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LazStats: Refactor ChiSqrUnit.
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7805 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
@ -59,6 +59,35 @@ type
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FRowColPropsReportFrame: TReportFrame;
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FCellChiSqrReportFrame: TReportFrame;
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function CalcGStatistic(const AFrequencies: IntDyneMat;
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const AExpected: DblDyneMat): Double;
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function CalcLikelihoodRatio(const AFrequencies: IntDyneMat;
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const AExpected: DblDyneMat): Double;
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function CalcPearsonR(const AFrequencies: IntDyneMat): Double;
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procedure GetExpectedAndCellChiSqr(const AFrequencies: IntDyneMat;
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out AExpected, ACellChiSqr: DblDyneMat;
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out AChiSqr: Double);
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procedure GetFrequencies(const AColNoSelected: IntDyneVec;
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ARowIndex, AColIndex, ADepIndex: Integer;
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out ANumRows, ANumCols, ANumCases: Integer;
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out AFrequencies: IntDyneMat);
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procedure GetYatesCorrection(const AFrequencies: IntDyneMat;
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out AdjChiSqr: Double);
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procedure GetColProportions(const AFrequencies: IntDyneMat;
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out AProportions: DblDyneMat);
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procedure GetRowProportions(const AFrequencies: IntDyneMat;
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out AProportions: DblDyneMat);
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procedure GetTotalProportions(const AFrequencies: IntDyneMat;
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out AProportions: DblDyneMat);
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protected
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procedure AdjustConstraints; override;
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procedure Compute; override;
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@ -79,7 +108,7 @@ implementation
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uses
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Math,
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Utils, GridProcs;
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Utils, GridProcs, MatrixUnit;
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{ TChiSqrFrm }
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@ -145,6 +174,75 @@ begin
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end;
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function TChiSqrFrm.CalcGStatistic(const AFrequencies: IntDyneMat;
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const AExpected: DblDyneMat): Double;
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var
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numRows, numCols: Integer;
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i, j: Integer;
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begin
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MatSize(AExpected, numRows, numCols);
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Result := 0.0;
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for i := 0 to numRows-1 do
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for j := 0 to numCols-1 do
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if (AExpected[i, j] > 0) then
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Result := Result + AFrequencies[i, j] * ln(AFrequencies[i, j] / AExpected[i, j]);
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Result := 2.0 * Result;
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end;
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function TChiSqrFrm.CalcLikelihoodRatio(const AFrequencies: IntDyneMat;
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const AExpected: DblDyneMat): Double;
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var
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numRows, numCols: Integer;
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i, j: Integer;
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begin
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MatSize(AExpected, numRows, numCols);
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Result := 0.0;
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for i := 0 to numRows-1 do
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for j := 0 to numCols-1 do
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if (AFrequencies[i, j] > 0.0) then
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Result := Result + AFrequencies[i, j] * ln(AExpected[i, j] / AFrequencies[i, j]);
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Result := -2.0 * Result;
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end;
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function TChiSqrFrm.CalcPearsonR(const AFrequencies: IntDyneMat): Double;
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var
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numRows, numCols, numCases: Integer;
