pascal/lazarus-ccr
1
0
Fork 0
Code Issues Releases Activity

LazStats: Refactor WithinANOVAUnit.

Browse Source 
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7794 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
2020-10-23 17:58:24 +00:00
parent f76d424ce3
commit 41ce82784b
2 changed files with 484 additions and 245 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
applications/lazstats/source/forms/analysis/comparisons/withinanovaunit.lfm
View File

@ -186,13 +186,11 @@ inherited WithinANOVAFrm: TWithinANOVAFrm
inherited ReportPage: TTabSheet inherited ReportPage: TTabSheet
Caption = 'ANOVA Results' Caption = 'ANOVA Results'
end end
object ReliabilityPage: TTabSheet[1] object ReliabilityPage: TTabSheet[2]
Caption = 'Reliability Estimates' Caption = 'Reliability Estimates'
end end
object TestAssumptionsPage: TTabSheet[2] object TestAssumptionsPage: TTabSheet[3]
Caption = 'Test Assumptions' Caption = 'Test Assumptions'
end end
inherited ChartPage: TTabSheet[3]
end
end end
end end

721
applications/lazstats/source/forms/analysis/comparisons/withinanovaunit.pas
View File

@ -16,6 +16,21 @@ type
{ TWithinANOVAFrm } { TWithinANOVAFrm }
TWithinANOVAResults = record
// Sum of squares
SSRows, SScols, SSwithinRows, SStotal, SSresidual: Double;
// Mean square errors
MSRows, MScols, MSwithinRows, MStotal, MSresidual: Double;
// Degrees of freedom
DFRows, DFcols, DFWithinRows, DFtotal, DFresidual: Integer;
// Grand mean
GrandMean: Double;
// F value
F: Double;
// Probability for > F
Probability: Double;
end;
TWithinANOVAFrm = class(TBasicStatsReportAndChartForm) TWithinANOVAFrm = class(TBasicStatsReportAndChartForm)
AssumpChk: TCheckBox; AssumpChk: TCheckBox;
PlotChk: TCheckBox; PlotChk: TCheckBox;
@ -38,8 +53,39 @@ type
private private
FReliabilityReportFrame: TReportFrame; FReliabilityReportFrame: TReportFrame;
FTestAssumptionsReportFrame: TReportFrame; FTestAssumptionsReportFrame: TReportFrame;
procedure CalcANOVA(
const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
const AGrandSum, AGrandSumOfSquares: Double;
out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
out AResults: TWithinANOVAResults);
procedure CalcReliability(const AResults: TWithinANOVAResults;
ANumSelected: Integer; out R1, R2, R3, R4: Double);
procedure GetData(
out ASelected: IntDyneVec; out AColLabels: StrDyneVec;
out ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
out AGrandSum, AGrandSumOfSquares: Double);
procedure Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec); procedure Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec);
procedure TestAssumptions(const ASelected: IntDyneVec;
out ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
out ADeterminant1, ADeterminant2, Chi2, AProbability: Double;
out DF: Integer; out ErrorFound: Boolean);
procedure WriteANOVAReport(const AColLabels: StrDyneVec;
const AColMeans, AColVariances: DblDyneVec; const AResults: TWithinANOVAResults);
procedure WriteReliabilityReport(const R1, R2, R3, R4: Double);
procedure WriteTestAssumptionsReport(
const ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
const AColLabels: StrDyneVec;
ADeterminant1, ADeterminant2, Chi2, AProbability: Double; DF: Integer;
ErrorFound: Boolean);
protected protected
