LazStats: More general usability of the calculations in DescriptiveUnit
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7739 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
parent
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commit
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@ -1563,6 +1563,11 @@
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<DebugInfoType Value="dsDwarf2"/>
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</Debugging>
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<LinkSmart Value="True"/>
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<Options>
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<Win32>
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<GraphicApplication Value="True"/>
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</Win32>
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</Options>
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</Linking>
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</CompilerOptions>
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<Debugging>
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@ -15,48 +15,52 @@ type
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{ TDescriptiveStats }
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TDescriptiveOption = (doAlternativeQuartiles, doPercentileRanks, doCasewiseDeletion);
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TDescriptiveOptions = set of TDescriptiveOption;
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TQuartileMethod = 1..8;
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TQuartile = 1..3;
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TQuartiles = array[TQuartileMethod, TQuartile] of Double;
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TDescriptiveStats = class
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private
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FDataGrid: TStringGrid;
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FColIndex: Integer;
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FConfLevel: Double; // usually 0.95
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FColsSelected: IntDyneVec;
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FMean, FStdErrorMean, FDeltaMean: Double;
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FValues: DblDyneVec;
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FMean, FStdErrorMean: Double;
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FMin, FMax: Double;
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FSum: Double;
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FVariance, FStdDev: Double;
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FSkew, FStdErrorSkew: Double;
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FKurtosis, FStdErrorKurtosis: Double;
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FFirstQuartile, FMedian, FThirdQuartile: Double;
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FCategoryValues, FPercentiles: DblDyneVec;
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FFreqValues: IntDyneVec;
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FOptions: TDescriptiveOptions;
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FNumCases: Integer;
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FQuartiles: array[TQuartileMethod, TQuartile] of Double;
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procedure Calc_AlternativeQuartiles(const AValues: DblDyneVec);
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function Calc_DeltaMean(AStdErrorOfMean: Double): Double;
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procedure Calc_Moments(const AValues: DblDyneVec; AMean: Double;
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out M2, M3, M4: Double);
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procedure Calc_Quartiles(const AValues: DblDyneVec; out Q1, Median, Q3: Double);
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procedure Calc_Skew_Kurtosis(StdDev, M2, M3, M4: Double; ANumCases: Integer;
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out Skew, StdErrorSkew, Kurtosis, StdErrorKurtosis: Double);
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procedure Calc_Sum_SumOfSquares_Min_Max(const AValues: DblDyneVec;
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out ASum, ASumOfSquares, AMin, AMax: Double);
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procedure CollectValues(out AValues: DblDyneVec);
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procedure PercentileRank(const AValues: DblDyneVec;
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out ACategoryValues, APercentiles: DblDyneVec; out AFreq: IntDyneVec);
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procedure Calc_Quartiles;
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procedure Calc_Skew_Kurtosis;
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// function GetMeanLimits(AIndex: Integer; AConfLevel: Double): Double;
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function GetMeanLimits(AConfLevel: Double; AIndex: Integer): Double;
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procedure Reset;
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public
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constructor Create(ADataGrid: TStringGrid; AColsSelected: IntDyneVec; AConfLevel: Double);
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procedure Analyze(AColIndex: Integer; AOptions: TDescriptiveOptions);
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procedure WriteToReport(AVarName: String; ADecPlaces: Integer; AReport: TStrings);
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constructor Create(ADataGrid: TStringGrid; AColsSelected: IntDyneVec = nil);
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procedure Analyze(AColIndex: Integer);
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procedure CalcQuartiles(out AQuartiles: TQuartiles);
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procedure PercentileRank(out ACategoryValues, APercentiles: DblDyneVec; out AFreq: IntDyneVec);
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property FirstQuartile: Double read FFirstQuartile;
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property Kurtosis: Double read FKurtosis;
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property Max: Double read FMax;
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property Median: Double read FMedian;
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property Mean: Double read FMean;
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property MeanLowerLimit[AConfLevel: Double]: Double index 0 read GetMeanLimits;
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property MeanUpperLimit[AConfLevel: Double]: Double index 1 read GetMeanLimits;
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property Min: Double read FMin;
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property NumCases: Integer read FNumCases;
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property Skew: Double read FSkew;
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property StdErrorSkew: Double read FStdErrorSkew;
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property StdDev: Double read FStdDev;
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// more can be added...
