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LazStats: Refactor WithinANOVAUnit.
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7794 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
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@ -186,13 +186,11 @@ inherited WithinANOVAFrm: TWithinANOVAFrm
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inherited ReportPage: TTabSheet
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inherited ReportPage: TTabSheet
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Caption = 'ANOVA Results'
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Caption = 'ANOVA Results'
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end
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end
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object ReliabilityPage: TTabSheet[1]
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object ReliabilityPage: TTabSheet[2]
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Caption = 'Reliability Estimates'
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Caption = 'Reliability Estimates'
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end
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end
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object TestAssumptionsPage: TTabSheet[2]
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object TestAssumptionsPage: TTabSheet[3]
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Caption = 'Test Assumptions'
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Caption = 'Test Assumptions'
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end
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end
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inherited ChartPage: TTabSheet[3]
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end
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end
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end
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end
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end
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@ -16,6 +16,21 @@ type
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{ TWithinANOVAFrm }
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{ TWithinANOVAFrm }
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TWithinANOVAResults = record
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// Sum of squares
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SSRows, SScols, SSwithinRows, SStotal, SSresidual: Double;
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// Mean square errors
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MSRows, MScols, MSwithinRows, MStotal, MSresidual: Double;
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// Degrees of freedom
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DFRows, DFcols, DFWithinRows, DFtotal, DFresidual: Integer;
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// Grand mean
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GrandMean: Double;
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// F value
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F: Double;
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// Probability for > F
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Probability: Double;
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end;
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TWithinANOVAFrm = class(TBasicStatsReportAndChartForm)
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TWithinANOVAFrm = class(TBasicStatsReportAndChartForm)
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AssumpChk: TCheckBox;
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AssumpChk: TCheckBox;
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PlotChk: TCheckBox;
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PlotChk: TCheckBox;
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@ -38,8 +53,39 @@ type
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private
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private
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FReliabilityReportFrame: TReportFrame;
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FReliabilityReportFrame: TReportFrame;
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FTestAssumptionsReportFrame: TReportFrame;
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FTestAssumptionsReportFrame: TReportFrame;
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procedure CalcANOVA(
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const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
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const AGrandSum, AGrandSumOfSquares: Double;
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out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
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out AResults: TWithinANOVAResults);
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procedure CalcReliability(const AResults: TWithinANOVAResults;
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ANumSelected: Integer; out R1, R2, R3, R4: Double);
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procedure GetData(
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out ASelected: IntDyneVec; out AColLabels: StrDyneVec;
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out ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
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out AGrandSum, AGrandSumOfSquares: Double);
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procedure Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec);
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procedure Plot(ColMeans: DblDyneVec; ColLabels: StrDyneVec);
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procedure TestAssumptions(const ASelected: IntDyneVec;
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out ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
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out ADeterminant1, ADeterminant2, Chi2, AProbability: Double;
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out DF: Integer; out ErrorFound: Boolean);
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procedure WriteANOVAReport(const AColLabels: StrDyneVec;
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const AColMeans, AColVariances: DblDyneVec; const AResults: TWithinANOVAResults);
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procedure WriteReliabilityReport(const R1, R2, R3, R4: Double);
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procedure WriteTestAssumptionsReport(
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const ASampleVarCovarMat, AssumedVarCovarMat: DblDyneMat;
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const AColLabels: StrDyneVec;
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ADeterminant1, ADeterminant2, Chi2, AProbability: Double; DF: Integer;
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ErrorFound: Boolean);
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protected
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protected
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procedure AdjustConstraints; override;
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procedure AdjustConstraints; override;
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procedure Compute; override;
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procedure Compute; override;