procedure AdjustConstraints; override; procedure AdjustConstraints; override;
procedure Compute; override; procedure Compute; override;
@ -62,7 +108,7 @@ implementation
uses uses
TAChartUtils, TACustomSeries, TAChartUtils, TACustomSeries,
GridProcs, GridProcs,
Utils, MathUnit, ChartFrameUnit; Utils, MathUnit, MatrixUnit, ChartFrameUnit;
{ TWithinANOVAFrm } { TWithinANOVAFrm }
@ -109,88 +155,62 @@ begin
end; end;
procedure TWithinANOVAFrm.Compute; procedure TWithinANOVAFrm.CalcANOVA(
const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
const AGrandSum, AGrandSumOfSquares: Double;
out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
out AResults: TWithinANOVAResults);
var var
i, j, k, f3: integer; S: Double = 0;
NoSelected, count, row: integer; SS: Double = 0;
SSrows, SScols, SSwrows, SSerr, SStot: double; term1, term2, term3, term4: Double;
MSrows, MScols, MSwrows, MSerr, MStot: double; noSelected: Integer;
dfrows, dfcols, dfwrows, dferr, dftot: double; i, count: Integer;
f1, probf1, GrandMean, Term1, Term2, Term3, Term4: double;
r1, r2, r3, r4, X, XSq, avgvar, avgcov: double;
determ1, determ2, M2, C2, chi2, prob: double;
errorfound: boolean;
Selected: IntDyneVec = nil;
ColLabels: StrDyneVec = nil;
ColMeans: DblDyneVec = nil;
ColVar: DblDyneVec = nil;
RowMeans: DblDyneVec = nil;
RowVar: DblDyneVec = nil;
ColStdDev: DblDyneVec = nil;
varcovmat: DblDyneMat = nil;
vcmat: dblDyneMat = nil;
workmat: DblDyneMat = nil;
title: string;
lReport: TStrings;
begin begin
errorfound := false; noSelected := SelList.Items.Count;
NoSelected := SelList.Items.Count; count := Length(ARowSums);
SetLength(Selected, NoSelected); term1 := sqr(AGrandSum) / (count * noSelected);
SetLength(ColLabels, NoSelected);
SetLength(ColMeans, NoSelected);
SetLength(ColVar, NoSelected);
SetLength(RowMeans, NoCases);
SetLength(RowVar, NoCases);
for i := 0 to NoSelected - 1 do term2 := AGrandSumOfSquares;
begin
Selected[i] := GetVariableIndex(OS3MainFrm.DataGrid, SelList.Items[i]);
ColLabels[i] := SelList.Items[i];
end;
// Initialize values SS := 0;
SScols := 0.0; for i := 0 to count-1 do
SSrows := 0.0; SS := SS + sqr(ARowSums[i]);
SStot := 0.0; term4 := SS / noSelected;
dfwrows := 0.0;
dftot := 0.0;
GrandMean := 0.0;
count := 0;
for i := 0 to NoSelected-1 do SS := 0;
begin for i := 0 to noSelected-1 do
ColMeans[i] := 0.0; SS := SS + sqr(AColSums[i]);
ColVar[i] := 0.0; term3 := SS / count;
end;
for j := 0 to NoCases-1 do AResults.SSrows := term4 - term1;
begin AResults.SScols := term3 - term1;
RowMeans[j] := 0.0; AResults.SSwithinRows := term2 - term4;
RowVar[j] := 0.0; AResults.SSresidual := term2 - term3 - term4 + term1;
end; AResults.SStotal := term2 - term1;
AResults.DFrows := count - 1;
AResults.DFcols := noSelected - 1;
AResults.DFwithinRows := count * (noSelected - 1);
AResults.DFresidual := (count - 1) * (noSelected - 1);
AResults.DFtotal := count * noSelected - 1;
AResults.MSrows := AResults.SSrows / AResults.DFRows;
AResults.MScols := AResults.SScols / AResults.DFcols;
AResults.MSwithinRows := AResults.SSwithinRows / AResults.DFwithinRows;
AResults.MSresidual := AResults.SSresidual / AResults.DFresidual;
AResults.MStotal := AResults.SStotal / AResults.DFtotal; // variance of all scores
AResults.GrandMean := AGrandSum / (count * noSelected);
(*