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property StdErrorKurtosis: Double read FStdErrorKurtosis;
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property StdErrorMean: Double read FStdErrorMean;
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property StdErrorSkey: Double read FStdErrorSkew;
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property ThirdQuartile: Double read FThirdQuartile;
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property Variance: Double read FVariance;
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end;
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@ -90,6 +94,7 @@ type
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private
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function GetReportFrame(APageIndex: Integer): TReportFrame;
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procedure WriteToReport(Stats: TDescriptiveStats; AVarName: String; AReport: TStrings);
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procedure zScoresToGrid(AColIndex: Integer; const AColsSelected: IntDyneVec;
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AMean, AStdDev: Double);
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@ -113,7 +118,7 @@ implementation
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uses
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Math,
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Utils;
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Utils, MathUnit, GridProcs;
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{===============================================================================
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@ -125,218 +130,149 @@ uses
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*==============================================================================}
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constructor TDescriptiveStats.Create(ADataGrid: TStringGrid;
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AColsSelected: IntDyneVec; AConfLevel: Double);
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AColsSelected: IntDyneVec = nil);
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begin
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inherited Create;
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FDataGrid := ADataGrid;
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FColsSelected := AColsSelected;
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FConfLevel := AConfLevel;
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Reset;
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end;
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procedure TDescriptiveStats.Analyze(AColIndex: Integer; AOptions: TDescriptiveOptions);
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var
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SS: Double;
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values: DblDyneVec;
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M2, M3, M4: Double;
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procedure TDescriptiveStats.Analyze(AColIndex: Integer);
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begin
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FMean := NaN;
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FVariance := NaN;
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FStdDev := NaN;
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FStdErrorMean := NaN;
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FDeltaMean := NaN;
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FSkew := NaN;
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FStdErrorSkew := NaN;
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Reset;
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FColIndex := AColIndex;
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FOptions := AOptions;
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CollectValues(values);
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FNumCases := Length(values);
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if Length(FColsSelected) = 0 then
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FValues := CollectValues(FDataGrid, AColIndex, FColsSelected)
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else
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FValues := CollectValues(FDataGrid, AColIndex);
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FNumCases := Length(FValues);
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SortOnX(values);
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SortOnX(FValues);
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Calc_Sum_SumOfSquares_Min_Max(values, FSum, SS, FMin, FMax);
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if FNumCases > 0 then begin
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FMean := FSum / FNumCases;
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if FNumCases > 1 then
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MathUnit.Calc_MaxMin(FValues, FMax, FMin);
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MathUnit.Calc_MeanVarStdDev(FValues, FMean, FVariance, FStdDev);
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if FNumCases > 1 then
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FStdErrorMean := sqrt(FVariance / FNumCases);
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Calc_Skew_Kurtosis;
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Calc_Quartiles;
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end;
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procedure TDescriptiveStats.Calc_Quartiles;
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begin
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FFirstQuartile := Quartiles(2, 0.25, FNumCases, FValues);
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FMedian := Quartiles(2, 0.5, FNumCases, FValues);
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FThirdQuartile := Quartiles(2, 0.75, FNumCases, FValues);
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end;
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procedure TDescriptiveStats.CalcQuartiles(out AQuartiles: TQuartiles);
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var
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q: TQuartile;
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m: TQuartileMethod;
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begin
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for m := Low(TQuartileMethod) to High(TQuartileMethod) do
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for q := Low(TQuartile) to High(TQuartile) do
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AQuartiles[m, q] := Quartiles(m, 0.25*q, FNumCases, FValues);
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end;
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procedure TDescriptiveStats.Calc_Skew_Kurtosis;
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procedure Moments(out M2, M3, M4: Double);
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var
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i: Integer;
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dev, devSqr: Double;
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begin
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M2 := 0;
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M3 := 0;
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M4 := 0;
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for i := 0 to High(FValues) do
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begin
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FVariance := (SS - sqr(FSum) / FNumCases) / (FNumCases - 1);
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FStdDev := sqrt(FVariance);
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FStdErrorMean := sqrt(FVariance / FNumCases);
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FDeltaMean := Calc_DeltaMean(FStdErrorMean);
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dev := FValues[i] - FMean;
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devSqr := Sqr(dev);
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M2 := M2 + devSqr;
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M3 := M3 + dev * devSqr;
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M4 := M4 + sqr(devSqr);
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end;
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end;
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Calc_Moments(values, FMean, M2, M3, M4);
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Calc_Skew_Kurtosis(FStdDev, M2, M3, M4, FNumCases, FSkew, FStdErrorSkew, FKurtosis, FStdErrorKurtosis);
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var
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num, denom: Double;
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stdDev3, stdDev4: Double;
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M2, M3, M4: Double;
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begin
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FSkew := NaN;
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FStdErrorSkew := NaN;
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FKurtosis := NaN;
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FStdErrorKurtosis := NaN;
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Calc_Quartiles(values, FFirstQuartile, FMedian, FThirdQuartile);
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if FNumCases < 2 then
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exit;
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if (doAlternativeQuartiles in FOptions) then
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Calc_AlternativeQuartiles(values);
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if (doPercentileRanks in FOptions) then
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PercentileRank(values, FCategoryValues, FPercentiles, FFreqValues);
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stdDev3 := FStdDev * FStdDev * FStdDev;
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stdDev4 := StdDev3 * FStdDev;
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Moments(M2, M3, M4);
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if FNumCases > 2 then
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begin
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FSkew := FNumCases * M3 / ((FNumCases - 1) * (FNumCases - 3) * stdDev3);
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num := 6.0 * FNumCases * (FNumCases - 1);
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denom := (FNumCases - 2) * (FNumCases + 1) * (FNumCases + 3);
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FStdErrorSkew := sqrt(num / denom);
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end;
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if FNumCases > 3 then
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begin
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num := FNumCases * (FNumCases + 1) * M4 - 3 * M2 * M2 * (FNumCases - 1);
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denom := (FNumCases - 1) * (FNumCases - 2) * (FNumCases - 3) * stdDev4;
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FKurtosis := num / denom;
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num := 4.0 * (sqr(FNumCases) - 1) * sqr(FStdErrorSkew);