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sumX, sumY: Double;
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varX, varY: Double;
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i, j: Integer;
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begin
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MatSize(AFrequencies, numRows, numCols);
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dec(numRows); // Do not iterate into the totals row and column
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dec(numCols);
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numCases := AFrequencies[numRows, numCols];
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SumX := 0;
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SumY := 0;
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VarX := 0;
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VarY := 0;
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for i := 0 to numRows-1 do
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sumX := sumX + ( (i+1) * AFrequencies[i, numCols] );
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for j := 0 to numCols-1 do
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sumY := sumY + ( (j+1) * AFrequencies[numRows, j] );
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for i := 0 to numRows-1 do
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varX := varX + ( sqr(i+1) * AFrequencies[i, numCols] );
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for j := 0 to numCols-1 do
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varY := varY + ( sqr(j+1) * AFrequencies[numRows, j] );
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varX := varX - sqr(sumX) / numCases;
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varY := varY - sqr(sumY) / numCases;
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Result := 0;
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for i := 0 to numRows-1 do
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for j := 0 to numCols-1 do
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Result := Result + ((i+1)*(j+1) * AFrequencies[i, j]);
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Result := Result - (sumX * sumY / numCases);
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Result := Result / sqrt(varX * varY);
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end;
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procedure TChiSqrFrm.ColInClick(Sender: TObject);
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var
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index: integer;
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@ -179,20 +277,19 @@ var
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CellChi: DblDyneMat = nil;
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RowLabels: StrDyneVec = nil;
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ColLabels: StrDyneVec = nil;
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yates : boolean = false;
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yates : boolean;
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NoSelected, NCases, NRows, NCols: Integer;
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i, j, RowNo, ColNo, DepNo, MinRow, MaxRow, MinCol, MaxCol: integer;
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Row, Col, FObs, df: integer;
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PObs, ChiSquare, ProbChi, phi, SumX, SumY, VarX, VarY, likelihood: double;
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i, j, rowNo, colNo, depNo: integer;
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Row, Col, df: integer;
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ChiSquare, probChi, phi: double;
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title : string;
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AdjChiSqr, AdjProbChi, probLikelihood, G, pearsonr, MantelHaenszel, MHprob: double;
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AdjChiSqr, AdjProbChi, pearsonr, G, likelihood, MantelHaenszel, prob: double;
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CoefCont, CramerV: double;
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lReport: TStrings;
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begin
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RowNo := GetVariableIndex(OS3MainFrm.DataGrid, RowEdit.Text);
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ColNo := GetVariableIndex(OS3MainFrm.DataGrid, ColEdit.Text);
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DepNo := GetVariableIndex(OS3MainFrm.DataGrid, DepEdit.Text);
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rowNo := GetVariableIndex(OS3MainFrm.DataGrid, RowEdit.Text);
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colNo := GetVariableIndex(OS3MainFrm.DataGrid, ColEdit.Text);
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depNo := GetVariableIndex(OS3MainFrm.DataGrid, DepEdit.Text);
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SetLength(ColNoSelected, NoVariables);
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ColNoSelected[0] := RowNo;
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@ -203,126 +300,29 @@ begin
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NoSelected := 3;
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ColNoSelected[2] := DepNo;
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end;
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SetLength(ColNoSelected, NoSelected);
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SetLength(ColNoSelected, NoSelected); // trim length