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@ -62,7 +108,7 @@ implementation
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uses
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uses
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TAChartUtils, TACustomSeries,
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TAChartUtils, TACustomSeries,
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GridProcs,
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GridProcs,
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Utils, MathUnit, ChartFrameUnit;
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Utils, MathUnit, MatrixUnit, ChartFrameUnit;
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{ TWithinANOVAFrm }
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{ TWithinANOVAFrm }
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@ -109,88 +155,62 @@ begin
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end;
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end;
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procedure TWithinANOVAFrm.Compute;
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procedure TWithinANOVAFrm.CalcANOVA(
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const ARowSums, ARowSumsOfSquares, AColSums, AColSumsOfSquares: DblDyneVec;
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const AGrandSum, AGrandSumOfSquares: Double;
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out ARowMeans, ARowVariances, AColMeans,AColVariances: DblDyneVec;
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out AResults: TWithinANOVAResults);
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var
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var
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i, j, k, f3: integer;
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S: Double = 0;
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NoSelected, count, row: integer;
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SS: Double = 0;
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SSrows, SScols, SSwrows, SSerr, SStot: double;
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term1, term2, term3, term4: Double;
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MSrows, MScols, MSwrows, MSerr, MStot: double;
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noSelected: Integer;
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dfrows, dfcols, dfwrows, dferr, dftot: double;
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i, count: Integer;
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f1, probf1, GrandMean, Term1, Term2, Term3, Term4: double;
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r1, r2, r3, r4, X, XSq, avgvar, avgcov: double;
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determ1, determ2, M2, C2, chi2, prob: double;
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errorfound: boolean;
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Selected: IntDyneVec = nil;
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ColLabels: StrDyneVec = nil;
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ColMeans: DblDyneVec = nil;
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ColVar: DblDyneVec = nil;
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RowMeans: DblDyneVec = nil;
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RowVar: DblDyneVec = nil;
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ColStdDev: DblDyneVec = nil;
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varcovmat: DblDyneMat = nil;
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vcmat: dblDyneMat = nil;
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workmat: DblDyneMat = nil;
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title: string;
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lReport: TStrings;
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begin
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errorfound := false;
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NoSelected := SelList.Items.Count;
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SetLength(Selected, NoSelected);
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SetLength(ColLabels, NoSelected);
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SetLength(ColMeans, NoSelected);
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SetLength(ColVar, NoSelected);
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SetLength(RowMeans, NoCases);
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SetLength(RowVar, NoCases);
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for i := 0 to NoSelected - 1 do
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begin
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begin
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Selected[i] := GetVariableIndex(OS3MainFrm.DataGrid, SelList.Items[i]);
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noSelected := SelList.Items.Count;
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ColLabels[i] := SelList.Items[i];
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count := Length(ARowSums);
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end;
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// Initialize values
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term1 := sqr(AGrandSum) / (count * noSelected);
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SScols := 0.0;
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SSrows := 0.0;
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SStot := 0.0;
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dfwrows := 0.0;
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dftot := 0.0;
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GrandMean := 0.0;
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count := 0;
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for i := 0 to NoSelected-1 do
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term2 := AGrandSumOfSquares;
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begin
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ColMeans[i] := 0.0;
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SS := 0;
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ColVar[i] := 0.0;
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for i := 0 to count-1 do
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end;
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SS := SS + sqr(ARowSums[i]);
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for j := 0 to NoCases-1 do
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term4 := SS / noSelected;
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begin
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RowMeans[j] := 0.0;
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SS := 0;
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RowVar[j] := 0.0;
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for i := 0 to noSelected-1 do
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end;
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SS := SS + sqr(AColSums[i]);
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term3 := SS / count;
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AResults.SSrows := term4 - term1;
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AResults.SScols := term3 - term1;
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AResults.SSwithinRows := term2 - term4;
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AResults.SSresidual := term2 - term3 - term4 + term1;