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denom := (FNumCases - 3) * (FNumCases + 5);
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FStdErrorKurtosis := sqrt(num / denom);
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end;
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end;
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procedure TDescriptiveStats.Calc_AlternativeQuartiles(const AValues: DblDyneVec);
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var
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nCases: Integer;
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q: TQuartile;
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m: TQuartileMethod;
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begin
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nCases := Length(AValues);
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for m := Low(TQuartileMethod) to High(TQuartileMethod) do
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for q := Low(TQuartile) to High(TQuartile) do
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FQuartiles[m, q] := Quartiles(m, 0.25*q, nCases, AValues);
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end;
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// Tolerance around the mean
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function TDescriptiveStats.Calc_DeltaMean(AStdErrorOfMean: Double): Double;
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function TDescriptiveStats.GetMeanLimits(AConfLevel: Double; AIndex: Integer): Double;
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var
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alpha: Double;
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confLev: Double;
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DOF: Integer;
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delta: Double;
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begin
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alpha := (1 - FConfLevel) / 2;
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alpha := (1 - AConfLevel) / 2;
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confLev := 1 - alpha;
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if FNumCases < 120 then
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begin
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DOF := FNumCases - 1;
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Result := AStdErrorOfMean * InverseT(confLev, DOF);
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delta := FStdErrorMean * InverseT(confLev, DOF);
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end else
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Result := AStdErrorOfMean * InverseZ(confLev);
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end;
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delta := FStdErrorMean * InverseZ(confLev);
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procedure TDescriptiveStats.Calc_Moments(const AValues: DblDyneVec;
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AMean: Double; out M2, M3, M4: Double);
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var
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i: Integer;
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dev, devSqr: Double;
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begin
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M2 := 0;
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M3 := 0;
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M4 := 0;
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for i := 0 to High(AValues) do
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begin
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dev := AValues[i] - AMean;
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devSqr := Sqr(dev);
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M2 := M2 + devSqr;
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M3 := M3 + dev * devSqr;
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M4 := M4 + sqr(devSqr);
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case AIndex of
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0: Result := FMean - delta;
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1: Result := FMean + delta;
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end;
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end;
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procedure TDescriptiveStats.Calc_Quartiles(const AValues: DblDyneVec;
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out Q1, Median, Q3: Double);
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var
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n: Integer;
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begin
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n := Length(AValues);
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Q1 := Quartiles(2, 0.25, n, AValues);
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Median := Quartiles(2, 0.5, n, AValues);
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Q3 := Quartiles(2, 0.75, n, AValues);
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end;
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procedure TDescriptiveStats.Calc_Skew_Kurtosis(StdDev, M2, M3, M4: Double;
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ANumCases: Integer; out Skew, StdErrorSkew, Kurtosis, StdErrorKurtosis: Double);
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var
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num, denom: Double;
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stdDev3, stdDev4: Double;
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begin
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Skew := NaN;
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StdErrorSkew := NaN;
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Kurtosis := NaN;
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StdErrorKurtosis := NaN;
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stdDev3 := StdDev * StdDev * StdDev;
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stdDev4 := StdDev3 * StdDev;
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if ANumCases > 2 then
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begin
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Skew := ANumCases * M3 / ((ANumCases - 1) * (ANumCases - 3) * stdDev3);
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num := 6.0 * ANumCases * (ANumCases - 1);
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denom := (ANumCases - 2) * (ANumCases + 1) * (ANumCases + 3);
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StdErrorSkew := sqrt(num / denom);
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end;
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if ANumCases > 3 then
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begin
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num := ANumCases * (ANumCases + 1) * M4 - 3 * M2 * M2 * (ANumCases - 1);
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denom := (ANumCases - 1) * (ANumCases - 2) * (ANumCases - 3) * stdDev4;
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Kurtosis := num / denom;
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num := 4.0 * (sqr(ANumCases) - 1) * sqr(StdErrorSkew);
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denom := (ANumCases - 3) * (ANumCases + 5);
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StdErrorKurtosis := sqrt(num / denom);
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end;
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end;
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procedure TDescriptiveStats.Calc_Sum_SumOfSquares_Min_Max(const AValues: DblDyneVec;
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out ASum, ASumOfSquares, AMin, AMax: Double);
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var
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i: Integer;
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begin
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ASum := 0.0;
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ASumOfSquares := 0;
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AMin := Infinity;
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AMax := -Infinity;
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for i := 0 to High(AValues) do
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begin
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ASum := ASum + AValues[i];
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ASumOfSquares := ASumOfSquares + sqr(AValues[i]);
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if AValues[i] < AMin then AMin := AValues[i];
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if AValues[i] > AMax then AMax := AValues[i];
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end;
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end;
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procedure TDescriptiveStats.CollectValues(out AValues: DblDyneVec);
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var
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i, n: Integer;
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begin
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AValues := nil; // silence the compiler
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SetLength(AValues, NoCases);
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n := 0;
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for i := 1 to NoCases do
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begin
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if (doCasewiseDeletion in FOptions) then
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begin
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// Do not consider a case when any variable is empty
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if not ValidValue(i, FColIndex) then
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continue;
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end else
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begin
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// Do not consider a case when the current variable is empty
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if not GoodRecord(i, Length(FColsSelected), FColsSelected) then
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continue;
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end;
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if TryStrToFloat(FDataGrid.Cells[FColIndex, i], AValues[n]) then
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inc(n)
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else
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raise Exception.CreateFmt('Invalid number: variable "%s", case "%s"',
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[FDataGrid.cells[FColIndex, 0], FDataGrid.Cells[0, i]]);
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end;
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SetLength(AValues, n);
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end;
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// Computes the percentile ranks of values stored in the data grid at the
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// loaded columns. The values are assumed to be sorted.