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// Get min and max of row and col numbers
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MinRow := MaxInt;
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MaxRow := -MinRow;
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MinCol := MaxInt;
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MaxCol := -MinCol;
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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, ColNoSelected) then continue;
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Row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[RowNo, i])));
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Col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ColNo, i])));
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if Row > MaxRow then MaxRow := Row;
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if Row < MinRow then MinRow := Row;
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if Col > MaxCol then MaxCol := Col;
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if Col < MinCol then MinCol := Col;
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end;
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NRows := MaxRow - MinRow + 1;
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NCols := MaxCol - MinCol + 1;
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// Get frequencies from the grid
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GetFrequencies(ColNoselected, rowNo, colNo, depNo, nRows, nCols, nCases, Freq);
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df := (nRows - 1) * (nCols - 1);
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// allocate and initialize
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SetLength(Freq, NRows+1, NCols+1);
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SetLength(Prop, NRows+1, NCols+1);
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SetLength(Expected, NRows, NCols);
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SetLength(CellChi, NRows, NCols);
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SetLength(RowLabels, NRows+1);
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SetLength(ColLabels, NCols+1);
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for i := 1 to NRows + 1 do
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for j := 1 to NCols + 1 do Freq[i-1, j-1] := 0;
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// get cell data
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NCases := 0;
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case InputGrp.ItemIndex of
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0 : begin // count number of cases in each row and column combination
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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, ColNoSelected) then continue;
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NCases := NCases + 1;
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Row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[RowNo, i])));
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Col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ColNo, i])));
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Row := Row - MinRow + 1;
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Col := Col - MinCol + 1;
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Freq[Row-1, Col-1] := Freq[Row-1, Col-1] + 1;
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end;
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end;
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1 : begin // read frequencies data from grid
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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, ColNoSelected) then continue;
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Row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[RowNo, i])));
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Col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ColNo, i])));
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Row := Row - MinRow + 1;
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Col := Col - MinCol + 1;
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FObs := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[DepNo, i])));
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Freq[Row-1, Col-1] := Freq[Row-1, Col-1] + FObs;
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NCases := NCases + FObs;
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end;
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end;
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2 : begin // get no. of cases and proportions for each cell
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NCases := StrToInt(NCasesEdit.Text);
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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, ColNoSelected) then continue;
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Row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[RowNo, i])));
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Col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ColNo, i])));
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Row := Row - MinRow + 1;
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Col := Col - MinCol + 1;
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PObs := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[DepNo, i]));
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Freq[Row-1, Col-1] := Freq[Row-1, Col-1] + round(PObs * NCases);
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end;
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end;