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AResults.SStotal := term2 - term1;
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AResults.DFrows := count - 1;
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AResults.DFcols := noSelected - 1;
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AResults.DFwithinRows := count * (noSelected - 1);
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AResults.DFresidual := (count - 1) * (noSelected - 1);
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AResults.DFtotal := count * noSelected - 1;
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AResults.MSrows := AResults.SSrows / AResults.DFRows;
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AResults.MScols := AResults.SScols / AResults.DFcols;
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AResults.MSwithinRows := AResults.SSwithinRows / AResults.DFwithinRows;
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AResults.MSresidual := AResults.SSresidual / AResults.DFresidual;
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AResults.MStotal := AResults.SStotal / AResults.DFtotal; // variance of all scores
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AResults.GrandMean := AGrandSum / (count * noSelected);
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(*
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AResults.SSRows := VecSum(ARowMeans);
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term1 := sqr(AGrandSum) / (count * noSelected);
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term2 := AGrandSumOfSquares);
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// Read data and compute sums while reading
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row := 0;
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for i := 1 to NoCases do
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begin
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if not GoodRecord(OS3MainFrm.DataGrid, i, Selected) then continue;
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count := count + 1;
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for j := 1 to NoSelected do
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begin
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k := Selected[j-1];
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X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[k,i]));
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Xsq := X*X;
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RowMeans[row] := RowMeans[row] + X;
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RowVar[row] := RowVar[row] + Xsq;
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ColMeans[j-1] := ColMeans[j-1] + X;
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ColVar[j-1] := ColVar[j-1] + Xsq;
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GrandMean := GrandMean + X;
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SStot := SStot + XSq;
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end;
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row := row + 1;
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end;
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// Calculate ANOVA results
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Term1 := sqr(GrandMean) / (count * NoSelected);
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Term1 := sqr(GrandMean) / (count * NoSelected);
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Term2 := SStot;
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Term2 := SStot;
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for i := 0 to count-1 do
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for i := 0 to count-1 do
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@ -229,185 +249,178 @@ begin
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end;
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end;
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f1 := MScols / MSerr; // treatment F statistic
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f1 := MScols / MSerr; // treatment F statistic
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probf1 := ProbF(f1, dfcols, dferr);
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probf1 := ProbF(f1, dfcols, dferr);
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*)
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SetLength(ARowMeans, count);
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SetLength(ARowVariances, count);
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for i := 0 to count-1 do
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begin
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ARowVariances[i] := (ARowSumsOfSquares[i] - (ARowSums[i] * ARowSums[i]) / noSelected) / (noSelected - 1);
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ARowMeans[i] := ARowSums[i] / noSelected;
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end;
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SetLength(AColMeans, noSelected);
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SetLength(AColVariances, noSelected);
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for i := 0 to noSelected-1 do
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begin
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AColVariances[i] := (AColSumsOfSquares[i] - (AColSums[i] * AColSums[i]) / count) / (count - 1);
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AColMeans[i] := AColSums[i] / count;
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end;
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with AResults do
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begin
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F := MScols / MSresidual; // treatment F statistic
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Probability := ProbF(F, DFcols, DFresidual);
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end;
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end;
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procedure TWithinANOVAFrm.CalcReliability(const AResults: TWithinANOVAResults;
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ANumSelected: Integer; out R1, R2, R3, R4: Double);
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begin
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with AResults do
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begin
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// unadjusted reliability of test
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R1 := 1.0 - (MSwithinRows / MSrows);
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// R2 is unadjusted reliability of a single item
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R2 := (MSrows - MSwithinRows) / (MSrows + (ANumSelected - 1) * MSwithinRows);
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// Cronbach alpha for test
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R3 := (MSrows - MSresidual) / MSrows;
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// R4 is adjusted reliability of a single item
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R4 := (MSrows - MSresidual) / (MSrows + (ANumSelected - 1) * MSresidual);
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end;
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end;
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procedure TWithinANOVAFrm.Compute;
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var