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procedure TDescriptiveStats.PercentileRank(const AValues: DblDyneVec; out
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ACategoryValues, APercentiles: DblDyneVec; out AFreq: IntDyneVec);
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procedure TDescriptiveStats.PercentileRank(out ACategoryValues, APercentiles: DblDyneVec;
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out AFreq: IntDyneVec);
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var
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i, nCases, iCat, nCategories: Integer;
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i, iCat, nCategories: Integer;
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lastCategoryValue: Double;
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cumFreqCentered: Double;
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cumFreq: Integer;
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@ -346,24 +282,23 @@ begin
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AFreq := nil;
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APercentiles := nil;
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nCases := Length(AValues);
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SetLength(ACategoryValues, nCases); // over-dimension; will be trimmed later
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SetLength(AFreq, nCases);
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SetLength(ACategoryValues, FNumCases); // over-dimension; will be trimmed later
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SetLength(AFreq, FNumCases);
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// Get count of unique values and frequencies of each
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lastCategoryValue := AValues[0];
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lastCategoryValue := FValues[0];
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ACategoryValues[0] := lastCategoryValue;
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AFreq[0] := 1;
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iCat := 0;
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for i := 1 to nCases-1 do
|
||||
for i := 1 to FNumCases-1 do
|
||||
begin
|
||||
if (lastCategoryValue = AValues[i]) then
|
||||
if (lastCategoryValue = FValues[i]) then
|
||||
AFreq[iCat] := AFreq[iCat] + 1
|
||||
else
|
||||
begin // new value
|
||||
inc(iCat);
|
||||
AFreq[iCat] := 1;
|
||||
lastCategoryValue := AValues[i];
|
||||
lastCategoryValue := FValues[i];
|
||||
ACategoryValues[iCat] := lastCategoryValue;
|
||||
end;
|
||||
end;
|
||||
@ -375,94 +310,32 @@ begin
|
||||
|
||||
// Get cumulative frequencies and percentile ranks
|
||||
SetLength(APercentiles, nCategories);
|
||||
APercentiles[0] := AFreq[0] * 0.5 / nCases;
|
||||
APercentiles[0] := AFreq[0] * 0.5 / FNumCases;
|
||||
cumFreq := AFreq[0];
|
||||
for i := 1 to nCategories-1 do // NOTE: This loop must begin at index 1
|
||||
begin
|
||||
cumFreqCentered := cumFreq + AFreq[i]*0.5; // cum frequencies at mid-point
|
||||
APercentiles[i] := cumFreqCentered / nCases;
|
||||
APercentiles[i] := cumFreqCentered / FNumCases;
|
||||
cumFreq := cumFreq + AFreq[i];
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TDescriptiveStats.WriteToReport(AVarName: String; ADecPlaces: Integer;
|
||||
AReport: TStrings);
|
||||
var
|
||||
w: Integer;
|
||||
nCategories: Integer;
|
||||
i: Integer;
|
||||
cumFreq: Integer;
|
||||
m: TQuartileMethod;
|
||||
procedure TDescriptiveStats.Reset;
|
||||
begin
|
||||
w := 10 + ADecPlaces - 3;
|
||||
AReport.Add('VARIABLE: %*s', [W, '"' + AVarName + '"']);
|
||||
AReport.Add('');
|
||||
AReport.Add('Number of cases: %*d', [W, FNumCases]);
|
||||
AReport.Add('Sum: %*.*f', [W, ADecPlaces, FSum]);
|
||||
AReport.Add('Mean: %*.*f', [W, ADecPlaces, FMean]);
|
||||