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end; // end case
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Freq[Nrows, Ncols] := NCases;
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// Calculate expected values
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// Get row totals first
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for i := 1 to NRows do
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for j := 1 to Ncols do
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Freq[i-1, NCols] := Freq[i-1, NCols] + Freq[i-1, j-1];
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// Get col totals next
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for j := 1 to NCols do
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for i := 1 to NRows do
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Freq[NRows, j-1] := Freq[NRows, j-1] + Freq[i-1, j-1];
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// Then get expected values and cell chi-squares
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ChiSquare := 0.0;
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AdjChisqr := 0.0;
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if (YatesChk.Checked) and (NRows = 2) and (NCols = 2) then
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yates := true;
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for i := 1 to NRows do
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begin
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for j := 1 to Ncols do
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begin
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Expected[i-1, j-1] := Freq[NRows, j-1] * Freq[i-1, NCols] / NCases;
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if Expected[i-1, j-1] > 0.0 then
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CellChi[i-1, j-1] := sqr(Freq[i-1, j-1] - Expected[i-1, j-1]) / Expected[i-1, j-1]
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else begin
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ErrorMsg('Zero expected value found.');
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CellChi[i-1,j-1] := 0.0;
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end;
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ChiSquare := ChiSquare + CellChi[i-1, j-1];
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end;
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end;
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df := (Nrows - 1) * (Ncols - 1);
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if yates then // 2 x 2 corrected chi-square
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begin
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AdjChiSqr := abs((Freq[0,0] * Freq[1,1]) - (Freq[0,1] * Freq[1,0]));
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AdjChiSqr := sqr(AdjChiSqr - NCases / 2.0) * NCases; // numerator
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AdjChiSqr := AdjChiSqr / (Freq[0,2] * Freq[1,2] * Freq[2,0] * Freq[2,1]);
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AdjProbChi := 1.0 - ChiSquaredProb(AdjChiSqr, df);
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end;
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// Calculate expected values and cell chi-squares
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GetExpectedAndCellChiSqr(Freq, Expected, CellChi, ChiSquare);
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ProbChi := 1.0 - ChiSquaredProb(ChiSquare, df); // prob. larger chi
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yates := YatesChk.Checked and (nRows = 2) and (nCols = 2);
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if yates then begin
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GetYatesCorrection(Freq, AdjChiSqr);
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AdjProbChi := 1.0 - ChiSquaredProb(AdjChiSqr, df);
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end else
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AdjChiSqr := 0;
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// Get row and column labels for reports
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SetLength(RowLabels, NRows+1);
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for i := 1 to NRows do RowLabels[i-1] := Format('Row %d', [i]);
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RowLabels[NRows] := 'Total';
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SetLength(ColLabels, NCols+1);
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for j := 1 to NCols do ColLabels[j-1] := Format('Col.%d', [j]);
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ColLabels[NCols] := 'Total';
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@ -356,53 +356,24 @@ begin
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if PropsChk.Checked then
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begin
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RowColPage.TabVisible := true;
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title := 'ROW PROPORTIONS';
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for i := 1 to NRows + 1 do
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begin
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for j := 1 to NCols do
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begin
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if Freq[i-1, NCols] > 0.0 then
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Prop[i-1, j-1] := Freq[i-1, j-1] / Freq[i-1, NCols]
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else
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Prop[i-1, j-1] := 0.0;
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end;