AResults.SSRows := VecSum(ARowMeans);
term1 := sqr(AGrandSum) / (count * noSelected);
term2 := AGrandSumOfSquares);
// Read data and compute sums while reading
row := 0;
for i := 1 to NoCases do
begin
if not GoodRecord(OS3MainFrm.DataGrid, i, Selected) then continue;
count := count + 1;
for j := 1 to NoSelected do
begin
k := Selected[j-1];
X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[k,i]));
Xsq := X*X;
RowMeans[row] := RowMeans[row] + X;
RowVar[row] := RowVar[row] + Xsq;
ColMeans[j-1] := ColMeans[j-1] + X;
ColVar[j-1] := ColVar[j-1] + Xsq;
GrandMean := GrandMean + X;
SStot := SStot + XSq;
end;
row := row + 1;
end;
// Calculate ANOVA results
Term1 := sqr(GrandMean) / (count * NoSelected); Term1 := sqr(GrandMean) / (count * NoSelected);
Term2 := SStot; Term2 := SStot;
for i := 0 to count-1 do for i := 0 to count-1 do
@ -229,185 +249,178 @@ begin
end; end;
f1 := MScols / MSerr; // treatment F statistic f1 := MScols / MSerr; // treatment F statistic
probf1 := ProbF(f1, dfcols, dferr); probf1 := ProbF(f1, dfcols, dferr);
*)
SetLength(ARowMeans, count);
SetLength(ARowVariances, count);
for i := 0 to count-1 do
begin
ARowVariances[i] := (ARowSumsOfSquares[i] - (ARowSums[i] * ARowSums[i]) / noSelected) / (noSelected - 1);
ARowMeans[i] := ARowSums[i] / noSelected;
end;
SetLength(AColMeans, noSelected);
SetLength(AColVariances, noSelected);
for i := 0 to noSelected-1 do
begin
AColVariances[i] := (AColSumsOfSquares[i] - (AColSums[i] * AColSums[i]) / count) / (count - 1);
AColMeans[i] := AColSums[i] / count;
end;
with AResults do
begin
F := MScols / MSresidual; // treatment F statistic
Probability := ProbF(F, DFcols, DFresidual);
end;
end;
procedure TWithinANOVAFrm.CalcReliability(const AResults: TWithinANOVAResults;
ANumSelected: Integer; out R1, R2, R3, R4: Double);
begin
with AResults do
begin
// unadjusted reliability of test
R1 := 1.0 - (MSwithinRows / MSrows);
// R2 is unadjusted reliability of a single item
R2 := (MSrows - MSwithinRows) / (MSrows + (ANumSelected - 1) * MSwithinRows);
// Cronbach alpha for test
R3 := (MSrows - MSresidual) / MSrows;
// R4 is adjusted reliability of a single item
R4 := (MSrows - MSresidual) / (MSrows + (ANumSelected - 1) * MSresidual);
end;
end;
procedure TWithinANOVAFrm.Compute;
var
j, noSelected, DF: integer;
r1, r2, r3, r4: double;
grandSum, grandSS: Double;
determ1, determ2, chi2, prob: Double;
errorfound: boolean;
selected: IntDyneVec = nil;
colLabels: StrDyneVec = nil;
colSums: DblDyneVec = nil;
colMeans: DblDyneVec = nil;
colSS: DblDyneVec = nil;
colVars: DblDyneVec = nil;
rowSums: DblDyneVec = nil;
rowMeans: DblDyneVec = nil;
rowSS: DblDyneVec = nil;
rowVars: DblDyneVec = nil;
sampleVarCovarMat: DblDyneMat = nil;
assumedVarCovarMat: DblDyneMat = nil;
res: TWithinANOVAResults;
begin
noSelected := SelList.Items.Count;
// Read data and compute sums while reading
GetData(selected, colLabels, rowSums, rowSS, colSums, colSS, grandSum, grandSS);
// Calculate ANOVA
CalcANOVA(rowSums, rowSS, colSums, colSS, grandSum, grandSS, rowMeans, rowVars, colMeans, colVars, res);
WriteANOVAReport(colLabels, colMeans, colVars, res);
// Do reliability terms if requested // Do reliability terms if requested
if RelChk.Checked then if RelChk.Checked then
begin begin