AReport.Add('Variance: %*.*f', [W, ADecPlaces, FVariance]);
|
||||
AReport.Add('Std.Dev.: %*.*f', [W, ADecPlaces, FStdDev]);
|
||||
AReport.Add('Std.Error of Mean %*.*f', [W, ADecPlaces, FStdErrorMean]);
|
||||
AReport.Add('%.2f%% Conf.Interval Mean: %.*f to %.*f', [
|
||||
FConfLevel*100.0, ADecPlaces, FMean - FDeltaMean, ADecPlaces, FMean + FDeltaMean]);
|
||||
AReport.Add('');
|
||||
AReport.Add('Minimum: %*.*f', [W, ADecPlaces, FMin]);
|
||||
AReport.Add('Maximum: %*.*f', [W, ADecPlaces, FMax]);
|
||||
AReport.Add('Range: %*.*f', [W, ADecPlaces, FMax - FMin]);
|
||||
AReport.Add('');
|
||||
AReport.Add('Skewness: %*.*f', [W, ADecPlaces, FSkew]);
|
||||
AReport.Add('Std.Error of Skew: %*.*f', [W, ADecPlaces, FStdErrorSkew]);
|
||||
AReport.Add('Kurtosis: %*.*f', [W, ADecPlaces, FKurtosis]);
|
||||
AReport.Add('Std. Error of Kurtosis: %*.*f', [W, ADecPlaces, FStdErrorKurtosis]);
|
||||
AReport.Add('');
|
||||
AReport.Add('First Quartile: %*.*f', [W, ADecPlaces, FFirstQuartile]);
|
||||
AReport.Add('Median: %*.*f', [W, ADecPlaces, FMedian]);
|
||||
AReport.Add('Third Quartile: %*.*f', [W, ADecPlaces, FThirdQuartile]);
|
||||
AReport.Add('Interquartile range: %*.*f', [W, ADecPlaces, FThirdQuartile - FFirstQuartile]);
|
||||
|
||||
if (doAlternativeQuartiles in FOptions) then
|
||||
begin
|
||||
AReport.Add('');
|
||||
AReport.Add('');
|
||||
AReport.Add('ALTERNATIVE METHODS FOR OBTAINING QUARTILES');
|
||||
AReport.Add('');
|
||||
AReport.Add('Method First Quartile Median Third Quartile');
|
||||
AReport.Add('------ -------------- ---------- --------------');
|
||||
for m := Low(TQuartileMethod) to High(TQuartileMethod) do
|
||||
AReport.Add(' %d %12.3f %12.3f %12.3f', [m, FQuartiles[m, 1], FQuartiles[m, 2], FQuartiles[m, 3]]);
|
||||
AReport.Add('');
|
||||
AReport.Add('NOTES:');
|
||||
AReport.Add('Method 1 is the weighted average at X[np] where ');
|
||||
AReport.Add(' n is no. of cases, p is percentile / 100');
|
||||
AReport.Add('Method 2 is the weighted average at X[(n+1)p] This is used in this program.');
|
||||
AReport.Add('Method 3 is the empirical distribution function.');
|
||||
AReport.Add('Method 4 is called the empirical distribution function - averaging.');
|
||||
AReport.Add('Method 5 is called the empirical distribution function = Interpolation.');
|
||||
AReport.Add('Method 6 is the closest observation method.');
|
||||
AReport.Add('Method 7 is from the TrueBasic Statistics Graphics Toolkit.');
|
||||
AReport.Add('Method 8 was used in an older Microsoft Excel version.');
|
||||
AReport.Add('See the internet site http://www.xycoon.com/ for the above.');
|
||||
end;
|
||||
|
||||
if (doPercentileRanks in FOptions) then
|
||||
begin
|
||||
nCategories := Length(FCategoryValues);
|
||||
cumFreq := 0;
|
||||
AReport.Add('');
|
||||
AReport.Add('');
|
||||
AReport.Add('PERCENTILE RANKS');
|
||||
AReport.Add('');
|
||||
AReport.Add('Score Value Frequency Cum.Freq. Percentile Rank');
|
||||
AReport.Add('----------- --------- --------- ---------------');
|
||||
for i := 0 to nCategories-1 do
|
||||
begin
|
||||
cumFreq := cumFreq + FFreqValues[i];
|
||||
AReport.Add(' %8.3f %8d %8d %12.2f%%', [
|
||||
FCategoryValues[i], FFreqValues[i], cumFreq, FPercentiles[i]*100.0
|
||||
]);
|
||||
end;
|
||||
end;
|
||||
FValues := nil;
|
||||
FMean := NaN;
|
||||
FStdErrorMean := NaN;
|
||||
FMin := NaN;
|
||||
FMax := NaN;
|
||||
FVariance := NaN;
|
||||
FStdDev := NaN;
|
||||
FStdErrorMean := NaN;
|
||||
FSkew := NaN;
|
||||
FStdErrorSkew := NaN;
|
||||
FKurtosis := NaN;
|
||||
FStdErrorKurtosis := NaN;
|
||||
FNumCases := 0;
|
||||
end;
|
||||
|
||||
|
||||
@ -514,8 +387,7 @@ var
|
||||
page: TTabSheet;
|
||||
reportFrame: TReportFrame;
|
||||
lReport: TStrings;
|
||||
lDescrStats: TDescriptiveStats;
|
||||
options: TDescriptiveOptions;
|
||||
lStats: TDescriptiveStats;
|
||||
begin
|
||||
noSelected := SelList.Items.Count;
|
||||
