; ACmat[p,j] := ACmat[p,j] + ACmat[i,j]; BCmat[i,p] := BCmat[i,p] + BCmat[i,j]; BCmat[p,j] := BCmat[p,j] + BCmat[i,j]; for k := 0 to p-1 do sumABCsqr := sumABCsqr + (ABCmat[i,j,k] * ABCmat[i,j,k]); end; for i := 0 to p-1 do begin sumAsqr := sumAsqr + (Atotals[i] * Atotals[i]); sumBsqr := sumBsqr + (Btotals[i] * Btotals[i]); SumCsqr := sumCsqr + (Ctotals[i] * Ctotals[i]); sumDsqr := sumDsqr + (Dtotals[i] * Dtotals[i]); end; G := GrandMean; term1 := (G * G) / (n * p * p * p); term2 := sumxsqr; term3 := sumAsqr / (n * p * p); term4 := sumBsqr / (n * p * p); term5 := sumCsqr / (n * p * p); term9 := sumDsqr / (n * p * p); term6 := sumABsqr / (n * p); term7 := SumACsqr / (n * p); term8 := SumBCsqr / (n * p); term10 := sumABCsqr / n; SSA := term3 - term1; SSB := term4 - term1; SSC := term5 - term1; SSD := term9 - term1; SSAB := term6 - term3 - term4 + term1; SSAC := term7 - term3 - term5 + term1; SSBC := term8 - term4 - term5 + term1; SSABC := term10 - term6 - term7 - term8 + term3 + term4 + term5 - term1; SSABC := SSABC - (term9 - term1); // get ss within for i := 0 to p - 1 do for j := 0 to p - 1 do for k := 0 to p - 1 do for m := 0 to p - 1 do SSwithin := SSwithin + (celltotals[i,j,k,m] * celltotals[i,j,k,m]); SSwithin := sumXsqr - (SSwithin / n); // get SS residual SStotal := sumXsqr - term1; dfa := p-1; dfb := p-1; dfc := p-1; dfd := p-1; dfab := (p - 1) * (p - 1); dfac := dfab; dfbc := dfab; dfabc := (p-1) * (p-1) * (p-1) - (p-1); dfwithin := p * p * p * (n - 1); dftotal := n * p * p * p - 1; MSa := SSA / dfa; MSb := SSB / dfb; MSc := SSC / dfc; MSd := SSD / dfd; MSab := SSAB / dfab; MSac := SSAC / dfac; MSbc := SSBC / dfbc; MSabc := SSABC / dfabc; // MSres := SSres / dfres; MSwithin := SSwithin / dfwithin; fa := MSa / MSwithin; fb := MSb / MSwithin; fc := MSc / MSwithin; fd := MSd / MSwithin; fab := MSab / MSwithin; fac := MSac / MSwithin; fbc := MSbc / MSwithin; fabc := MSabc / MSwithin; proba := ProbF(fa,dfa,dfwithin); probb := ProbF(fb,dfb,dfwithin); probc := ProbF(fc,dfc,dfwithin); probd := ProbF(fd,dfd,dfwithin); probab := ProbF(fab,dfab,dfwithin); probac := ProbF(fac,dfac,dfwithin); probbc := ProbF(fbc,dfbc,dfwithin); probabc := ProbF(fabc,dfabc,dfwithin); // show ANOVA table results lReport := TStringList.Create; try lReport.Add('LATIN SQUARE ANALYSIS Plan 3 Results'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSA, dfa, MSa, fa, proba]); lReport.Add('Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSB, dfb, MSb, fb, probb]); lReport.Add('Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSC, dfc, MSc, fc, probc]); lReport.Add('Factor D %9.3f %9.0f %9.3f %9.3f %9.3f', [SSD, dfd, MSd, fd, probd]); lReport.Add('A x B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSAB, dfab, MSab, fab, probab]); lReport.Add('A x C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSAC, dfac, MSac, fac, probac]); lReport.Add('B x C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSBC, dfbc, MSbc, fbc, probbc]); lReport.Add('A x B x C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSABC, dfabc, MSabc, fabc, probabc]); lReport.Add('Within %9.3f %9.0f %9.3f', [SSwithin, dfwithin, MSwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for each block for k := 0 to rangeD - 1 do begin lReport.Add(''); lReport.Add('Experimental Design for block %d', [k+1]); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add('%10s', [FactorA]); for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); block := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Dcol,i])); if block = minD + k then Design[row-1,col-1] := 'C' + IntToStr(slice); end; for i := 0 to p - 1 do begin cellstring := format(' %3d ',[i+1]); for j := 0 to p - 1 do cellstring := cellstring + format('%5s',[Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); end; // get cell means for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to p - 1 do for m := 0 to p - 1 do celltotals[i,j,k,m] := celltotals[i,j,k,m] / n; for i := 0 to p-1 do begin for j := 0 to p - 1 do begin for k := 0 to p - 1 do begin for m := 0 to p - 1 do begin celltotals[p,j,k,m] := celltotals[p,j,k,m] / (p * n); celltotals[i,p,k,m] := celltotals[i,p,k,m] / (p * n); celltotals[i,j,p,m] := celltotals[i,j,p,m] / (p * n); celltotals[i,j,k,p] := celltotals[i,j,k,p] / (p * n); end; end; end; end; for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to p-1 do ABCmat[i,j,k] := ABCmat[i,j,k] / n; for j := 0 to p-1 do for k := 0 to p-1 do ABCmat[p,j,k] := ABCmat[p,j,k] / (p * n); for i := 0 to p-1 do for k := 0 to p-1 do ABCmat[i,p,k] := ABCmat[i,p,k] / (p * n); for i := 0 to p - 1 do for j := 0 to p - 1 do ABCmat[i,j,p] := ABCmat[i,j,p] / (p * n); GrandMean := GrandMean / (p * p * p * n ); for i := 0 to p-1 do begin Atotals[i] := Atotals[i] / (p * p * n); Btotals[i] := Btotals[i] / (p * p * n); Ctotals[i] := Ctotals[i] / (p * p * n); Dtotals[i] := Dtotals[i] / (p * p * n); end; // show table of means for each block for k := 0 to p-1 do begin lReport.Add(''); lReport.Add('BLOCK %d', [k+1]); lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + format(' %3d ',[i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add('%10s', [FactorA]); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [ABCmat[i,j,k]]); cellstring := cellstring + Format(' %8.3f ', [ABCmat[i,p,k]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [ABCmat[p,j,k]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); end; // show category means lReport.Add(''); lReport.Add('Means for each variable'); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Atotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Btotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorC]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Ctotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorD]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Dtotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally LReport.Free; Design := nil; Dtotals := nil; Ctotals := nil; Btotals := nil; Atotals := nil; ABmat := nil; ACmat := nil; BCmat := nil; ABCmat := nil; celltotals := nil; cellcnts := nil; end; end; procedure TLatinSqrsFrm.Plan4; var n: integer; // no. of subjects per cell Acol, Bcol, Ccol, Dcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; FactorC: string; FactorD: string; DataVar: string; cellstring: string; i, j, k: integer; rangeA, rangeB, rangeC, rangeD: integer; mn, mx: Integer; cellcnts: IntDyneMat; ABmat: DblDyneMat; ABCmat: DblDyneCube; Atotals: DblDyneVec; Btotals: DblDyneVec; Ctotals: DblDyneVec; Dtotals: DblDyneVec; design: StrDyneMat; G, term1, term2, term3, term4, term5, term6, term7: double; sumxsqr: double; sumAsqr, sumBsqr, sumCsqr, sumDsqr, SSA, SSB, SSC, SSD: double; SSwithin, SSres, SStotal: double; MSa, MSb, MSc, MSd, MSres, MSwithin: double; data, GrandMean: double; p, row, col, slice, block: integer; dfa, dfb, dfc, dfres, dfwithin, dftotal, fa, fb, fc: double; dfd, fd, fres: double; proba, probb, probc, probd, probres: double; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(4); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; FactorD := LatinSpecsFrm.DCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = FactorD) then Dcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and C if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not GetRange(DCol, rangeD, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; p := rangeA; // check for squareness if (rangeA <> rangeB) or (rangeA <> rangeC) or (rangeB <> rangeC) then begin ErrorMsg('In a Latin square the range of values should be equal for A,B and C.