r1 := 1.0 - (MSwrows / MSrows); // unadjusted reliability of test CalcReliability(res, noSelected, r1, r2, r3, r4);
r2 := (MSrows - MSwrows) / (MSrows + (NoSelected - 1) * MSwrows); WriteReliabilityReport(r1, r2, r3, r4);
// r2 is unadjusted reliability of a single item
r3 := (MSrows - MSerr) / MSrows; // Cronbach alpha for test
r4 := (MSrows - MSerr) / (MSrows + (NoSelected - 1) * MSerr);
// r4 is adjusted reliability of a single item
end;
// do homogeneity of variance and covariance checks if requested
lReport := TStringList.Create;
try
// print results
lReport.Add('TREATMENTS BY SUBJECTS (AxS) ANOVA RESULTS');
lReport.Add('');
lReport.Add('Data File: ' + OS3MainFrm.FileNameEdit.Text);
lReport.Add('');
lReport.Add('');
lReport.Add('-----------------------------------------------------------');
lReport.Add('SOURCE DF SS MS F Prob. > F');
lReport.Add('-----------------------------------------------------------');
lReport.Add('SUBJECTS %4.0f%10.3f%10.3f', [dfrows, SSrows, MSrows]);
lReport.Add('WITHIN SUBJECTS%4.0f%10.3f%10.3f', [dfwrows, SSwrows, MSwrows]);
lReport.Add(' TREATMENTS %4.0f%10.3f%10.3f%10.3f%10.3f', [dfcols, SScols, MScols, f1, probf1]);
lReport.Add(' RESIDUAL %4.0f%10.3f%10.3f', [dferr, SSerr, MSerr]);
lReport.Add('-----------------------------------------------------------');
lReport.Add('TOTAL %4.0f%10.3f%10.3f', [dftot, SStot, MStot]);
lReport.Add('-----------------------------------------------------------');
lReport.Add('');
lReport.Add('');
lReport.Add('TREATMENT (COLUMN) MEANS AND STANDARD DEVIATIONS');
lReport.Add('VARIABLE MEAN STD.DEV. ');
lReport.Add('-------- ---------- ----------');
for i := 1 to NoSelected do
lReport.Add('%-8s %10.3f %10.3f', [ColLabels[i-1], ColMeans[i-1], sqrt(ColVar[i-1])]);
lReport.Add('');
lReport.Add('Mean of all scores: %8.3f', [GrandMean]);
lReport.Add(' with standard deviation: %8.3f', [sqrt(MStot)]);
FReportFrame.DisplayReport(lReport);
// Do reliability estimates if requested
if RelChk.Checked then
begin
lReport.Clear;
lReport.Add('RELIABILITY ESTIMATES');
lReport.Add('');
lReport.Add('TYPE OF ESTIMATE VALUE ');
lReport.Add('---------------------------- -------');
lReport.Add('Unadjusted total reliability %7.3f', [r1]);
lReport.Add('Unadjusted item reliability %7.3f', [r2]);
lReport.Add('Adjusted total (Cronbach) %7.3f', [r3]);
lReport.Add('Adjusted item reliability %7.3f', [r4]);
FReliabilityReportFrame.DisplayReport(lReport);
end;
ReliabilityPage.TabVisible := RelChk.Checked; ReliabilityPage.TabVisible := RelChk.Checked;
// Test assumptions of variance - covariance homogeneity if requested
if AssumpChk.Checked then
begin
SetLength(varcovmat,NoSelected+1,NoSelected+1);
SetLength(vcmat,NoSelected+1,NoSelected+1);
SetLength(workmat,NoSelected+1,NoSelected+1);
SetLength(ColStdDev,NoSelected);
errorfound := false;
count := NoCases;
lReport.Clear;
lReport.Add('BOX TEST FOR HOMOGENEITY OF VARIANCE-COVARIANCE MATRIX');
lReport.Add('');
GridCovar(NoSelected, Selected, varcovmat, ColMeans, ColVar, ColStdDev, errorfound, count);
title := 'SAMPLE COVARIANCE MATRIX';
MatPrint(varcovmat, NoSelected, NoSelected, title, ColLabels, ColLabels, NoCases, lReport);
if errorfound then
ErrorMsg('Zero variance found for a variable.');
// get average of variances into workmat diagonal and average of