if noSelected = 0 then
|
||||
@ -555,29 +427,23 @@ begin
|
||||
for i := 0 to NoSelected-1 do
|
||||
PageControl.Pages[i].Caption := OS3MainFrm.DataGrid.Cells[selected[i], 0];
|
||||
|
||||
// Prepare options
|
||||
options := [];
|
||||
if PercentileChk.Checked then Include(options, doPercentileRanks);
|
||||
if AllQuartilesChk.Checked then Include(options, doAlternativeQuartiles);
|
||||
if CaseChk.Checked then Include(options, doCasewiseDeletion);
|
||||
|
||||
//
|
||||
lReport := TStringList.Create;
|
||||
lDescrStats := TDescriptiveStats.Create(OS3MainFrm.DataGrid, selected, StrToFloat(CIEdit.Text)/100);
|
||||
if not CaseChk.Checked then
|
||||
lStats := TDescriptiveStats.Create(OS3MainFrm.DataGrid)
|
||||
else
|
||||
lStats := TDescriptiveStats.Create(OS3MainFrm.DataGrid, selected);
|
||||
try
|
||||
for i := 0 to noSelected-1 do
|
||||
begin
|
||||
// Analyze the data and get descriptive stats
|
||||
lDescrStats.Analyze(selected[i], options);
|
||||
lStats.Analyze(selected[i]);
|
||||
|
||||
// Store z values, (value - mean) / stdDev, to grid, if needed
|
||||
zScoresToGrid(selected[i], selected, lDescrStats.Mean, lDescrStats.StdDev);
|
||||
zScoresToGrid(selected[i], selected, lStats.Mean, lStats.StdDev);
|
||||
|
||||
// Write descriptive stats to report
|
||||
lReport.Clear;
|
||||
lReport.Add('DISTRIBUTION PARAMETER ESTIMATES');
|
||||
lReport.Add('');
|
||||
lDescrStats.WriteToReport(trim(OS3MainFrm.DataGrid.Cells[selected[i], 0]),
|
||||
DecPlacesEdit.Value, lReport);
|
||||
WriteToReport(lStats, trim(OS3MainFrm.DataGrid.Cells[selected[i], 0]), lReport);
|
||||
|
||||
// Display report in the page of the variable
|
||||
reportFrame := GetReportFrame(i);
|
||||
@ -585,7 +451,7 @@ begin
|
||||
end;
|
||||
finally
|
||||
// Clean up
|
||||
lDescrStats.Free;
|
||||
lStats.Free;
|
||||
lReport.Free;
|
||||
end;
|
||||
end;
|
||||
@ -651,7 +517,6 @@ begin
|
||||
|
||||
for i := PageControl.PageCount-1 downto 1 do
|
||||
PageControl.Pages[i].Free;
|
||||
|
||||
PageControl.Pages[0].Caption := 'Report';
|
||||
|
||||
CIEdit.Text := FormatFloat('0.0', DEFAULT_CONFIDENCE_LEVEL_PERCENT);
|
||||
@ -698,12 +563,16 @@ var
|
||||
F: TReportFrame;
|
||||
begin
|
||||
inherited;
|
||||
|
||||
for i := 0 to PageControl.PageCount-1 do
|
||||
(*
|
||||
for i := PageControl.PageCount-1 downto 0 do
|
||||
begin
|
||||
F := GetReportFrame(i);
|
||||
if Assigned(F) then F.Clear;
|
||||
end;
|
||||
if i > 0 then
|
||||
PageControl.Pages[i].Free
|
||||
else begin
|
||||
F := GetReportFrame(i);
|
||||
if Assigned(F) then F.Clear;
|
||||
end;
|
||||
end; *)
|
||||
|
||||
lSelected := false;
|
||||
for i := 0 to VarList.Items.Count-1 do
|
||||
@ -733,6 +602,103 @@ begin
|
||||
end;
|
||||
|
||||
|
||||
procedure TDescriptiveFrm.WriteToReport(Stats: TDescriptiveStats;
|
||||
AVarName: String; AReport: TStrings);
|
||||
var
|
||||
w: Integer;
|
||||
i: Integer;
|
||||
confLevel: Double;
|
||||
decPlaces: Integer;
|
||||
m: TQuartileMethod;
|
||||
Q: TQuartiles;
|
||||
cumFreq: Integer;
|
||||
nCategories: Integer;
|
||||
categories: DblDyneVec = nil;
|
||||
freq: IntDyneVec = nil;
|
||||
percentiles: DblDyneVec = nil;
|
||||
begin
|
||||
confLevel := StrToFloat(CIEdit.Text) / 100;
|
||||
decPlaces := DecPlacesEdit.Value;
|
||||
w := 10 + decPlaces - 3;
|
||||
|
||||
AReport.Clear;
|
||||
|
||||
AReport.Add('DISTRIBUTION PARAMETER ESTIMATES');
|
||||
AReport.Add('');
|
||||
|
||||
AReport.Add('VARIABLE: %*s', [W, '"' + AVarName + '"']);
|
||||
AReport.Add('');
|
||||
AReport.Add('Number of cases: %*d', [W, Stats.NumCases]);
|
||||
// AReport.Add('Sum: %*.*f', [W, decPlaces, Stats.Sum]);
|
||||
AReport.Add('Mean: %*.*f', [W, decPlaces, Stats.Mean]);
|
||||
AReport.Add('Variance: %*.*f', [W, decPlaces, Stats.Variance]);
|
||||
AReport.Add('Std.Dev.: %*.*f', [W, decPlaces, Stats.StdDev]);
|
||||
AReport.Add('Std.Error of Mean %*.*f', [W, decPlaces, Stats.StdErrorMean]);