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(ABmat, p+1, p+1); SetLength(ABCmat, p+1, p+1, p+1); SetLength(cellcnts, p+1, p+1); SetLength(Atotals, p); SetLength(Btotals, p); SetLength(Ctotals, p); SetLength(Dtotals, p); SetLength(Design, p, p); for i := 0 to p do for j := 0 to p do for k := 0 to p do ABCmat[i,j,k] := 0.0; for i := 0 to p-1 do for j := 0 to p-1 do begin cellcnts[i,j] := 0; ABmat[i,j] := 0.0; end; for i := 0 to p-1 do begin Atotals[i] := 0.0; Btotals[i] := 0.0; Ctotals[i] := 0.0; Dtotals[i] := 0.0; end; G := 0.0; sumxsqr := 0.0; sumAsqr := 0.0; sumBsqr := 0.0; sumCsqr := 0.0; sumDsqr := 0.0; SSwithin := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; GrandMean := 0.0; // Read in the data for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); block := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Dcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[row-1,col-1] := cellcnts[row-1,col-1] + 1; ABCmat[row-1,col-1,slice-1] := ABCmat[row-1,col-1,slice-1] + data; Atotals[row-1] := Atotals[row-1] + data; Btotals[col-1] := Btotals[col-1] + data; Ctotals[slice-1] := Ctotals[slice-1] + data; Dtotals[block-1] := Dtotals[block-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // collapse c's into a x b for k := 0 to p-1 do for i := 0 to p-1 do for j := 0 to p-1 do ABmat[i,j] := ABmat[i,j] + ABCmat[i,j,k]; // get sum of squared cells for i := 0 to p - 1 do for j := 0 to p - 1 do SSwithin := SSwithin + (ABmat[i,j] * ABmat[i,j]); // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do if cellcnts[i,j] <> n then begin ErrorMsg('Cell sizes are not equal,'); Exit; end; for i := 0 to p-1 do begin sumAsqr := sumAsqr + (Atotals[i] * Atotals[i]); sumBsqr := sumBsqr + (Btotals[i] * Btotals[i]); sumCsqr := sumCsqr + (Ctotals[i] * Ctotals[i]); sumDsqr := sumDsqr + (Dtotals[i] * Dtotals[i]); end; G := GrandMean; term1 := (G * G) / (n * p * p); term2 := sumxsqr; term3 := sumAsqr / (n * p); term4 := sumBsqr / (n * p); term5 := sumCsqr / (n * p); term6 := sumDsqr / (n * p); term7 := SSwithin / n; SSA := term3 - term1; SSB := term4 - term1; SSC := term5 - term1; SSD := term6 - term1; SSres := term7 - term3 - term4 - term5 - term6 + 3 * term1; SSwithin := term2 - term7; SStotal := term2 - term1; dfa := p-1; dfb := p-1; dfc := p-1; dfd := p-1; dfres := (p-1) * (p-3); dfwithin := p * p * (n - 1); dftotal := n * p * p - 1; MSa := SSA / dfa; MSb := SSB / dfb; MSc := SSC / dfc; MSd := SSD / dfd; if dfres > 0 then MSres := SSres / dfres; MSwithin := SSwithin / dfwithin; fa := MSa / MSwithin; fb := MSb / MSwithin; fc := MSc / MSwithin; fd := MSd / MSwithin; if dfres > 0 then fres := MSres / MSwithin; proba := probf(fa,dfa,dfwithin); probb := probf(fb,dfb,dfwithin); probc := probf(fc,dfc,dfwithin); probd := probf(fd,dfd,dfwithin); if dfres > 0 then probres := probf(fres,dfres,dfwithin); // show ANOVA table results lReport := TStringList.Create; try lReport.Add('GRECO-LATIN SQUARE ANALYSIS (No Interactions)'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSA, dfa, MSa, fa, proba]); lReport.Add('Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSB, dfb, MSb, fb, probb]); lReport.Add('Latin Sqr.%9.3f %9.0f %9.3f %9.3f %9.3f', [SSC, dfc, MSc, fc, probc]); lReport.Add('Greek Sqr.%9.3f %9.0f %9.3f %9.3f %9.3f', [SSD, dfd, MSd, fd, probd]); if dfres > 0 then lReport.Add('Residual %9.3f %9.0f %9.3f %9.3f %9.3f', [SSres, dfres, MSres, fres, probres]) else lReport.Add('Residual - - - - -'); lReport.Add('Within %9.3f %9.0f %9.3f', [SSwithin, dfwithin, MSwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for Latin Square lReport.Add(''); lReport.Add('Experimental Design for Latin Square '); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add('%10s', [FactorA]); for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); Design[row-1,col-1] := 'C' + IntToStr(slice); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); // show design for Greek Square lReport.Add(''); lReport.Add('Experimental Design for Greek Square '); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); lReport.Add(cellstring); for i := 1 to NoCases do begin row := StrToInt(OS3MainFrm.DataGrid.Cells[Acol,i]); col := StrToInt(OS3MainFrm.DataGrid.Cells[Bcol,i]); block := StrToInt(OS3MainFrm.DataGrid.Cells[Dcol,i]); Design[row-1,col-1] := 'C' + IntToStr(block); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); for i := 0 to p-1 do begin for j := 0 to p - 1 do begin ABmat[i,p] := ABmat[i,p] + ABmat[i,j]; ABmat[p,j] := ABmat[p,j] + ABmat[i,j]; end; end; for i := 0 to p-1 do for j := 0 to p-1 do ABmat[i,j] := ABmat[i,j] / n; for i := 0 to p-1 do ABmat[i,p] := ABmat[i,p] / (n * p); for j := 0 to p-1 do ABmat[p,j] := ABmat[p,j] / (n * p); GrandMean := GrandMean / (p * p * n ); for i := 0 to p-1 do begin Atotals[i] := Atotals[i] / (p * n); Btotals[i] := Btotals[i] / (p * n); Ctotals[i] := Ctotals[i] / (p * n); Dtotals[i] := Dtotals[i] / (p * n); end; // show table of means for ABmat lReport.Add(''); lReport.Add('Cell means and totals'); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[i,j]]); cellstring := cellstring + Format(' %8.3f ', [ABmat[i,p]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[p,j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // show category means lReport.Add(''); lReport.Add('Means for each variable'); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Atotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Btotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorC]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Ctotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to rangeD + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorD]); for i := 1 to rangeD do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to rangeD + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to rangeD - 1 do cellstring := cellstring + Format(' %8.3f ', [Dtotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to rangeD + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; Design := nil; Dtotals := nil; Ctotals := nil; Btotals := nil; Atotals := nil; cellcnts := nil; ABCmat := nil; ABmat := nil; end; end; procedure TLatinSqrsFrm.Plan5; var n: integer; // no. of subjects per cell Acol, Bcol, SbjCol, Grpcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; SubjectFactor: string; GroupFactor: string; DataVar: string; cellstring: string; i, j, k: integer; mn, mx: Integer; rangeA, rangeB, rangeGrp: integer; cellcnts: IntDyneMat; ABmat: DblDyneMat; ABCmat: DblDyneCube; GBmat: DblDyneMat; Atotals: DblDyneVec; Btotals: DblDyneVec; Grptotals: DblDyneVec; Subjtotals: DblDyneMat; design: StrDyneMat; term1, term2, term3, term4, term5, term6, term7: double; sumxsqr: double; SSbetsubj, SSgroups, SSsubwGrps, SSwithinsubj, SSa, SSb, SSab: double; SSerrwithin, SStotal, MSgroups, MSsubwGrps, MSa, MSb, MSab: double; MSerrwithin, DFbetsubj, DFgroups, DFsubwGrps, DFwithinsubj: double; DFa, DFb, DFab, DFerrwithin, DFtotal: double; data, GrandMean: double; p, row, col, subject, group: integer; proba, probb, probab, probgrps: double; fa, fb, fab, fgroups: double; RowLabels, ColLabels: StrDyneVec; Title: string; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(5); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; SubjectFactor := LatinSpecsFrm.CCodeEdit.Text; GroupFactor := LatinSpecsFrm.GrpCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = GroupFactor) then Grpcol := i; if (cellstring = SubjectFactor) then Sbjcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and Group if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(GrpCol, rangeGrp, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; p := rangeA; // check for squareness if (rangeA <> rangeGrp) then begin ErrorMsg('ERROR! In a Latin square the range of values should be equal for A,B and C.