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if Freq[i-1, NCols] > 0.0 then
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Prop[i-1, NCols] := 1.0
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else
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Prop[i-1, NCols] := 0.0;
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end;
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GetRowProportions(Freq, Prop);
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lReport.Add('CHI-SQUARE ANALYSIS RESULTS');
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lReport.Add('');
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title := 'ROW PROPORTIONS';
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MatPrint(Prop, NRows+1, NCols+1, title, RowLabels, ColLabels, NCases, lReport);
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lReport.Add(DIVIDER_SMALL_AUTO);
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lReport.Add('');
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GetColProportions(Freq, Prop);
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title := 'COLUMN PROPORTIONS';
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for j := 1 to Ncols + 1 do
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begin
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for i := 1 to Nrows do
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begin
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if Freq[Nrows,j-1] > 0.0 then
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Prop[i-1,j-1] := Freq[i-1,j-1] / Freq[Nrows,j-1]
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else
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Prop[i-1,j-1] := 0.0;
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end;
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if Freq[Nrows,j-1] > 0.0 then
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Prop[NRows,j-1] := 1.0
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else
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Prop[NRows,j-1] := 0.0;
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end;
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MatPrint(Prop, NRows+1, NCols+1, title, RowLabels, ColLabels, NCases, lReport);
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lReport.Add(DIVIDER_SMALL_AUTO);
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lReport.Add('');
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GetTotalProportions(Freq, Prop);
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Title := 'PROPORTIONS OF TOTAL N';
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for i := 1 to NRows + 1 do
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for j := 1 to NCols + 1 do
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Prop[i-1,j-1] := Freq[i-1,j-1] / NCases;
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Prop[Nrows, Ncols] := 1.0;
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MatPrint(Prop, NRows+1, NCols+1, title, RowLabels, ColLabels, NCases, lReport);
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lReport.Add(DIVIDER_SMALL_AUTO);
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@ -438,26 +409,16 @@ begin
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lReport.Add('');
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end;
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likelihood := 0.0;
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for i := 0 to NRows-1 do
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for j := 0 to NCols-1 do
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if (Freq[i, j] > 0.0) then
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likelihood := Likelihood + (Freq[i, j] * (ln(Expected[i, j] / Freq[i,j ])));
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likelihood := -2.0 * likelihood;
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probLikelihood := 1.0 - ChiSquaredProb(likelihood, df);
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likelihood := CalcLikelihoodRatio(Freq, Expected);
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prob := 1.0 - ChiSquaredProb(likelihood, df);
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lReport.Add('Likelihood Ratio: %.3f', [likelihood]);
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lReport.Add(' Probability > value is %.4f', [probLikelihood]);
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lReport.Add(' Probability > value is %.4f', [prob]);
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lReport.Add('');
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G := 0.0;
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for i := 0 to NRows-1 do
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for j := 0 to NCols-1 do
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if (Expected[i, j] > 0) then
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G := G + Freq[i, j] * (ln(Freq[i, j] / Expected[i, j]));
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G := 2.0 * G;
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probLikelihood := 1.0 - ChiSquaredProb(G, df);
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G := CalcGStatistic(Freq, Expected);
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prob := 1.0 - ChiSquaredProb(G, df);
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lReport.Add('G statistic: %.3f ', [G]);
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lReport.Add(' Probability > value is %.4f', [G, probLikelihood]);
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lReport.Add(' Probability > value is %.4f', [prob]);
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lReport.Add('');