// covariances into workmat off-diagonals (See Winer, pg 371)
avgvar := 0.0;
avgcov := 0.0;
for i := 0 to NoSelected-1 do
vcmat[i,i] := varcovmat[i,i];
for i := 0 to NoSelected-2 do
begin
for j := i+1 to NoSelected-1 do
begin
vcmat[i,j] := varcovmat[i,j];
vcmat[j,i] := vcmat[i,j];
end;
end;
for i := 0 to NoSelected-1 do
avgvar := avgvar + varcovmat[i,i];
for i := 0 to NoSelected-2 do
for j := i+1 to NoSelected-1 do
avgcov := avgcov + varcovmat[i,j];
avgvar := avgvar / NoSelected;
avgcov := avgcov / (NoSelected * NoSelected - 1) / 2.0;
for i := 0 to NoSelected-1 do
workmat[i,i] := avgvar;
for i := 0 to NoSelected-2 do
begin
for j := i+1 to NoSelected-1 do
begin
workmat[i,j] := avgcov;
workmat[j,i] := workmat[i,j];
end;
end;
// get determinants of varcov and workmat
determ1 := 0.0;
determ2 := 0.0;
M2 := 0.0;
C2 := 0.0;
chi2 := 0.0;
prob := 0.0;
Determ(vcmat,NoSelected,NoSelected,determ1,errorfound);
if determ1 < 0.0 then determ1 := 0.0;
Determ(workmat,NoSelected,NoSelected,determ2,errorfound);
if determ2 < 0.0 then determ2 := 0.0;
count := NoCases;
GridCovar(NoSelected,Selected,varcovmat,ColMeans,ColVar,ColStdDev,errorfound,count);
errorfound := false;
if ((determ1 > 0.0) and (determ2 > 0.0)) then
M2 := -(NoCases*NoSelected - 1) * ln(determ1 / determ2)
else
begin
M2 := 0.0;
errorfound := true;
ErrorMsg('A determinant <= zero was found.');
end;
if not errorfound then
begin
C2 := NoSelected * (NoSelected+1) * (NoSelected + 1) * (2 * NoSelected - 3);
C2 := C2 / (6 * (count - 1)*(NoSelected - 1) * (NoSelected * NoSelected + NoSelected - 4));
chi2 := (1.0 - C2) * M2;
f3 := (NoSelected * NoSelected + NoSelected - 4) div 2;
if ((chi2 > 0.01) and (chi2 < 1000.0)) then
prob := chisquaredprob(chi2,f3)
else
begin
if chi2 <= 0.0 then prob := 1.0;
if chi2 >= 1000.0 then prob := 0.0;
end;
end;
title := 'ASSUMED POP. COVARIANCE MATRIX';
for i := 0 to NoSelected-1 do
for j := 0 to NoSelected-1 do
varcovmat[i,j] := workmat[i,j];
MatPrint(varcovmat, NoSelected, NoSelected, title, ColLabels, ColLabels, NoCases, lReport);
lReport.Add('Determinant of variance-covariance matrix: %10.3g', [determ1]);
lReport.Add('Determinant of homogeneity matrix: %10.3g', [determ2]);
if not errorfound then
begin
lReport.Add('ChiSquare: %10.3f', [chi2]);
lReport.Add(' with %d degrees of freedom', [f3]);
lReport.Add('Probability of larger chisquare: %10.3f', [1.0-prob]);
end;
FTestAssumptionsReportFrame.DisplayReport(lReport);
end;
TestAssumptionsPage.TabVisible := AssumpChk.Checked;
finally
lReport.Free;
end; end;
{ Finally, plot values if indicated in options list } // Test assumptions of variance - covariance homogeneity if requested
if AssumpChk.Checked then
begin
TestAssumptions(selected, sampleVarCovarMat, assumedVarCovarMat, determ1, determ2, chi2, prob, DF, errorFound);
WriteTestAssumptionsReport(sampleVarCovarMat, assumedVarCovarMat, colLabels, determ1, determ2, chi2, prob, DF, errorFound);
end;
TestAssumptionsPage.TabVisible := AssumpChk.Checked;
// Finally, plot values if indicated in options list
if PlotChk.Checked then if PlotChk.Checked then
Plot(ColMeans, ColLabels); Plot(ColMeans, ColLabels);
ChartPage.TabVisible := PlotChk.Checked; ChartPage.TabVisible := PlotChk.Checked;
// Make sure that the chart tab is at the end of the pagecontrol.