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(ABmat, p+1, p+1); SetLength(ABCmat, p+1, p+1, n+1); SetLength(cellcnts, p+1, p+1); SetLength(Atotals, p+1); SetLength(Btotals, p+1); SetLength(Grptotals, p+1); SetLength(Design, p, p); SetLength(Subjtotals ,p+1, n+1); SetLength(RowLabels, p+1); SetLength(ColLabels, n+1); SetLength(GBmat, p+1, p+1); for i := 0 to p-1 do begin RowLabels[i] := IntToStr(i+1); ColLabels[i] := RowLabels[i]; end; RowLabels[p] := 'Total'; ColLabels[p] := 'Total'; for i := 0 to p do for j := 0 to p do for k := 0 to n do ABCmat[i,j,k] := 0.0; for i := 0 to p do for j := 0 to p do begin cellcnts[i,j] := 0; ABmat[i,j] := 0.0; GBmat[i,j] := 0.0; end; for i := 0 to p do begin Atotals[i] := 0.0; Btotals[i] := 0.0; Grptotals[i] := 0.0; end; for i := 0 to p do for j := 0 to n do Subjtotals[i,j] := 0.0; sumxsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; GrandMean := 0.0; // Read in the data for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); group := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); subject := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Sbjcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[group-1,row-1] := cellcnts[group-1,row-1] + 1; ABCmat[group-1,row-1,subject-1] := ABCmat[group-1,row-1,subject-1] + data; Subjtotals[group-1,subject-1] := Subjtotals[group-1,subject-1] + data; GBmat[group-1,col-1] := GBmat[group-1,col-1] + data; Atotals[col-1] := Atotals[col-1] + data; Btotals[group-1] := Btotals[group-1] + data; Grptotals[group-1] := Grptotals[group-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do if cellcnts[i,j] <> n then begin ErrorMsg('Cell sizes are not equal.'); Exit; end; // collapse subjects's into group x a matrix for i := 0 to p-1 do // group for j := 0 to p-1 do // factor a for k := 0 to n-1 do // subject ABmat[i,j] := ABmat[i,j] + ABCmat[i,j,k]; // get marginal totals for ABmat and GBmat for i := 0 to p-1 do for j := 0 to p-1 do begin ABmat[p,j] := ABmat[p,j] + ABmat[i,j]; ABmat[i,p] := ABmat[i,p] + ABmat[i,j]; GBmat[p,j] := GBmat[p,j] + GBmat[i,j]; GBmat[i,p] := GBmat[i,p] + GBmat[i,j]; end; // get grand total for ABmat and GBmat for i := 0 to p-1 do begin ABmat[p,p] := ABmat[p,p] + ABmat[p,i]; GBmat[p,p] := GBmat[p,p] + GBmat[p,i]; end; // Get marginal totals for Subjtotals for i := 0 to p-1 do for j := 0 to n-1 do begin Subjtotals[p,j] := Subjtotals[p,j] + Subjtotals[i,j]; Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; end; for i := 0 to p-1 do Subjtotals[p,n] := Subjtotals[p,n] + Subjtotals[i,n]; // test block lReport := TStringList.Create; try lReport.Add('Sums for ANOVA Analysis'); lReport.Add(''); cellstring := 'Group (rows) times A Factor (columns) sums'; MatPrint(ABmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); cellstring := 'Group (rows) times B (cells Factor) sums'; MatPrint(GBmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); Title := 'Groups (rows) times Subjects (columns) matrix'; for i := 0 to n-1 do ColLabels[i] := IntToStr(i+1); ColLabels[n] := 'Total'; MatPrint(Subjtotals, p+1, n+1, Title, RowLabels, ColLabels, n*p*p, lReport); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // get squared sum of subject's totals in each group for i := 0 to p-1 do // group term7 := term7 + sqr(Subjtotals[i,n]); term7 := term7 / (n*p); // Sum G^2 sub k // now square each person score in each group and get sum for group for i := 0 to p-1 do for j := 0 to n-1 do Subjtotals[i,j] := Subjtotals[i,j] * Subjtotals[i,j]; for i := 0 to p-1 do Subjtotals[i,n] := 0.0; for i := 0 to p-1 do for j := 0 to n-1 do Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; for i := 0 to p-1 do term6 := term6 + Subjtotals[i,n]; SSsubwgrps := term6 / p - term7; // get correction term term1 := (GrandMean * GrandMean) / (n * p * p); term2 := sumxsqr; // get sum of squared a's for term3 for j := 0 to p-1 do term3 := term3 + (ABmat[p,j] * ABmat[p,j]); term3 := term3 / (n * p); // get sum of squared groups for term4 for i := 0 to p-1 do term4 := term4 + (ABmat[i,p] * ABmat[i,p]); term4 := term4 / (n * p); // get squared sum of b's (across groups) for term5 for j := 0 to p-1 do term5 := term5 + (GBmat[p,j] * GBmat[p,j]); term5 := term5 / (n * p); SSgroups := term4 - term1; SSbetsubj := SSgroups + SSsubwgrps; SStotal := sumxsqr - term1; SSwithinsubj := SStotal - SSbetsubj; SSa := term3 - term1; SSb := term5 - term1; // get sum of squared AB cells for term6 term6 := 0.0; for i := 0 to p-1 do for j := 0 to p-1 do term6 := term6 + (ABmat[i,j] * ABmat[i,j]); term6 := term6 / n; SSab := term6 - term3 - term5 + term1; SSab := SSab - SSgroups; SSerrwithin := ( sumxsqr - term6) - SSsubwgrps; // record degrees of freedom for sources dfbetsubj := n * p - 1; dfsubwgrps := p * (n-1); dfgroups := p - 1; dftotal := n * p * p - 1; dfwithinsubj := n * p * (p-1); dfa := p - 1; dfb := p - 1; dfab := (p - 1) * (p - 2); dferrwithin := p * (n - 1) * (p - 1); MSsubwgrps := SSsubwgrps / dfsubwgrps; MSgroups := SSgroups / dfgroups; MSa := SSa / dfa; MSb := SSb / dfb; MSab := SSab / dfab; MSerrwithin := SSerrwithin / dferrwithin; fgroups := MSgroups / MSsubwgrps; fa := MSa / MSerrwithin; fb := MSb / MSerrwithin; fab := MSab / MSerrwithin; probgrps := probf(fgroups,dfgroups,dfsubwgrps); proba := probf(fa,dfa,dferrwithin); probb := probf(fb,dfb,dferrwithin); probab := probf(fab,dfab,dferrwithin); // show ANOVA table results lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 5 (Partial Interactions)'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Betw.Subj.%9.3f %9.0f', [SSbetsubj, dfbetsubj]); lReport.Add(' Groups %9.3f %9.0f %9.3f %9.3f %9.3f', [SSgroups, dfgroups, MSgroups, fgroups, probgrps]); lReport.Add(' Subj.w.g.%9.3f %9.0f %9.3f', [SSsubwgrps, dfsubwgrps, MSsubwgrps]); lReport.Add(''); lReport.Add('Within Sub%9.3f %9.0f', [SSwithinsubj, dfwithinsubj]); lReport.Add(' Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSa, dfa, MSa, fa, proba]); lReport.Add(' Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSb, dfb, MSb, fb, probb]); lReport.Add(' Factor AB%9.3f %9.0f %9.3f %9.3f %9.3f', [SSab, dfab, MSab, fab, probab]); lReport.Add(' Error w. %9.3f %9.0f %9.3f', [SSerrwithin, dferrwithin, MSerrwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for Square lReport.Add(''); lReport.Add('Experimental Design for Latin Square '); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); lReport.Add(cellstring); for i := 1 to NoCases do begin row := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); // A (column) effect col := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); // B (cell) effect group := Round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); // group (row) Design[group-1,row-1] := 'B' + IntToStr(col); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); for i := 0 to p-1 do for j := 0 to p-1 do ABmat[i,j] := ABmat[i,j] / n; for i := 0 to p-1 do ABmat[i,p] := ABmat[i,p] / (n * p); for j := 0 to p-1 do ABmat[p,j] := ABmat[p,j] / (n * p); GrandMean := GrandMean / (p * p * n ); for i := 0 to p-1 do begin Atotals[i] := Atotals[i] / (p * n); Btotals[i] := Btotals[i] / (p * n); Grptotals[i] := Grptotals[i] / (p * n); end; // show table of means for ABmat lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[i,j]]); cellstring := cellstring + Format(' %8.3f ', [ABmat[i,p]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[p,j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // show category means lReport.Add(''); lReport.Add('Means for each variable'); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Atotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Btotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Grptotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; GBmat := nil; ColLabels := nil; RowLabels := nil; Subjtotals := nil; Design := nil; Grptotals := nil; Btotals := nil; Atotals := nil; cellcnts := nil; ABCmat := nil; ABmat := nil; end; end; procedure TLatinSqrsFrm.Plan6; var n: integer; // no. of subjects per cell Acol, Bcol, SbjCol, GrpCol, DataCol: Integer; // variable columns in grid FactorA: string; FactorB: string; SubjectFactor: string; GroupFactor: string; DataVar: string; cellstring: string; i, j, k: integer; rangeA, rangeB, rangeGrp: integer; mn, mx: Integer; cellcnts: IntDyneMat; ABmat: DblDyneMat; ABCmat: DblDyneCube; GBmat: DblDyneMat; Atotals: DblDyneVec; Btotals: DblDyneVec; Grptotals: DblDyneVec; Subjtotals: DblDyneMat; design: StrDyneMat; term1, term2, term3, term4, term5, term6, term7: double; sumxsqr: double; SSbetsubj, SSgroups, SSsubwGrps, SSwithinsubj, SSa, SSb, SSab: double; SSerrwithin, SStotal, MSgroups, MSsubwGrps, MSa, MSb, MSab: double; MSerrwithin, DFbetsubj, DFgroups, DFsubwGrps, DFwithinsubj: double; DFa, DFb, DFab, DFerrwithin, DFtotal: double; data, GrandMean: double; p, row, col, subject, group: integer; proba, probb, probab, probgrps: double; fa, fb, fab, fgroups: double; RowLabels, ColLabels: StrDyneVec; Title: string; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(6); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; SubjectFactor := LatinSpecsFrm.CCodeEdit.Text; GroupFactor := LatinSpecsFrm.GrpCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then ACol := i; if (cellstring = FactorB) then BCol := i; if (cellstring = GroupFactor) then Grpcol := i; if (cellstring = SubjectFactor) then Sbjcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B and Group if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(GrpCol, rangeGrp, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; p := rangeA; // check for squareness if (rangeA <> rangeGrp) then begin ErrorMsg('In a Latin square the range of values should be equal for A, B and C.