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if ((NRows > 1) and (NCols > 1)) then
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@ -466,29 +427,14 @@ begin
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lReport.Add('phi correlation: %.4f', [phi]);
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lReport.Add('');
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pearsonr := 0.0;
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SumX := 0.0;
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SumY := 0.0;
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VarX := 0.0;
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VarY := 0.0;
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for i := 0 to NRows-1 do SumX := SumX + ( (i+1) * Freq[i, NCols] );
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for j := 0 to NCols-1 do SumY := SumY + ( (j+1) * Freq[NRows, j] );
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for i := 0 to NRows-1 do VarX := VarX + ( sqr(i+1) * Freq[i, NCols] );
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for j := 0 to NCols-1 do VarY := VarY + ( sqr(j+1) * Freq[NRows, j] );
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VarX := VarX - sqr(SumX) / NCases;
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VarY := VarY - sqr(SumY) / NCases;
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for i := 0 to NRows-1 do
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for j := 0 to NCols-1 do
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pearsonR := pearsonR + ((i+1)*(j+1) * Freq[i, j]);
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pearsonR := pearsonR - (SumX * SumY / Ncases);
|
||||
pearsonR := pearsonR / sqrt(VarX * VarY);
|
||||
pearsonR := CalcPearsonR(Freq);
|
||||
lReport.Add('Pearson Correlation r: %.4f', [pearsonR]);
|
||||
lReport.Add('');
|
||||
|
||||
MantelHaenszel := (NCases-1) * sqr(pearsonR);
|
||||
MHprob := 1.0 - ChiSquaredProb(MantelHaenszel, 1);
|
||||
prob := 1.0 - ChiSquaredProb(MantelHaenszel, 1);
|
||||
lReport.Add('Mantel-Haenszel Test of Linear Association: %.3f', [MantelHaenszel]);
|
||||
lReport.Add(' Probability > value is %.4f', [MantelHaenszel, MHprob]);
|
||||
lReport.Add(' Probability > value is %.4f', [prob]);
|
||||
lReport.Add('');
|
||||
|
||||
CoefCont := sqrt(ChiSquare / (ChiSquare + NCases));
|
||||
@ -496,9 +442,9 @@ begin
|
||||
lReport.Add('');
|
||||
|
||||
if (Nrows < Ncols) then
|
||||
CramerV := sqrt(ChiSquare / (NCases * ((NRows-1))))
|
||||
CramerV := sqrt(ChiSquare / (NCases * ((NRows-1))))
|
||||
else
|
||||
CramerV := sqrt(ChiSquare / (NCases * ((NCols-1))));
|
||||
CramerV := sqrt(ChiSquare / (NCases * ((NCols-1))));
|
||||
lReport.Add('Cramers V is %.3f', [CramerV]);
|
||||
lReport.Add('');
|
||||
end;
|
||||
@ -511,57 +457,48 @@ begin
|
||||
// save frequency data file if elected
|
||||
if SaveFChk.Checked then
|
||||
begin
|
||||
OS3MainFrm.mnuFileCloseClick(self);
|
||||
OS3MainFrm.FileNameEdit.Text := '';
|
||||
for i := 1 to DictionaryFrm.DictGrid.RowCount - 1 do
|
||||
for j := 0 to 7 do DictionaryFrm.DictGrid.Cells[j,i] := '';
|
||||
DictionaryFrm.DictGrid.RowCount := 1;
|
||||
// DictionaryFrm.FileNameEdit.Text := '';
|
||||
OS3MainFrm.mnuFileCloseClick(self);
|
||||
OS3MainFrm.FileNameEdit.Text := '';
|
||||
for i := 1 to DictionaryFrm.DictGrid.RowCount - 1 do
|
||||
for j := 0 to 7 do DictionaryFrm.DictGrid.Cells[j,i] := '';
|
||||
DictionaryFrm.DictGrid.RowCount := 1;
|
||||
|
||||
// get labels for new file
|
||||
ColLabels[0] := 'ROW';
|
||||
ColLabels[1] := 'COL';
|
||||
ColLabels[2] := 'FREQ';
|
||||
// create new variables
|
||||
Row := 0;
|
||||
OS3MainFrm.DataGrid.ColCount := 4;
|
||||
DictionaryFrm.DictGrid.ColCount := 8;
|
||||
NoVariables := 0;
|
||||
for i := 1 to 3 do
|
||||
begin
|
||||
col := NoVariables + 1;
|
||||
DictionaryFrm.NewVar(col);
|
||||
DictionaryFrm.DictGrid.Cells[1,col] := ColLabels[i-1];
|
||||
OS3MainFrm.DataGrid.Cells[col,0] := ColLabels[i-1];
|
||||
NoVariables := NoVariables + 1;
|
||||
end;
|
||||
OS3MainFrm.DataGrid.RowCount := (Nrows * NCols) + 1;
|
||||
for i := 1 to Nrows do
|
||||
begin
|
||||
for j := 1 to Ncols do
|
||||
begin
|
||||
Row := Row + 1;
|
||||
OS3MainFrm.DataGrid.Cells[0,Row] := Format('Case:%d',[Row]);
|
||||
OS3MainFrm.DataGrid.Cells[1,Row] := IntToStr(i);
|
||||
OS3MainFrm.DataGrid.Cells[2,Row] := IntToStr(j);
|
||||
OS3MainFrm.DataGrid.Cells[3,Row] := IntToStr(Freq[i-1,j-1]);
|
||||
end;
|
||||
end;
|
||||
NoCases := Row;
|
||||
OS3MainFrm.FileNameEdit.Text := 'ChiSqrFreq.LAZ';
|
||||
OS3MainFrm.NoCasesEdit.Text := IntToStr(NoCases);
|
||||
OS3MainFrm.NoVarsEdit.Text := IntToStr(NoVariables);
|
||||
// OS3MainFrm.SaveFileBtnClick(self);
|
||||
// get labels for new file
|
||||
ColLabels[0] := 'ROW';
|
||||
ColLabels[1] := 'COL';
|
||||
ColLabels[2] := 'FREQ';
|
||||
|
||||
// create new variables
|
||||
Row := 0;
|
||||
OS3MainFrm.DataGrid.ColCount := 4;
|
||||
DictionaryFrm.DictGrid.ColCount := 8;
|
||||
NoVariables := 0;
|
||||
for i := 1 to 3 do
|
||||
begin
|
||||
col := NoVariables + 1;
|
||||
DictionaryFrm.NewVar(col);
|
||||
DictionaryFrm.DictGrid.Cells[1,col] := ColLabels[i-1];
|
||||
OS3MainFrm.DataGrid.Cells[col,0] := ColLabels[i-1];
|
||||
NoVariables := NoVariables + 1;
|
||||
end;
|
||||
OS3MainFrm.DataGrid.RowCount := (Nrows * NCols) + 1;
|
||||
|
||||
for i := 1 to Nrows do
|
||||
begin
|
||||
for j := 1 to Ncols do
|
||||
begin
|
||||
Row := Row + 1;
|
||||
OS3MainFrm.DataGrid.Cells[0,Row] := Format('Case:%d',[Row]);
|
||||
OS3MainFrm.DataGrid.Cells[1,Row] := IntToStr(i);
|
||||
OS3MainFrm.DataGrid.Cells[2,Row] := IntToStr(j);
|
||||
OS3MainFrm.DataGrid.Cells[3,Row] := IntToStr(Freq[i-1,j-1]);