|
||||
AReport.Add('%.2f%% Conf.Interval Mean: %.*f to %.*f', [
|
||||
confLevel*100.0, decPlaces, Stats.MeanLowerLimit[confLevel], decPlaces, Stats.MeanUpperLimit[confLevel]
|
||||
]);
|
||||
AReport.Add('');
|
||||
AReport.Add('Minimum: %*.*f', [W, decPlaces, Stats.Min]);
|
||||
AReport.Add('Maximum: %*.*f', [W, decPlaces, Stats.Max]);
|
||||
AReport.Add('Range: %*.*f', [W, decPlaces, Stats.Max - Stats.Min]);
|
||||
AReport.Add('');
|
||||
AReport.Add('Skewness: %*.*f', [W, decPlaces, Stats.Skew]);
|
||||
AReport.Add('Std.Error of Skew: %*.*f', [W, decPlaces, Stats.StdErrorSkew]);
|
||||
AReport.Add('Kurtosis: %*.*f', [W, decPlaces, Stats.Kurtosis]);
|
||||
AReport.Add('Std. Error of Kurtosis: %*.*f', [W, decPlaces, Stats.StdErrorKurtosis]);
|
||||
AReport.Add('');
|
||||
AReport.Add('First Quartile: %*.*f', [W, decPlaces, Stats.FirstQuartile]);
|
||||
AReport.Add('Median: %*.*f', [W, decPlaces, Stats.Median]);
|
||||
AReport.Add('Third Quartile: %*.*f', [W, decPlaces, Stats.ThirdQuartile]);
|
||||
AReport.Add('Interquartile range: %*.*f', [W, decPlaces, Stats.ThirdQuartile - Stats.FirstQuartile]);
|
||||
|
||||
if AllQuartilesChk.Checked then
|
||||
begin
|
||||
Stats.CalcQuartiles(Q);
|
||||
AReport.Add('');
|
||||
AReport.Add('');
|
||||
AReport.Add('ALTERNATIVE METHODS FOR OBTAINING QUARTILES');
|
||||
AReport.Add('');
|
||||
AReport.Add('Method First Quartile Median Third Quartile');
|
||||
AReport.Add('------ -------------- ---------- --------------');
|
||||
for m := Low(TQuartileMethod) to High(TQuartileMethod) do
|
||||
AReport.Add(' %d %12.3f %12.3f %12.3f', [m, Q[m, 1], Q[m, 2], Q[m, 3]]);
|
||||
AReport.Add('');
|
||||
AReport.Add('NOTES:');
|
||||
AReport.Add('Method 1 is the weighted average at X[np] where ');
|
||||
AReport.Add(' n is no. of cases, p is percentile / 100');
|
||||
AReport.Add('Method 2 is the weighted average at X[(n+1)p] This is used in this program.');
|
||||
AReport.Add('Method 3 is the empirical distribution function.');
|
||||
AReport.Add('Method 4 is called the empirical distribution function - averaging.');
|
||||
AReport.Add('Method 5 is called the empirical distribution function = Interpolation.');
|
||||
AReport.Add('Method 6 is the closest observation method.');
|
||||
AReport.Add('Method 7 is from the TrueBasic Statistics Graphics Toolkit.');
|
||||
AReport.Add('Method 8 was used in an older Microsoft Excel version.');
|
||||
AReport.Add('See the internet site http://www.xycoon.com/ for the above.');
|
||||
end;
|
||||
|
||||
if PercentileChk.Checked then
|
||||
begin
|
||||
Stats.PercentileRank(categories, percentiles, freq);
|
||||
nCategories := Length(categories);
|
||||
cumFreq := 0;
|
||||
AReport.Add('');
|
||||
AReport.Add('');
|
||||
AReport.Add('PERCENTILE RANKS');
|
||||
AReport.Add('');
|
||||
AReport.Add('Score Value Frequency Cum.Freq. Percentile Rank');
|
||||
AReport.Add('----------- --------- --------- ---------------');
|
||||
for i := 0 to nCategories-1 do
|
||||
begin
|
||||
cumFreq := cumFreq + freq[i];
|
||||
AReport.Add(' %8.3f %8d %8d %12.2f%%', [
|
||||
categories[i], freq[i], cumFreq, percentiles[i]*100.0
|
||||
]);
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TDescriptiveFrm.zScoresToGrid(AColIndex: Integer;
|
||||
const AColsSelected: IntDyneVec; AMean, AStdDev: Double);
|
||||
var
|
||||
@ -759,10 +725,10 @@ begin
|
||||
begin
|
||||
if CaseChk.Checked then
|
||||
begin
|
||||
if not ValidValue(i, AColsSelected[AColIndex]) then continue;
|
||||
if not DataProcs.ValidValue(i, AColsSelected[AColIndex]) then continue;
|
||||
end
|
||||
else
|
||||
if not GoodRecord(i, Length(AColsSelected), AColsSelected) then continue;
|
||||
if not DataProcs.GoodRecord(i, Length(AColsSelected), AColsSelected) then continue;
|
||||
|
||||
value := StrToFloat(OS3MainFrm.DataGrid.Cells[AColIndex, i]);
|
||||
zValue := (value - AMean) / AStdDev;
|
||||
|
||||