ChartPage.PageIndex := PageControl.PageCount-1; ChartPage.PageIndex := PageControl.PageCount-1;
end; end;
procedure TWithinANOVAFrm.GetData(
out ASelected: IntDyneVec; out AColLabels: StrDyneVec;
out ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
out AGrandSum, AGrandSumOfSquares: Double);
var
i, j, row, count, noSelected: Integer;
k: Integer;
X, Xsq: Double;
begin
ARowSums := nil; // to silence FPC 3.2
ARowSumsOfSquares := nil;
AColSums := nil;
AColSumsOfSquares := nil;
AColLabels := nil;
ASelected := nil;
noSelected := SelList.Items.Count;
SetLength(ASelected, noSelected);
SetLength(AColLabels, noSelected);
SetLength(AColSums, noSelected);
SetLength(AColSumsOfSquares, noSelected);
SetLength(ARowSums, NoCases);
SetLength(ARowSumsOfSquares, NoCases);
for i := 0 to noSelected-1 do
begin
ASelected[i] := GetVariableIndex(OS3MainFrm.DataGrid, SelList.Items[i]);
AColLabels[i] := SelList.Items[i];
end;
for i := 0 to noSelected-1 do
begin
AColSums[i] := 0.0;
AColSumsOfSquares[i] := 0.0;
end;
for j := 0 to NoCases-1 do
begin
ARowSums[j] := 0.0;
ARowSumsOfSquares[j] := 0.0;
end;
AGrandSum := 0;
AGrandSumOfSquares := 0;
count := 0;
row := 0;
for i := 1 to NoCases do
begin
if not GoodRecord(OS3MainFrm.DataGrid, i, ASelected) then continue;
count := count + 1;
for j := 0 to High(ASelected) do
begin
k := ASelected[j];
X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[k, i]));
Xsq := X*X;
ARowSums[row] := ARowSums[row] + X;
ARowSumsOfSquares[row] := ARowSumsOfSquares[row] + Xsq;
AColSums[j] := AColSums[j] + X;
AColSumsOfSquares[j] := AColSumsOfSquares[j] + Xsq;
AGrandSum := AGrandSum + X;
AGrandSumOfSquares := AGrandSumOfSquares + XSq;
end;
row := row + 1;
end;
SetLength(ARowSums, count);
SetLength(ARowSumsOfSquares, count);
// Lengths of AColSums etc already correct.
end;
procedure TWithinANOVAFrm.InBtnClick(Sender: TObject); procedure TWithinANOVAFrm.InBtnClick(Sender: TObject);
var var
i: integer; i: integer;
@ -506,6 +519,121 @@ begin
end; end;
procedure TWithinANOVAFrm.TestAssumptions(const ASelected: IntDyneVec;
out ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
out ADeterminant1, ADeterminant2, Chi2, AProbability: Double;
out DF: Integer; out ErrorFound: Boolean);
var
vcMat: DblDyneMat = nil;
workMat: DblDyneMat = nil;
colMeans: DblDyneVec = nil;
colVars: DblDyneVec = nil;
colStdDevs: DblDyneVec = nil;
avgVar, avgCov, C2, M2: Double;
i, j, noSelected, count: Integer;
begin
ErrorFound := false;
noSelected := Length(ASelected);
count := NoCases;
DF := 0;
Chi2 := NaN;
AProbability := NaN;
SetLength(ASampleVarCovarMat, noSelected+1, noSelected+1); // +1 due to augmentation in GridCovar
SetLength(AssumedVarCovarMat, noSelected+1, noSelected+1);
SetLength(vcMat, noSelected+1, noSelected+1);
SetLength(workMat, noSelected+1, noSelected+1);
SetLength(colMeans, noSelected+1);
SetLength(colVars, noSelected+1);
SetLength(colStdDevs, noSelected+1);
GridCovar(noSelected, ASelected, ASampleVarCovarMat, colMeans, colVars, colStdDevs, ErrorFound, count);