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(ABmat, p+1, p+1); SetLength(ABCmat, p+1, p+1, n+1); SetLength(cellcnts, p+1, p+1); SetLength(Atotals, p+1); SetLength(Btotals, p+1); SetLength(Grptotals, p+1); SetLength(Design, p, p); SetLength(Subjtotals, p+1, n+1); SetLength(RowLabels, p+1); SetLength(ColLabels, n+1); SetLength(GBmat, p+1, p+1); for i := 0 to p-1 do begin RowLabels[i] := IntToStr(i+1); ColLabels[i] := RowLabels[i]; end; RowLabels[p] := 'Total'; ColLabels[p] := 'Total'; for i := 0 to p do for j := 0 to p do for k := 0 to n do ABCmat[i,j,k] := 0.0; for i := 0 to p do for j := 0 to p do begin cellcnts[i,j] := 0; ABmat[i,j] := 0.0; GBmat[i,j] := 0.0; end; for i := 0 to p do begin Atotals[i] := 0.0; Btotals[i] := 0.0; Grptotals[i] := 0.0; end; for i := 0 to p do for j := 0 to n do Subjtotals[i,j] := 0.0; sumxsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; GrandMean := 0.0; // Read in the data for i := 1 to NoCases do begin row := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); group := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); subject := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Sbjcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[group-1,row-1] := cellcnts[group-1,row-1] + 1; ABCmat[group-1,row-1,subject-1] := ABCmat[group-1,row-1,subject-1] + data; Subjtotals[group-1,subject-1] := Subjtotals[group-1,subject-1] + data; GBmat[group-1,col-1] := GBmat[group-1,col-1] + data; Atotals[col-1] := Atotals[col-1] + data; Btotals[group-1] := Btotals[group-1] + data; Grptotals[group-1] := Grptotals[group-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do if cellcnts[i,j] <> n then begin ErrorMsg('Cell sizes are not equal.'); exit; end; // collapse subjects's into group x a matrix for i := 0 to p-1 do // group for j := 0 to p-1 do // factor a for k := 0 to n-1 do // subject ABmat[i,j] := ABmat[i,j] + ABCmat[i,j,k]; // get marginal totals for ABmat and GBmat for i := 0 to p-1 do for j := 0 to p-1 do begin ABmat[p,j] := ABmat[p,j] + ABmat[i,j]; ABmat[i,p] := ABmat[i,p] + ABmat[i,j]; GBmat[p,j] := GBmat[p,j] + GBmat[i,j]; GBmat[i,p] := GBmat[i,p] + GBmat[i,j]; end; // get grand total for ABmat and GBmat for i := 0 to p-1 do begin ABmat[p,p] := ABmat[p,p] + ABmat[p,i]; GBmat[p,p] := GBmat[p,p] + GBmat[p,i]; end; // Get marginal totals for Subjtotals for i := 0 to p-1 do for j := 0 to n-1 do begin Subjtotals[p,j] := Subjtotals[p,j] + Subjtotals[i,j]; Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; end; for i := 0 to p-1 do Subjtotals[p,n] := Subjtotals[p,n] + Subjtotals[i,n]; // test block lReport := TStringList.Create; try lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 6'); lReport.Add(''); lReport.Add('Sums for ANOVA Analysis'); lReport.Add(''); cellstring := 'Group - C (rows) times A Factor (columns) sums'; MatPrint(ABmat, p+1, p+1, cellstring, RowLabels, ColLabels,n*p*p, lReport); cellstring := 'Group - C (rows) times B (cells Factor) sums'; MatPrint(GBmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); Title := 'Group - C (rows) times Subjects (columns) matrix'; for i := 0 to n-1 do ColLabels[i] := IntToStr(i+1); ColLabels[n] := 'Total'; MatPrint(Subjtotals, p+1, n+1, Title, RowLabels, ColLabels, n*p*p, lReport); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // get squared sum of subject's totals in each group for i := 0 to p-1 do // group term7 := term7 + (Subjtotals[i,n] * Subjtotals[i,n]); term7 := term7 / (n*p); // Sum G^2 sub k // now square each person score in each group and get sum for group for i := 0 to p-1 do for j := 0 to n-1 do Subjtotals[i,j] := Subjtotals[i,j] * Subjtotals[i,j]; for i := 0 to p-1 do Subjtotals[i,n] := 0.0; for i := 0 to p-1 do for j := 0 to n-1 do Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; for i := 0 to p-1 do term6 := term6 + Subjtotals[i,n]; SSsubwgrps := term6 / p - term7; // get correction term term1 := sqr(GrandMean) / (n * p * p); term2 := sumxsqr; // get sum of squared a's for term3 for j := 0 to p-1 do term3 := term3 + sqr(ABmat[p,j]); term3 := term3 / (n * p); // get sum of squared groups for term4 for i := 0 to p-1 do term4 := term4 + sqr(ABmat[i,p]); term4 := term4 / (n * p); // get squared sum of b's (across groups) for term5 for j := 0 to p-1 do term5 := term5 + sqr(GBmat[p,j]); term5 := term5 / (n * p); SSgroups := term4 - term1; SSbetsubj := SSgroups + SSsubwgrps; SStotal := sumxsqr - term1; SSwithinsubj := SStotal - SSbetsubj; SSa := term3 - term1; SSb := term5 - term1; // get sum of squared AB cells for term6 term6 := 0.0; for i := 0 to p-1 do for j := 0 to p-1 do term6 := term6 + sqr(ABmat[i,j]); term6 := term6 / n; SSab := term6 - term3 - term5 + term1; SSab := SSab - SSgroups; SSerrwithin := ( sumxsqr - term6) - SSsubwgrps; // record degrees of freedom for sources dfbetsubj := n * p - 1; dfsubwgrps := p * (n-1); dfgroups := p - 1; dftotal := n * p * p - 1; dfwithinsubj := n * p * (p-1); dfa := p - 1; dfb := p - 1; dfab := (p - 1) * (p - 2); dferrwithin := p * (n - 1) * (p - 1); MSsubwgrps := SSsubwgrps / dfsubwgrps; MSgroups := SSgroups / dfgroups; MSa := SSa / dfa; MSb := SSb / dfb; MSab := SSab / dfab; MSerrwithin := SSerrwithin / dferrwithin; fgroups := MSgroups / MSsubwgrps; fa := MSa / MSerrwithin; fb := MSb / MSerrwithin; fab := MSab / MSerrwithin; probgrps := probf(fgroups,dfgroups,dfsubwgrps); proba := probf(fa,dfa,dferrwithin); probb := probf(fb,dfb,dferrwithin); probab := probf(fab,dfab,dferrwithin); // show ANOVA table results lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 6'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Betw.Subj.%9.3f %9.0f', [SSbetsubj, dfbetsubj]); lReport.Add(' Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSgroups, dfgroups, MSgroups, fgroups, probgrps]); lReport.Add(' Subj.w.g.%9.3f %9.0f %9.3f', [SSsubwgrps, dfsubwgrps, MSsubwgrps]); lReport.Add(''); lReport.Add('Within Sub%9.3f %9.0f',[ SSwithinsubj, dfwithinsubj]); lReport.Add(' Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSa, dfa, MSa, fa, proba]); lReport.Add(' Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSb, dfb, MSb, fb, probb]); lReport.Add(' Residual %9.3f %9.0f %9.3f %9.3f %9.3f', [SSab, dfab, MSab, fab, probab]); lReport.Add(' Error w. %9.3f %9.0f %9.3f', [SSerrwithin, dferrwithin, MSerrwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for Square lReport.Add(''); lReport.Add('Experimental Design for Latin Square '); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add(' G C '); for i := 1 to NoCases do begin row := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); // A (column) effect col := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); // B (cell) effect group := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); // group (row) Design[group-1,row-1] := 'B' + IntToStr(col); end; for i := 0 to p - 1 do begin cellstring := Format('%3d %3d ', [i+1,i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); for i := 0 to p-1 do for j := 0 to p-1 do ABmat[i,j] := ABmat[i,j] / n; for i := 0 to p-1 do ABmat[i,p] := ABmat[i,p] / (n * p); for j := 0 to p-1 do ABmat[p,j] := ABmat[p,j] / (n * p); GrandMean := GrandMean / (p * p * n ); for i := 0 to p-1 do begin Atotals[i] := Atotals[i] / (p * n); Btotals[i] := Btotals[i] / (p * n); Grptotals[i] := Grptotals[i] / (p * n); end; // show table of means for ABmat lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[i,j]]); cellstring := cellstring + Format(' %8.3f ', [ABmat[i,p]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[p,j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // show category means lReport.Add(''); lReport.Add('Means for each variable'); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Atotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Btotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Grptotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; GBmat := nil; ColLabels := nil; RowLabels := nil; Subjtotals := nil; Design := nil; Grptotals := nil; Btotals := nil; Atotals := nil; cellcnts := nil; ABCmat := nil; ABmat := nil; end; end; procedure TLatinSqrsFrm.Plan7; var n: integer; // no. of subjects per cell Acol, Bcol, Ccol, SbjCol, Grpcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; SubjectFactor: string; FactorC: string; GroupFactor: string; DataVar: string; cellstring: string; i, j, k: integer; rangeA, rangeB, rangeC, rangeGrp: integer; mn, mx: Integer; cellcnts: IntDyneMat; ABmat: DblDyneMat; ABCmat: DblDyneCube; GBmat: DblDyneMat; GCmat: DblDyneMat; Atotals: DblDyneVec; Btotals: DblDyneVec; Ctotals: DblDyneVec; Grptotals: DblDyneVec; Subjtotals: DblDyneMat; design: StrDyneMat; term1, term2, term3, term4, term5, term6, term7, term8, term9: double; sumxsqr: double; SSbetsubj, SSgroups, SSsubwGrps, SSwithinsubj, SSa, SSb, SSc, SSab: double; SSerrwithin, SStotal, MSgroups, MSsubwGrps, MSa, MSb, MSc, MSab: double; MSerrwithin, DFbetsubj, DFgroups, DFsubwGrps, DFwithinsubj: double; DFa, DFb, DFc, DFab, DFerrwithin, DFtotal: double; data, GrandMean: double; p, row, col, slice, subject, group: integer; proba, probb, probc, probab, probgrps: double; fa, fb, fc, fab, fgroups: double; RowLabels, ColLabels: StrDyneVec; Title: string; lReport: TStrings; begin LatinSpecsFrm.PrepareForPlan(7); if LatinSpecsFrm.ShowModal <> mrOK then exit; n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; SubjectFactor := LatinSpecsFrm.DCodeEdit.Text; GroupFactor := LatinSpecsFrm.GrpCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then Acol := i; if (cellstring = FactorB) then Bcol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = GroupFactor) then Grpcol := i; if (cellstring = SubjectFactor) then Sbjcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B, C and Group if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not GetRange(GrpCol, rangeGrp, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; p := rangeA; // check for squareness if (rangeA <> rangeB) or (rangeA <> rangeC) or (rangeA <> rangeGrp) then begin ErrorMsg('In a Latin square the range of values should be equal for A, B and C.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(ABmat, p+1, p+1); SetLength(ABCmat, p+1, p+1, n+1); SetLength(cellcnts, p+1, p+1); SetLength(Atotals, p+1); SetLength(Btotals, p+1); SetLength(Ctotals, p+1); SetLength(Grptotals, p+1); SetLength(Design, p, p); SetLength(Subjtotals, p+1, n+1); SetLength(RowLabels, p+1); SetLength(ColLabels, n+1); SetLength(GBmat, p+1, p+1); SetLength(GCmat, p+1, p+1); for i := 0 to p-1 do begin RowLabels[i] := IntToStr(i+1); ColLabels[i] := RowLabels[i]; end; RowLabels[p] := 'Total'; ColLabels[p] := 'Total'; for i := 0 to p do for j := 0 to p do for k := 0 to n do ABCmat[i,j,k] := 0.0; for i := 0 to p do for j := 0 to p do begin cellcnts[i,j] := 0; ABmat[i,j] := 0.0; GBmat[i,j] := 0.0; GCmat[i,j] := 0.0; end; for i := 0 to p do begin Atotals[i] := 0.0; Btotals[i] := 0.0; Ctotals[i] := 0.0; Grptotals[i] := 0.0; end; for i := 0 to p do for j := 0 to n do Subjtotals[i,j] := 0.0; sumxsqr := 0.0; term1 := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; term8 := 0.0; term9 := 0.0; GrandMean := 0.0; // Read in the data for i := 1 to NoCases do begin row := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); col := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); slice := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); group := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); subject := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Sbjcol,i])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,i]); cellcnts[group-1,row-1] := cellcnts[group-1,row-1] + 1; ABCmat[group-1,row-1,slice-1] := ABCmat[group-1,row-1,slice-1] + data; Subjtotals[group-1,subject-1] := Subjtotals[group-1,subject-1] + data; GBmat[group-1,col-1] := GBmat[group-1,col-1] + data; GCmat[group-1,slice-1] := GCmat[group-1,slice-1] + data; Atotals[row-1] := Atotals[row-1] + data; Btotals[col-1] := Btotals[col-1] + data; Ctotals[slice-1] := Ctotals[slice-1] + data; Grptotals[group-1] := Grptotals[group-1] + data; sumxsqr := sumxsqr + (data * data); GrandMean := GrandMean + data; end; // check for equal cell counts for i := 0 to p-1 do for j := 0 to p-1 do if cellcnts[i,j] <> n then begin ErrorMsg('Cell sizes are not equal.'); exit; end; // collapse slices into group x a matrix // result is the group times A matrix with BC cells containing n cases each for i := 0 to p-1 do // group for j := 0 to p-1 do // factor a for k := 0 to n-1 do // factor c ABmat[i,j] := ABmat[i,j] + ABCmat[i,j,k]; // get marginal totals for ABmat, GBmat and GCmat for i := 0 to p-1 do for j := 0 to p-1 do begin ABmat[p,j] := ABmat[p,j] + ABmat[i,j]; ABmat[i,p] := ABmat[i,p] + ABmat[i,j]; GBmat[p,j] := GBmat[p,j] + GBmat[i,j]; GBmat[i,p] := GBmat[i,p] + GBmat[i,j]; GCmat[p,j] := GCmat[p,j] + GCmat[i,j]; GCmat[i,p] := GCmat[i,p] + GCmat[i,j]; end; // get grand total for ABmat, GBmat and GCmat for i := 0 to p-1 do begin ABmat[p,p] := ABmat[p,p] + ABmat[p,i]; GBmat[p,p] := GBmat[p,p] + GBmat[p,i]; GCmat[p,p] := GCmat[p,p] + GCmat[p,i]; end; // Get marginal totals for Subjtotals for i := 0 to p-1 do // groups 1-p for j := 0 to n-1 do // subjects 1-n begin Subjtotals[p,j] := Subjtotals[p,j] + Subjtotals[i,j]; Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; end; for i := 0 to p-1 do Subjtotals[p,n] := Subjtotals[p,n] + Subjtotals[i,n]; lReport := TStringList.Create; try // test block lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 7 (superimposed squares)'); lReport.Add(''); lReport.Add('Sums for ANOVA Analysis'); lReport.Add(''); cellstring := 'Group (rows) times A Factor (columns) sums'; MatPrint(ABmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); cellstring := 'Group (rows) times B (cells Factor) sums'; MatPrint(GBmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); cellstring := 'Group (rows) times C (cells Factor) sums'; MatPrint(GCmat, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p, lReport); for i := 0 to n-1 do ColLabels[i] := IntToStr(i+1); ColLabels[n] := 'Total'; Title := 'Group (rows) times Subjects (columns) sums'; MatPrint(Subjtotals, p+1, n+1, Title, RowLabels, ColLabels, n*p*p, lReport); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // get squared sum of subject's totals in each group for i := 0 to p-1 do // group term7 := term7 + (Subjtotals[i,n] * Subjtotals[i,n]); term7 := term7 / (n*p); // Sum G^2 sub k // now square each person score in each group and get sum for group for i := 0 to p-1 do // groups for j := 0 to n-1 do // subjects Subjtotals[i,j] := Subjtotals[i,j] * Subjtotals[i,j]; for i := 0 to p-1 do Subjtotals[i,n] := 0.0; // clear group totals // get sum of squared person scores in each group for i := 0 to p-1 do // groups for j := 0 to n-1 do // subjects Subjtotals[i,n] := Subjtotals[i,n] + Subjtotals[i,j]; // get sum of squares for subjects within groups for i := 0 to p-1 do term6 := term6 + Subjtotals[i,n]; SSsubwgrps := (term6 / p) - term7; // get correction term and term for total sum of squares term1 := sqr(GrandMean) / (n * p * p); term2 := sumxsqr; // get sum of squared groups for term4 of sum of squares for groups for i := 0 to p-1 do term4 := term4 + sqr(Grptotals[i]); term4 := term4 / (n * p); // get sum of squared a's for term3 for j := 0 to p-1 do // levels of a term3 := term3 + sqr(Atotals[j]); term3 := term3 / (n * p); // get squared sum of b's (across groups) for term5 of sum of squares b for j := 0 to p-1 do term5 := term5 + sqr(Btotals[j]); term5 := term5 / (n * p); // get squared sum of c's (across groups) for term8 of SS for c for j := 0 to p-1 do term8 := term8 + sqr(Ctotals[j]); term8 := term8 / (n * p); SSgroups := term4 - term1; SSbetsubj := SSgroups + SSsubwgrps; SStotal := term2 - term1; SSwithinsubj := SStotal - SSbetsubj; SSa := term3 - term1; SSb := term5 - term1; SSc := term8 - term1; // get sum of squared AB cells for term6 term6 := 0.0; for i := 0 to p-1 do for j := 0 to p-1 do term6 := term6 + sqr(ABmat[i,j]); term9 := term6 / n - term1; term6 := sumxsqr - (term6 / n); // SS within cells from sum squared x's SSerrwithin := term6 - SSsubwgrps; SSab := term9 - (SSa + SSb + SSc + SSgroups); // residual // record degrees of freedom for sources dfbetsubj := n * p - 1; dfsubwgrps := p * (n-1); dfgroups := p - 1; dftotal := n * p * p - 1; dfwithinsubj := n * p * (p-1); dfa := p - 1; dfb := p - 1; dfc := p - 1; dfab := (p - 1) * (p - 3); dferrwithin := p * (n - 1) * (p - 1); MSsubwgrps := SSsubwgrps / dfsubwgrps; MSgroups := SSgroups / dfgroups; MSa := SSa / dfa; MSb := SSb / dfb; MSc := SSc / dfc; if dfab > 0 then MSab := SSab / dfab; MSerrwithin := SSerrwithin / dferrwithin; fgroups := MSgroups / MSsubwgrps; fa := MSa / MSerrwithin; fb := MSb / MSerrwithin; fc := MSc / MSerrwithin; if dfab > 0 then fab := MSab / MSerrwithin; probgrps := probf(fgroups, dfgroups, dfsubwgrps); proba := probf(fa, dfa, dferrwithin); probb := probf(fb, dfb, dferrwithin); probc := probf(fc, dfc, dferrwithin); probab := probf(fab, dfab, dferrwithin); // show ANOVA table results lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 7 (superimposed squares)'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Betw.Subj.%9.3f %9.0f', [SSbetsubj, dfbetsubj]); lReport.Add(' Groups %9.3f %9.0f %9.3f %9.3f %9.3f', [SSgroups, dfgroups, MSgroups, fgroups, probgrps]); lReport.Add(' Subj.w.g.%9.3f %9.0f %9.3f', [SSsubwgrps, dfsubwgrps, MSsubwgrps]); lReport.Add(''); lReport.Add('Within Sub%9.3f %9.0f', [SSwithinsubj, dfwithinsubj]); lReport.Add(' Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSa, dfa, MSa, fa, proba]); lReport.Add(' Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSb, dfb, MSb, fb, probb]); lReport.Add(' Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSc, dfc, MSc, fc, probc]); if dfab > 0 then lReport.Add(' residual %9.3f %9.0f %9.3f %9.3f %9.3f', [SSab, dfab, MSab, fab, probab]) else lReport.Add(' residual - %9.0f -', [dfab]); lReport.Add(' Error w. %9.3f %9.0f %9.3f', [SSerrwithin, dferrwithin, MSerrwithin]); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); // show design for Square lReport.Add(''); lReport.Add('Experimental Design for Latin Square '); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); lReport.Add(cellstring); for i := 1 to NoCases do begin row := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); // A (column) effect col := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); // B (cell) effect slice := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); // C (cell) effect group := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); // group (row) Design[group-1,row-1] := 'BC' + IntToStr(col) + IntToStr(slice); end; for i := 0 to p - 1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); // get means for i := 0 to p-1 do for j := 0 to p-1 do ABmat[i,j] := ABmat[i,j] / n; for i := 0 to p-1 do ABmat[i,p] := ABmat[i,p] / (n * p); for j := 0 to p-1 do ABmat[p,j] := ABmat[p,j] / (n * p); GrandMean := GrandMean / (p * p * n ); for i := 0 to p-1 do begin Atotals[i] := Atotals[i] / (p * n); Btotals[i] := Btotals[i] / (p * n); Ctotals[i] := Ctotals[i] / (p * n); Grptotals[i] := Grptotals[i] / (p * n); end; // show table of means for ABmat // means for Groups by A matrix lReport.Add(''); lReport.Add('Cell means and totals'); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); lReport.Add(cellstring); for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[i,j]]); cellstring := cellstring + Format(' %8.3f ', [ABmat[i,p]]); lReport.Add(cellstring); end; cellstring := 'Total '; for j := 0 to p-1 do cellstring := cellstring + Format(' %8.3f ', [ABmat[p,j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // show category means lReport.Add(''); lReport.Add('Means for each variable'); lReport.Add(''); // factor A means cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Atotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // means for B lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorB]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Btotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // C means lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [FactorC]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Ctotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); // Group means lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := Format('%10s', [GroupFactor]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); cellstring := cellstring + ' Total'; lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); cellstring := ' '; for j := 0 to p - 1 do cellstring := cellstring + Format(' %8.3f ', [Grptotals[j]]); cellstring := cellstring + Format(' %8.3f ', [GrandMean]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '----------'; lReport.Add(cellstring); DisplayReport(lReport); finally lReport.Free; GCmat := nil; GBmat := nil; ColLabels := nil; RowLabels := nil; Subjtotals := nil; Design := nil; Grptotals := nil; Ctotals := nil; Btotals := nil; Atotals := nil; cellcnts := nil; ABCmat := nil; ABmat := nil; end; end; procedure TLatinSqrsFrm.Plan9; var row, col, slice, group, index: integer; Acol, Bcol, Ccol, SbjCol, Grpcol, DataCol: integer; // variable columns in grid FactorA: string; FactorB: string; FactorC: string; SubjectFactor: string; GroupFactor: string; DataVar: string; cellstring: string; i, j, k, m: integer; mn, mx: Integer; n, subject, nosubjects, rangeA, rangeB, rangeC, rangeGrp: integer; p, q, rows: integer; ABC, AGC: DblDyneCube; AB, AC, BC, RC: DblDyneMat; A, B, C, Persons, Gm, R: DblDyneVec; cellcnts: IntDyneVec; Design: StrDyneMat; RowLabels: StrDyneVec; ColLabels: StrDyneVec; G, sumxsqr, sumAsqr, sumBsqr, sumABsqr, sumACsqr: double; sumBCsqr, sumABCsqr, sumPsqr, sumGmsqr, sumRsqr: double; SSbetsubj, SSc, SSrows, SScxrow, SSsubwgrps, SSa: double; SSwithinsubj, SSerrwithin: double; SSb, SSac, SSbc, SSabprime, SSABCprime, SStotal: double; term1, term2, term3, term4, term5, term6, term7, term8, term9, term10: double; term11, term12: double; dfc, dfrows, dfcxrow, dfsubwgrps, dfwithinsubj, dfa, dfb,dfac: double; dfbc, dfabprime, dfabcprime,dferrwithin, dftotal, dfbetsubj: double; MSc, MSrows, MScxrow, MSsubwgrps, MSa: double; MSb, MSac, MSbc, MSabprime, MSabcprime, MSerrwithin: double; fc, frows, fcxrow, fsubwgrps, fa, fb, fac, fbc, fabprime, fabcprime: double; probc, probrows, probcxrow, probsubwgrps, proba, probb: double; probac, probbc, probabprime, probabcprime: double; data, value: double; lReport: TStrings; begin cellstring := LatinSpecsFrm.DCodeLabel.Caption; // get current label LatinSpecsFrm.DCodeLabel.Caption := 'Subject No.'; // set new label LatinSpecsFrm.PrepareForPlan(9); if LatinSpecsFrm.ShowModal <> mrOK then exit; LatinSpecsFrm.DCodeLabel.Caption := cellstring; // restore label n := StrToInt(LatinSpecsFrm.nPerCellEdit.Text); // no. persons per cell FactorA := LatinSpecsFrm.ACodeEdit.Text; FactorB := LatinSpecsFrm.BCodeEdit.Text; FactorC := LatinSpecsFrm.CCodeEdit.Text; SubjectFactor := LatinSpecsFrm.DCodeEdit.Text; GroupFactor := LatinSpecsFrm.GrpCodeEdit.Text; DataVar := LatinSpecsFrm.DepVarEdit.Text; for i := 1 to NoVariables do begin cellstring := OS3MainFrm.DataGrid.Cells[i,0]; if (cellstring = FactorA) then Acol := i; if (cellstring = FactorB) then Bcol := i; if (cellstring = FactorC) then Ccol := i; if (cellstring = GroupFactor) then Grpcol := i; if (cellstring = SubjectFactor) then Sbjcol := i; if (cellstring = DataVar) then DataCol := i; end; // determine no. of levels in A, B, C and Group if not GetRange(ACol, rangeA, mn, mx) then exit; if not GetRange(BCol, rangeB, mn, mx) then exit; if not GetRange(CCol, rangeC, mn, mx) then exit; if not GetRange(GrpCol, rangeGrp, mn, mx) then exit; if not CheckDataCol(DataCol) then exit; p := rangeA; q := rangeC; nosubjects := 0; for i := 1 to NoCases do begin if TryStrToFloat(OS3MainFrm.DataGrid.Cells[SbjCol,i], value) then begin if value > nosubjects then nosubjects := round(value); end else begin ErrorMsg(NO_VALID_NUMBER_ERROR, [i, SubjectFactor]); exit; end; end; // check for squareness if (rangeA <> rangeB) then begin ErrorMsg('In a Latin square the range of values should be equal for A,B and C.'); exit; end; // set up an array for cell counts and for cell sums and marginal sums SetLength(ABC, p+1, p+1, q+1); SetLength(AGC, p+1, rangegrp+1, q+1); SetLength(AB, p+1, p+1); SetLength(AC, p+1, q+1); SetLength(BC, p+1, q+1); SetLength(RC, (rangegrp div q)+1, q+1); SetLength(A, p+1); SetLength(B, p+1); SetLength(C, q+1); SetLength(Persons, nosubjects+1); SetLength(Gm, rangegrp+1); SetLength(R, p+1); SetLength(cellcnts, p+1); SetLength(Design, rangegrp, p); SetLength(RowLabels, MaxValue([n, p, rangegrp, nosubjects])+1); SetLength(ColLabels, MaxValue([n, p, rangeGrp, nosubjects])+1); // initialize arrays for i := 0 to p-1 do begin RowLabels[i] := IntToStr(i+1); ColLabels[i] := RowLabels[i]; end; RowLabels[p] := 'Total'; ColLabels[p] := 'Total'; for i := 0 to p do for j := 0 to p do for k := 0 to q do ABC[i,j,k] := 0.0; for i := 0 to p do for j := 0 to rangegrp do for k := 0 to q do AGC[i,j,k] := 0.0; for i := 0 to p do for j := 0 to p do AB[i,j] := 0.0; for i := 0 to p do for j := 0 to q do AC[i,j] := 0.0; for i := 0 to p do for j := 0 to q do BC[i,j] := 0.0; for i := 0 to p do for j := 0 to q do RC[i,j] := 0.0; for i := 0 to p do A[i] := 0.0; for i := 0 to p do B[i] := 0.0; for i := 0 to q do C[i] := 0.0; for i := 0 to nosubjects do Persons[i] := 0.0; for i := 0 to rangegrp do Gm[i] := 0.0; for i := 0 to p do R[i] := 0.0; for i := 0 to p do cellcnts[i] := 0; // initialize single values G := 0.0; sumxsqr := 0.0; sumAsqr := 0.0; sumBsqr := 0.0; sumABsqr := 0.0; sumACsqr := 0.0; sumBCsqr := 0.0; sumABCsqr := 0.0; sumRsqr := 0.0; sumGmsqr := 0.0; sumRsqr := 0.0; sumPsqr := 0.0; term2 := 0.0; term3 := 0.0; term4 := 0.0; term5 := 0.0; term6 := 0.0; term7 := 0.0; term8 := 0.0; term9 := 0.0; term10 := 0.0; term11 := 0.0; term12 := 0.0; // Read in the data for index := 1 to NoCases do begin i := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,index])); j := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,index])); k := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,index])); m := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,index])); subject := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Sbjcol,index])); data := StrToFloat(OS3MainFrm.DataGrid.Cells[DataCol,index]); cellcnts[j-1] := cellcnts[j-1] + 1; ABC[i-1,j-1,k-1] := ABC[i-1,j-1,k-1] + data; AGC[i-1,m-1,k-1] := AGC[i-1,m-1,k-1] + data; AB[i-1,j-1] := AB[i-1,j-1] + data; AC[i-1,k-1] := AC[i-1,k-1] + data; BC[j-1,k-1] := BC[j-1,k-1] + data; A[i-1] := A[i-1] + data; B[j-1] := B[j-1] + data; C[k-1] := C[k-1] + data; Gm[m-1] := Gm[m-1] + data; Persons[subject-1] := Persons[subject-1] + data; sumxsqr := sumxsqr + (data * data); G := G + data; end; // check for equal cell counts in b treatments for i := 1 to p-1 do if cellcnts[i-1] <> cellcnts[i] then begin ErrorMsg('Cell sizes are not equal.'); exit; end; // get sums in the RC matrix rows := rangegrp div q; for i := 0 to rows - 1 do for j := 0 to q-1 do begin // k := (i * q) + j; k := i + q * j; RC[i,j] := Gm[k]; end; // get marginal totals for RC array for i := 0 to rows -1 do for j := 0 to q-1 do begin RC[i,q] := RC[i,q] + RC[i,j]; RC[rows,j] := RC[rows,j] + RC[i,j]; end; // get marginal totals for arrays ABC and AGC for i := 0 to p-1 do for j := 0 to p-1 do begin for k := 0 to q-1 do begin ABC[i,j,q] := ABC[i,j,q] + ABC[i,j,k]; ABC[i,p,k] := ABC[i,p,k] + ABC[i,j,k]; ABC[p,j,k] := ABC[p,j,k] + ABC[i,j,k]; end; end; for i := 0 to p-1 do for j := 0 to rangegrp - 1 do for k := 0 to q-1 do begin AGC[i,j,q] := AGC[i,j,q] + AGC[i,j,k]; AGC[i,rangegrp,k] := AGC[i,rangegrp,k] + AGC[i,j,k]; AGC[p,j,k] := AGC[p,j,k] + AGC[i,j,k]; end; for i := 0 to p-1 do for j := 0 to q-1 do begin AC[p,j] := AC[p,j] + AC[i,j]; AC[i,q] := AC[i,q] + AC[i,j]; BC[p,j] := BC[p,j] + BC[i,j]; BC[i,q] := BC[i,q] + BC[i,j]; end; // get grand total for AC, BC and RC for i := 0 to q-1 do begin AC[p,q] := AC[p,q] + AC[p,i]; BC[p,q] := BC[p,q] + BC[p,i]; RC[p,q] := RC[p,q] + RC[p,i]; end; // get margins and totals in AB matrix for i := 0 to p-1 do for j := 0 to p-1 do begin AB[p,j] := AB[p,j] + AB[i,j]; AB[i,p] := AB[i,p] + AB[i,j]; end; for i := 0 to p-1 do AB[p,p] := AB[p,p] + AB[i,p]; // get total for groups for m := 0 to rangegrp - 1 do Gm[rangegrp] := Gm[rangegrp] + Gm[m]; // test block lReport := TStringList.Create; try lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 9'); lReport.Add(''); lReport.Add('Sums for ANOVA Analysis'); lReport.Add(''); lReport.Add('ABC matrix'); lReport.Add(''); for k := 0 to q-1 do begin lReport.Add('C level %d', [k+1]); cellstring := ' '; for j := 0 to p-1 do cellstring := cellstring + Format(' %3d ', [j+1]); lReport.Add(cellstring); // row for i := 0 to p-1 do begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p-1 do cellstring := cellstring + Format('%9.3f ', [ABC[i,j,k]]); lReport.Add(cellstring); end; lReport.Add(''); lReport.Add(''); end; cellstring := 'AB sums'; MatPrint(AB, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*q, lReport); cellstring := 'AC sums'; MatPrint(AC, p+1, q+1, cellstring, RowLabels, ColLabels, n*p*q, lReport); cellstring := 'BC sums'; MatPrint(BC, p+1, q+1, cellstring, RowLabels, ColLabels, n*p*q, lReport); cellstring := 'RC sums'; MatPrint(RC, rows+1, q+1, cellstring, RowLabels, ColLabels, n*p*q, lReport); cellstring := 'Group totals'; for i := 0 to rangegrp-1 do ColLabels[i] := IntToStr(i+1); ColLabels[rangegrp] := 'Total'; DynVectorPrint(Gm, rangegrp+1, cellstring, ColLabels, n*p*q, lReport); for i := 0 to nosubjects-1 do ColLabels[i] := IntToStr(i+1); ColLabels[nosubjects] := 'Total'; cellstring := 'Subjects sums'; DynVectorPrint(Persons, nosubjects+1, cellstring, ColLabels, n*p*q, lReport); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); term1 := (G * G) / (n * p * p * q); term2 := sumXsqr; for i := 0 to p-1 do term3 := term3 + (A[i] * A[i]); term3 := term3 / (n * p * q); for i := 0 to p-1 do term4 := term4 + (B[i] * B[i]); term4 := term4 / (n * p * q); for i := 0 to q-1 do term5 := term5 + (C[i] * C[i]); term5 := term5 / (n * p * p); for i := 0 to p-1 do for j := 0 to p-1 do term6 := term6 + (AB[i,j] * AB[i,j]); term6 := term6 / (n * q); for i := 0 to p-1 do for j := 0 to q-1 do term7 := term7 + (AC[i,j] * AC[i,j]); term7 := term7 / (n * p); for i := 0 to p-1 do for j := 0 to q-1 do term8 := term8 + (BC[i,j] * BC[i,j]); term8 := term8 / (n * p); for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to q-1 do term9 := term9 + (ABC[i,j,k] * ABC[i,j,k]); term9 := term9 / n; for i := 0 to nosubjects-1 do term10 := term10 + (persons[i] * persons[i]); term10 := term10 / p; for i := 0 to rangegrp-1 do term11 := term11 + (Gm[i] * Gm[i]); term11 := term11 / (n * p); for i := 0 to rows-1 do term12 := term12 + (RC[i,q] * RC[i,q]); term12 := term12 / (n * p * q); // term check lReport.Add('COMPUTATION TERMS'); lReport.Add('Term1: %9.3f', [term1]); lReport.Add('Term2: %9.3f', [term2]); lReport.Add('Term3: %9.3f', [term3]); lReport.Add('Term4: %9.3f', [term4]); lReport.Add('Term5: %9.3f', [term5]); lReport.Add('Term6: %9.3f', [term6]); lReport.Add('Term7: %9.3f', [term7]); lReport.Add('Term8: %9.3f', [term8]); lReport.Add('Term9: %9.3f', [term9]); lReport.Add('Term10: %9.3f', [term10]); lReport.Add('Term11: %9.3f', [term11]); lReport.Add('Term12: %9.3f', [term12]); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // now get sums of squares SSbetsubj := term10 - term1; SSc := term5 - term1; SSrows := term12 - term1; SScxrow := term11 - term5 - term12 + term1; SSsubwgrps := term10 - term11; SSwithinsubj := term2 - term10; SSa := term3 - term1; SSb := term4 - term1; SSac := term7 - term3 - term5 + term1; SSbc := term8 - term4 - term5 + term1; SSabprime := (term6 - term3 - term4 + term1) - (term12 - term1); SSabcprime := (term9 - term6 - term7 - term8 + term3 + term4 + term5 - term1) - (term11 - term5 - term12 + term1); SSerrwithin := term2 - term10 - term9 + term11; SStotal := term2 - term1; // record degrees of freedom for sources dfbetsubj := n * p * q - 1; dfc := q - 1; dfrows := p - 1; dfcxrow := (p-1) * (q-1); dfsubwgrps := p * q * (n-1); dfwithinsubj := n * p * q * (p-1); dfa := p - 1; dfb := p - 1; dfac := (p - 1) * (q - 1); dfbc := (p - 1) * (q - 1); dfabprime := (p - 1) * (p - 2); dfabcprime := (p - 1) * (p - 2) * (q - 1); dferrwithin := p * q * (n - 1) * (p - 1); dftotal := n * p * p * q - 1; MSc := SSc / dfc; MSrows := SSrows / dfrows; MScxrow := SScxrow / dfcxrow; MSsubwgrps := SSsubwgrps / dfsubwgrps; MSa := SSa / dfa; MSb := SSb / dfb; MSac := SSac / dfac; MSbc := SSbc / dfbc; MSabprime := SSabprime / dfabprime; MSabcprime := SSabcprime / dfabcprime; MSerrwithin := SSerrwithin / dferrwithin; fc := MSc / MSsubwgrps; frows := MSrows / MSsubwgrps; fcxrow := MScxrow / MSsubwgrps; fsubwgrps := MSsubwgrps / MSerrwithin; fa := MSa / MSerrwithin; fb := MSb / MSerrwithin; fac := MSac / MSerrwithin; fbc := MSbc / MSerrwithin; fabprime := MSabprime / MSerrwithin; fabcprime := MSabcprime / MSerrwithin; probc := probf(fc,dfc,dfsubwgrps); probrows := probf(frows,dfrows,dfsubwgrps); probcxrow := probf(fcxrow,dfcxrow,dfsubwgrps); probsubwgrps := probf(fsubwgrps,dfsubwgrps,dferrwithin); proba := probf(fa,dfa,dferrwithin); probb := probf(fb,dfb,dferrwithin); probac := probf(fac,dfac,dferrwithin); probbc := probf(fbc,dfbc,dferrwithin); probabprime := probf(fabprime,dfabprime,dferrwithin); probabcprime := probf(fabcprime,dfabcprime,dferrwithin); // show ANOVA table results lReport.Add('LATIN SQUARES REPEATED ANALYSIS Plan 9'); lReport.Add(''); lReport.Add('-----------------------------------------------------------'); lReport.Add('Source SS DF MS F Prob.>F'); lReport.Add('-----------------------------------------------------------'); lReport.Add('Betw.Subj.%9.3f %9.0f', [SSbetsubj, dfbetsubj]); lReport.Add(' Factor C %9.3f %9.0f %9.3f %9.3f %9.3f', [SSc, dfc, MSc, fc, probc]); lReport.Add(' Rows %9.3f %9.0f %9.3f %9.3f %9.3f', [SSrows, dfrows, MSrows, frows, probrows]); lReport.Add(' C x row %9.3f %9.0f %9.3f %9.3f %9.3f', [SScxrow, dfcxrow, MScxrow, fcxrow, probcxrow]); lReport.Add(' Subj.w.g.%9.3f %9.0f %9.3f', [SSsubwgrps, dfsubwgrps, MSsubwgrps]); lReport.Add(''); lReport.Add('Within Sub%9.3f %9.0f', [SSwithinsubj, dfwithinsubj]); lReport.Add(' Factor A %9.3f %9.0f %9.3f %9.3f %9.3f', [SSa, dfa, MSa, fa, proba]); lReport.Add(' Factor B %9.3f %9.0f %9.3f %9.3f %9.3f', [SSb, dfb, MSb, fb, probb]); lReport.Add(' Factor AC%9.3f %9.0f %9.3f %9.3f %9.3f', [SSac, dfac, MSac, fac, probac]); lReport.Add(' Factor BC%9.3f %9.0f %9.3f %9.3f %9.3f', [SSbc, dfbc, MSbc, fbc, probbc]); lReport.Add(' AB prime %9.3f %9.0f %9.3f %9.3f %9.3f', [SSabprime, dfabprime, MSabprime, fabprime, probabprime]); lReport.Add(' ABC prime%9.3f %9.0f %9.3f %9.3f %9.3f', [SSabcprime, dfabcprime, MSabcprime, fabcprime, probabcprime]); lReport.Add(' Error w. %9.3f %9.0f %9.3f', [SSerrwithin, dferrwithin, MSerrwithin]); lReport.Add(''); lReport.Add('Total %9.3f %9.0f', [SStotal, dftotal]); lReport.Add('-----------------------------------------------------------'); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // show design for Squares c1, c2, etc. lReport.Add('Experimental Design for Latin Square '); lReport.Add(''); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); cellstring := format('%10s',[FactorA]); for i := 1 to p do cellstring := cellstring + Format(' %3d ', [i]); lReport.Add(cellstring); cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add('%10s', [GroupFactor]); for i := 1 to NoCases do begin row := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Acol,i])); // A (column) effect col := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Bcol,i])); // B (cell) effect slice := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Ccol,i])); // C (cell) effect group := round(StrToFloat(OS3MainFrm.DataGrid.Cells[Grpcol,i])); // group (row) Design[group-1, row-1] := 'B' + IntToStr(col); end; for i := 0 to rangegrp - 1 do begin cellstring := format(' %3d ',[i+1]); for j := 0 to p - 1 do cellstring := cellstring + format('%5s', [Design[i,j]]); lReport.Add(cellstring); end; cellstring := '----------'; for i := 1 to p + 1 do cellstring := cellstring + '-----'; lReport.Add(cellstring); lReport.Add(''); lReport.Add(DIVIDER); lReport.Add(''); // get means G := G / (p * p * q * n ); for i := 0 to p-1 do for j := 0 to p-1 do for k := 0 to q-1 do ABC[i,j,k] := ABC[i,j,k] / n; for i := 0 to p-1 do for j := 0 to p-1 do AB[i,j] := AB[i,j] / (n * p); for i := 0 to p-1 do AB[i,p] := AB[i,p] / (n * p * p); for j := 0 to p-1 do AB[p,j] := AB[p,j] / (n * p * p); AB[p,p] := G; for i := 0 to p-1 do for j := 0 to q-1 do AC[i,j] := AC[i,j] / (n * p); for i := 0 to p-1 do AC[i,q] := AC[i,q] / (n * p * p); for j := 0 to q-1 do AC[p,j] := AC[p,j] / (n * p * p); AC[p,q] := G; for i := 0 to p-1 do for j := 0 to q-1 do BC[i,j] := BC[i,j] / (n * p); for i := 0 to p-1 do BC[i,q] := BC[i,q] / (n * p * p); for j := 0 to q-1 do BC[p,j] := BC[p,j] / (n * p * p); BC[p,q] := G; for i := 0 to rows-1 do for j := 0 to q-1 do RC[i,j] := RC[i,j] / (p * n); for i := 0 to rows-1 do RC[i,q] := RC[i,q] / (p * q * n); for j := 0 to q-1 do RC[p,j] := RC[p,j] / (q * p * n); RC[p,q] := G; for i := 0 to p-1 do begin A[i] := A[i] / (p * n * q); B[i] := B[i] / (p * n * q); end; A[p] := G; B[p] := G; for i := 0 to q-1 do C[i] := C[i] / (p * q * n); C[q] := G; for i := 0 to rangegrp-1 do Gm[i] := Gm[i] / (p * n); Gm[rangegrp] := G; for i := 0 to nosubjects-1 do Persons[i] := Persons[i] / n; Persons[nosubjects] := G; lReport.Add('LATIN SQUARES REPEATED ANALYSIS PLAN 9'); lReport.Add(''); lReport.Add('Means for ANOVA Analysis'); lReport.Add(''); lReport.Add('ABC matrix'); lReport.Add(''); for k := 0 to q-1 do begin lReport.Add('C level %d', [k+1]); cellstring := ' '; for j := 0 to p-1 do cellstring := cellstring + Format(' %3d ', [j+1]); lReport.Add(cellstring); for i := 0 to p-1 do // row begin cellstring := Format(' %3d ', [i+1]); for j := 0 to p-1 do cellstring := cellstring + Format('%9.3f ', [ABC[i,j,k]]); lReport.Add(cellstring); end; lReport.Add(''); lReport.Add(''); end; cellstring := 'AB Means'; MatPrint(AB, p+1, p+1, cellstring, RowLabels, ColLabels, n*p*p*q, lReport); cellstring := 'AC Means'; MatPrint(AC, p+1, q+1, cellstring, RowLabels, ColLabels, n*p*p*q, lReport); cellstring := 'BC Means'; MatPrint(BC, p+1, q+1, cellstring, RowLabels, ColLabels, n*p*p*q, lReport); cellstring := 'RC Means'; MatPrint(RC, rows+1, q+1, cellstring, RowLabels, ColLabels, n*p*p*q, lReport); cellstring := 'Group Means'; for i := 0 to rangegrp-1 do ColLabels[i] := IntToStr(i+1); ColLabels[rangegrp] := 'Total'; DynVectorPrint(Gm, rangegrp+1, cellstring, ColLabels, n*p*p*q, lReport); for i := 0 to nosubjects-1 do ColLabels[i] := IntToStr(i+1); ColLabels[nosubjects] := 'Total'; cellstring := 'Subjects Means'; DynVectorPrint(Persons, nosubjects+1, cellstring, ColLabels, n*p*p*q, lReport); DisplayReport(lReport); finally lReport.Free; ColLabels := nil; RowLabels := nil; Design := nil; cellcnts := nil; R := nil; Gm := nil; Persons := nil; C := nil; B := nil; A := nil; RC := nil; BC := nil; AC := nil; AB := nil; AGC := nil; ABC := nil; end; end; initialization {$I latinsqrsunit.lrs} end.