@ -41,6 +41,8 @@ type
|
||||
LHelpPath: String;
|
||||
end;
|
||||
|
||||
ELazStats = class(Exception);
|
||||
|
||||
var
|
||||
NoCases : integer;
|
||||
NoVariables : integer;
|
||||
|
||||
@ -9,7 +9,7 @@ uses
|
||||
Globals, DictionaryUnit;
|
||||
|
||||
function CollectValues(AGrid: TStringGrid; AColIndex: Integer;
|
||||
AColCheck: IntDyneVec): DblDyneVec;
|
||||
AColCheck: IntDyneVec = nil): DblDyneVec;
|
||||
|
||||
procedure GetMinMax(AGrid: TStringGrid; AColIndex: Integer;
|
||||
const AColCheck: IntDyneVec; out AMin, AMax: Double);
|
||||
@ -42,6 +42,7 @@ uses
|
||||
function CollectValues(AGrid: TStringGrid; AColIndex: Integer; AColCheck: IntDyneVec): DblDyneVec;
|
||||
var
|
||||
row, n: Integer;
|
||||
val: Double;
|
||||
begin
|
||||
SetLength(Result, AGrid.RowCount);
|
||||
n := 0;
|
||||
@ -54,7 +55,11 @@ begin
|
||||
begin
|
||||
if not GoodRecord(AGrid, row, AColCheck) then continue;
|
||||
end;
|
||||
Result[n] := StrToFloat(trim(AGrid.Cells[AColIndex, row]));
|
||||
if TryStrToFloat(trim(AGrid.Cells[AColIndex, row]), val) then
|
||||
Result[n] := val
|
||||
else
|
||||
raise ELazStats.CreateFmt('Non-numeric string "%s" in column %d, row %d',
|
||||
[AGrid.Cells[AColIndex, row], AColIndex, row]);
|
||||
inc(n);
|
||||
end;
|
||||
SetLength(Result, n);
|
||||
|
||||
@ -7,7 +7,8 @@ unit MathUnit;
|
||||
interface
|
||||
|
||||
uses
|
||||
Classes, SysUtils;
|
||||
Classes, SysUtils,
|
||||
Globals;
|
||||
|
||||
const
|
||||
TWO_PI = 2.0 * PI;
|
||||
@ -43,6 +44,13 @@ function FactorialLn(n: Integer): Double;
|
||||
function PoissonPDF(n: integer; a: double): Double;
|
||||
function PoissonCDF(n: Integer; a: double): Double;
|
||||
|
||||
|
||||
procedure Calc_MaxMin(const AData: DblDyneVec; out AMax, AMin: Double);
|
||||
procedure Calc_MeanStdDev(const AData: DblDyneVec; out AMean, AStdDev: Double);
|
||||
procedure Calc_MeanVarStdDev(const AData: DblDyneVec; out AMean, AVariance, AStdDev: Double);
|
||||
procedure Calc_SumSS(const AData: DblDyneVec; out Sum, SS: Double);
|
||||
|
||||
|
||||
implementation
|
||||
|
||||
uses
|
||||
@ -474,6 +482,70 @@ begin
|
||||
end;
|
||||
|
||||
|
||||
|
||||
{===============================================================================
|
||||
* Vector-based calculations
|
||||
===============================================================================}
|
||||
procedure Calc_MaxMin(const AData: DblDyneVec; out AMax, AMin: Double);
|
||||
var
|
||||
i: Integer;
|
||||
begin
|
||||
AMin := Infinity;
|
||||
AMax := -Infinity;
|
||||
for i := Low(AData) to High(AData) do
|
||||
begin
|
||||
if AData[i] < AMin then AMin := AData[i];
|
||||
if AData[i] > AMax then AMax := AData[i];
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure Calc_MeanStdDev(const AData: DblDyneVec; out AMean, AStdDev: Double);
|
||||
var
|
||||
variance: Double;
|
||||
begin
|
||||
Calc_MeanVarStdDev(AData, AMean, variance, AStdDev);
|
||||
end;
|
||||
|
||||
|
||||
procedure Calc_MeanVarStdDev(const AData: DblDyneVec; out AMean, AVariance, AStdDev: Double);
|
||||
var
|
||||
sum, ss: Double;
|
||||
n: Integer;
|
||||
begin
|
||||
AMean := NaN;
|
||||
AVariance := NaN;
|
||||
AStdDev := NaN;
|
||||
|
||||
n := Length(AData);
|
||||
if n = 0 then
|
||||
exit;
|
||||
|
||||
Calc_SumSS(AData, sum, ss);
|
||||
|
||||
AMean := sum / n;
|
||||
if n = 1 then
|
||||
exit;
|
||||
|
||||
AVariance := ((ss - sqr(AMean)) / n) / (n - 1);
|
||||
AStdDev := sqrt(AVariance);
|
||||
end;
|
||||
|
||||
|
||||
procedure Calc_SumSS(const AData: DblDyneVec; out Sum, SS: Double);
|
||||
var
|
||||
i: Integer;
|
||||
begin
|
||||
Sum := 0;
|
||||
SS := 0;
|
||||
for i := Low(AData) to High(AData) do
|
||||
begin
|
||||
Sum := Sum + AData[i];
|
||||
SS := SS + sqr(AData[i]);
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
initialization
|
||||
InitFactLn();
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user