if Errorfound then
begin
ErrorMsg('Zero variance found for a variable.');
exit;
end;
// get average of variances into workmat diagonal and average of
// covariances into workmat off-diagonals (See Winer, pg 371)
avgVar := 0.0;
avgCov := 0.0;
for i := 0 to noSelected-1 do
vcMat[i, i] := ASampleVarCovarMat[i,i];
for i := 0 to noSelected-2 do
begin
for j := i+1 to noSelected-1 do
begin
vcMat[i, j] := ASampleVarCovarMat[i, j];
vcMat[j, i] := vcMat[i, j];
end;
end;
for i := 0 to noSelected-1 do
avgVar := avgVar + ASampleVarCovarMat[i, i];
for i := 0 to NoSelected-2 do
for j := i+1 to NoSelected-1 do
avgCov := avgCov + ASampleVarCovarMat[i, j];
avgVar := avgVar / noSelected;
avgCov := avgCov / (noSelected * noSelected - 1) / 2.0;
for i := 0 to noSelected-1 do
workMat[i, i] := avgVar;
for i := 0 to noSelected-2 do
begin
for j := i+1 to noSelected-1 do
begin
workMat[i, j] := avgCov;
workMat[j, i] := workMat[i, j];
end;
end;
// get determinants of SampleVarCovarMat and workMat
Determ(vcMat, noSelected, noSelected, ADeterminant1, ErrorFound);
if ADeterminant1 < 0.0 then ADeterminant1 := 0.0;
Determ(workMat, noSelected, noSelected, ADeterminant2, ErrorFound);
if ADeterminant2 < 0.0 then ADeterminant2 := 0.0;
// Get assumed var-covariance matrix
count := NoCases;
GridCovar(noSelected, ASelected, AssumedVarCovarMat, colMeans, colVars, colStdDevs, ErrorFound, count);
ErrorFound := false;
if ((ADeterminant1 > 0.0) and (ADeterminant2 > 0.0)) then
M2 := -(NoCases*noSelected - 1) * ln(ADeterminant1 / ADeterminant2)
else
begin
M2 := 0.0;
errorFound := true;
ErrorMsg('A determinant <= zero was found.');
end;
if not ErrorFound then
begin
C2 := noSelected * (noSelected+1) * (noSelected + 1) * (2 * noSelected - 3);
C2 := C2 / (6 * (count - 1) * (noSelected - 1) * (noSelected * noSelected + noSelected - 4));
Chi2 := (1.0 - C2) * M2;
DF := (noSelected * noSelected + noSelected - 4) div 2;
if ((Chi2 > 0.01) and (Chi2 < 1000.0)) then
AProbability := ChiSquaredProb(Chi2, DF)
else
begin
if Chi2 <= 0.0 then AProbability := 1.0;
if Chi2 >= 1000.0 then AProbability := 0.0;
end;
end;
for i := 0 to NoSelected-1 do
for j := 0 to NoSelected-1 do
AssumedVarCovarMat[i,j] := workMat[i, j];
end;
procedure TWithinANOVAFrm.UpdateBtnStates; procedure TWithinANOVAFrm.UpdateBtnStates;
var var
i: Integer; i: Integer;
@ -580,5 +708,118 @@ begin
end; end;
{ Write ANOVA results to ReportFrame }
procedure TWithinANOVAFrm.WriteANOVAReport(const AColLabels: StrDyneVec;
const AColMeans, AColVariances: DblDyneVec; const AResults: TWithinANOVAResults);
var
lReport: TStrings;
noSelected: Integer;
i: Integer;
begin
noSelected := Length(AColMeans);
lReport := TStringList.Create;
try
with AResults do
begin
lReport.Add('TREATMENTS BY SUBJECTS (AxS) ANOVA RESULTS');
lReport.Add('');
lReport.Add('Data File: ' + OS3MainFrm.FileNameEdit.Text);
lReport.Add('');
lReport.Add('-----------------------------------------------------------------');
lReport.Add('SOURCE DF SS MS F Prob. > F');