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j, noSelected, DF: integer;
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r1, r2, r3, r4: double;
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grandSum, grandSS: Double;
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determ1, determ2, chi2, prob: Double;
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errorfound: boolean;
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selected: IntDyneVec = nil;
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colLabels: StrDyneVec = nil;
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colSums: DblDyneVec = nil;
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colMeans: DblDyneVec = nil;
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colSS: DblDyneVec = nil;
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colVars: DblDyneVec = nil;
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rowSums: DblDyneVec = nil;
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rowMeans: DblDyneVec = nil;
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rowSS: DblDyneVec = nil;
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rowVars: DblDyneVec = nil;
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sampleVarCovarMat: DblDyneMat = nil;
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assumedVarCovarMat: DblDyneMat = nil;
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res: TWithinANOVAResults;
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begin
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noSelected := SelList.Items.Count;
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// Read data and compute sums while reading
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GetData(selected, colLabels, rowSums, rowSS, colSums, colSS, grandSum, grandSS);
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// Calculate ANOVA
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CalcANOVA(rowSums, rowSS, colSums, colSS, grandSum, grandSS, rowMeans, rowVars, colMeans, colVars, res);
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WriteANOVAReport(colLabels, colMeans, colVars, res);
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// Do reliability terms if requested
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// Do reliability terms if requested
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if RelChk.Checked then
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if RelChk.Checked then
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begin
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begin
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r1 := 1.0 - (MSwrows / MSrows); // unadjusted reliability of test
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CalcReliability(res, noSelected, r1, r2, r3, r4);
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r2 := (MSrows - MSwrows) / (MSrows + (NoSelected - 1) * MSwrows);
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WriteReliabilityReport(r1, r2, r3, r4);
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// r2 is unadjusted reliability of a single item
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r3 := (MSrows - MSerr) / MSrows; // Cronbach alpha for test
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r4 := (MSrows - MSerr) / (MSrows + (NoSelected - 1) * MSerr);
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// r4 is adjusted reliability of a single item
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end;
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// do homogeneity of variance and covariance checks if requested
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lReport := TStringList.Create;
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try
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// print results
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lReport.Add('TREATMENTS BY SUBJECTS (AxS) ANOVA RESULTS');
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lReport.Add('');
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lReport.Add('Data File: ' + OS3MainFrm.FileNameEdit.Text);
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lReport.Add('');
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lReport.Add('');
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lReport.Add('-----------------------------------------------------------');
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lReport.Add('SOURCE DF SS MS F Prob. > F');
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lReport.Add('-----------------------------------------------------------');
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lReport.Add('SUBJECTS %4.0f%10.3f%10.3f', [dfrows, SSrows, MSrows]);
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lReport.Add('WITHIN SUBJECTS%4.0f%10.3f%10.3f', [dfwrows, SSwrows, MSwrows]);
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lReport.Add(' TREATMENTS %4.0f%10.3f%10.3f%10.3f%10.3f', [dfcols, SScols, MScols, f1, probf1]);
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lReport.Add(' RESIDUAL %4.0f%10.3f%10.3f', [dferr, SSerr, MSerr]);
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lReport.Add('-----------------------------------------------------------');
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lReport.Add('TOTAL %4.0f%10.3f%10.3f', [dftot, SStot, MStot]);
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lReport.Add('-----------------------------------------------------------');
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lReport.Add('');
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lReport.Add('');
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lReport.Add('TREATMENT (COLUMN) MEANS AND STANDARD DEVIATIONS');
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lReport.Add('VARIABLE MEAN STD.DEV. ');
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lReport.Add('-------- ---------- ----------');
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for i := 1 to NoSelected do
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lReport.Add('%-8s %10.3f %10.3f', [ColLabels[i-1], ColMeans[i-1], sqrt(ColVar[i-1])]);
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lReport.Add('');
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lReport.Add('Mean of all scores: %8.3f', [GrandMean]);
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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;
|
||||||
|
end;
|
||||||
|
|
||||||
// Test assumptions of variance - covariance homogeneity if requested
|
// Test assumptions of variance - covariance homogeneity if requested
|
||||||
if AssumpChk.Checked then
|
if AssumpChk.Checked then
|
||||||
begin
|
begin
|
||||||
SetLength(varcovmat,NoSelected+1,NoSelected+1);
|
TestAssumptions(selected, sampleVarCovarMat, assumedVarCovarMat, determ1, determ2, chi2, prob, DF, errorFound);
|
||||||
SetLength(vcmat,NoSelected+1,NoSelected+1);
|
WriteTestAssumptionsReport(sampleVarCovarMat, assumedVarCovarMat, colLabels, determ1, determ2, chi2, prob, DF, errorFound);
|
||||||
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;
|
end;
|
||||||
TestAssumptionsPage.TabVisible := AssumpChk.Checked;
|
TestAssumptionsPage.TabVisible := AssumpChk.Checked;
|
||||||
|
|
||||||
finally
|
// Finally, plot values if indicated in options list
|
||||||
lReport.Free;
|
|
||||||
end;
|
|
||||||
|
|
||||||
{ 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.
|
||||||
|
|
||||||
|
|||||||
Reference in New Issue
Block a user