lReport.Add('-----------------------------------------------------------------');
lReport.Add('SUBJECTS %4d %10.3f %10.3f', [DFrows, SSrows, MSrows]);
lReport.Add('WITHIN SUBJECTS %4d %10.3f %10.3f', [DFwithinRows, SSwithinRows, MSwithinRows]);
lReport.Add(' TREATMENTS %4d %10.3f %10.3f %10.3f %10.3f', [DFcols, SScols, MScols, F, Probability]);
lReport.Add(' RESIDUAL %4d %10.3f %10.3f', [DFresidual, SSresidual, MSresidual]);
lReport.Add('-----------------------------------------------------------------');
lReport.Add('TOTAL %4d %10.3f %10.3f', [DFtotal, SStotal, MStotal]);
lReport.Add('-----------------------------------------------------------------');
lReport.Add('');
lReport.Add('');
lReport.Add('TREATMENT (COLUMN) MEANS AND STANDARD DEVIATIONS');
lReport.Add('');
lReport.Add('VARIABLE MEAN STD.DEV. ');
lReport.Add('-------- ---------- ----------');
for i := 1 to NoSelected do
lReport.Add('%-8s %10.3f %10.3f', [AColLabels[i-1], AColMeans[i-1], sqrt(AColVariances[i-1])]);
lReport.Add('');
lReport.Add('Mean of all scores: %8.3f', [GrandMean]);
lReport.Add(' with standard deviation: %8.3f', [sqrt(MStotal)]);
end;
FReportFrame.DisplayReport(lReport);
finally
lReport.Free;
end;
end;
procedure TWithinANOVAFrm.WriteReliabilityReport(const R1, R2, R3, R4: double);
var
lReport: TStrings;
begin
lReport := TStringList.Create;
try
lReport.Add('RELIABILITY ESTIMATES');
lReport.Add('');
lReport.Add('TYPE OF ESTIMATE VALUE ');
lReport.Add('---------------------------- -------');
lReport.Add('Unadjusted total reliability %7.3f', [R1]);
lReport.Add('Unadjusted item reliability %7.3f', [R2]);
lReport.Add('Adjusted total (Cronbach) %7.3f', [R3]);
lReport.Add('Adjusted item reliability %7.3f', [R4]);
FReliabilityReportFrame.DisplayReport(lReport);
finally
lReport.Free;
end;
end;
procedure TWithinANOVAFrm.WriteTestAssumptionsReport(
const ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
const AColLabels: StrDyneVec;
ADeterminant1, ADeterminant2, Chi2, AProbability: Double; DF: Integer;
ErrorFound: Boolean);
var
lReport: TStrings;
title: String;
noSelected: Integer;
begin
noSelected := SelList.Items.Count;
lReport := TStringList.Create;
try
lReport.Add('BOX TEST FOR HOMOGENEITY OF VARIANCE-COVARIANCE MATRIX');
lReport.Add('');
title := 'SAMPLE COVARIANCE MATRIX';
MatPrint(ASampleVarCovarMat, noSelected, noSelected, title, AColLabels, AColLabels, NoCases, lReport);
lReport.Add('');
title := 'ASSUMED POPULATION COVARIANCE MATRIX';
MatPrint(AssumedVarCovarMat, noSelected, noSelected, title, AColLabels, AColLabels, NoCases, lReport);
lReport.Add('');
lReport.Add('Determinant of variance-covariance matrix: %10.3g', [ADeterminant1]);
lReport.Add('Determinant of homogeneity matrix: %10.3g', [ADeterminant2]);
if not errorfound then
begin
lReport.Add('ChiSquare: %10.3f', [Chi2]);
lReport.Add(' with %d degrees of freedom', [DF]);
lReport.Add('Probability of larger chisquare: %10.3f', [1.0 - AProbability]);
end;
FTestAssumptionsReportFrame.DisplayReport(lReport);
finally
lReport.Free;
end;
end;
end. end.