|
||||
end;
|
||||
end;
|
||||
NoCases := Row;
|
||||
OS3MainFrm.FileNameEdit.Text := 'ChiSqrFreq.LAZ';
|
||||
OS3MainFrm.NoCasesEdit.Text := IntToStr(NoCases);
|
||||
OS3MainFrm.NoVarsEdit.Text := IntToStr(NoVariables);
|
||||
end;
|
||||
|
||||
//clean up
|
||||
ColLabels := nil;
|
||||
RowLabels := nil;
|
||||
CellChi := nil;
|
||||
Expected := nil;
|
||||
Prop := nil;
|
||||
Freq := nil;
|
||||
ColNoSelected := nil;
|
||||
end;
|
||||
|
||||
|
||||
@ -590,6 +527,207 @@ begin
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.GetExpectedAndCellChiSqr(const AFrequencies: IntDyneMat;
|
||||
out AExpected, ACellChiSqr: DblDyneMat;
|
||||
out AChiSqr: Double);
|
||||
var
|
||||
numRows, numCols, numCases: Integer;
|
||||
i, j: Integer;
|
||||
begin
|
||||
MatSize(AFrequencies, numRows, numCols); // contains the totals row/col
|
||||
numCases := AFrequencies[numRows-1, numCols-1];
|
||||
|
||||
SetLength(AExpected, numRows-1, numCols-1); // -1: we don't need the totals here
|
||||
SetLength(ACellChiSqr, numRows-1, numCols-1);
|
||||
|
||||
AChiSqr := 0;
|
||||
for i := 0 to numRows-2 do // -2 instead of -1 to skip the totals row
|
||||
begin
|
||||
for j := 0 to numCols-2 do // -2 instead of -1 to skip the totals column
|
||||
begin
|
||||
AExpected[i, j] := AFrequencies[numRows-1, j] * AFrequencies[i, numCols-1] / numCases;
|
||||
if AExpected[i, j] > 0 then
|
||||
ACellChiSqr[i, j] := sqr(AFrequencies[i, j] - AExpected[i, j]) / AExpected[i, j]
|
||||
else begin
|
||||
ErrorMsg('Zero expected value found.');
|
||||
ACellChiSqr[i, j] := 0;
|
||||
end;
|
||||
AChiSqr := AChiSqr + ACellChiSqr[i, j];
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.GetFrequencies(const AColNoSelected: IntDyneVec;
|
||||
ARowIndex, AColIndex, ADepIndex: Integer; out ANumRows, ANumCols, ANumCases: Integer;
|
||||
out AFrequencies: IntDyneMat);
|
||||
var
|
||||
i, j: Integer;
|
||||
row, col: Integer;
|
||||
minRow, maxRow, minCol, maxCol: Integer;
|
||||
FObs: Integer;
|
||||
PObs: Double;
|
||||
begin
|
||||
// Get min and max of row and col numbers
|
||||
minRow := MaxInt;
|
||||
maxRow := -MinRow;
|
||||
minCol := MaxInt;
|
||||
maxCol := -MinCol;
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not GoodRecord(OS3MainFrm.DataGrid, i, AColNoSelected) then continue;
|
||||
row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ARowIndex, i])));
|
||||
col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[AColIndex, i])));
|
||||
if row > maxRow then maxRow := row;
|
||||
if row < minRow then minRow := row;
|
||||
if col > maxCol then maxCol := col;
|
||||
if col < minCol then minCol := col;
|
||||
end;
|
||||
ANumRows := maxRow - minRow + 1;
|
||||
ANumCols := maxCol - minCol + 1;
|
||||
|
||||
AFrequencies := nil;
|
||||
SetLength(AFrequencies, ANumRows+1, ANumCols+1); // +1 for row and column totals
|
||||
|
||||
ANumCases := 0;
|
||||
case InputGrp.ItemIndex of
|
||||
0 : begin // count number of cases in each row and column combination
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not GoodRecord(OS3MainFrm.DataGrid, i, AColNoSelected) then continue;
|
||||
row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ARowIndex, i])));
|
||||
col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[AColIndex, i])));
|
||||
row := row - minRow;
|
||||
col := col - minCol;
|
||||
AFrequencies[row, col] := AFrequencies[row, col] + 1;
|
||||
ANumCases := ANumCases + 1;
|
||||
end;
|
||||
end;
|
||||
1 : begin // read frequencies data from grid
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not GoodRecord(OS3MainFrm.DataGrid, i, AColNoSelected) then continue;
|
||||
row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ARowIndex, i])));
|
||||
col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ARowIndex, i])));
|
||||
row := row - minRow;
|
||||
col := col - minCol;
|
||||
FObs := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ADepIndex, i])));
|
||||
AFrequencies[row, col] := AFrequencies[row, col] + FObs;
|
||||
ANumCases := ANumCases + FObs;
|
||||
end;
|
||||
end;
|
||||
2 : begin // get no. of cases and proportions for each cell
|
||||
ANumCases := StrToInt(NCasesEdit.Text);
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not GoodRecord(OS3MainFrm.Datagrid, i, AColNoSelected) then continue;
|
||||
row := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ARowIndex, i])));
|
||||
col := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[AColIndex, i])));
|
||||
row := row - minRow + 1;
|
||||
col := col - minCol + 1;
|
||||
PObs := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ADepIndex, i]));
|
||||
AFrequencies[row, col] := AFrequencies[row, col] + round(PObs * ANumCases);
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
// Get row totals
|
||||
for i := 0 to ANumRows-1 do
|
||||
for j := 0 to ANumCols-1 do
|
||||
AFrequencies[i, ANumCols] := AFrequencies[i, ANumCols] + AFrequencies[i, j];
|
||||
|
||||
// Get col totals
|
||||
for j := 0 to ANumCols-1 do
|
||||
for i := 0 to ANumRows-1 do
|
||||
AFrequencies[ANumRows, j] := AFrequencies[ANumRows, j] + AFrequencies[i, j];
|
||||
|
||||
// Grand total
|
||||
AFrequencies[ANumRows, ANumCols] := ANumCases;
|
||||
end;
|
||||
|
||||
|
||||
// 2 x 2 corrected chi-square
|
||||
procedure TChiSqrFrm.GetYatesCorrection(const AFrequencies: IntDyneMat;
|
||||
out AdjChiSqr: Double);
|
||||
var
|
||||
numRows, numCols, numCases: Integer;
|
||||
begin
|
||||
MatSize(AFrequencies, numRows, numCols);
|
||||
numCases := AFrequencies[numRows-1, numCols-1];
|
||||
|
||||
AdjChiSqr := abs((AFrequencies[0,0] * AFrequencies[1,1]) - (AFrequencies[0,1] * AFrequencies[1,0]));
|
||||
AdjChiSqr := sqr(AdjChiSqr - numCases / 2.0) * numCases; // numerator
|
||||
AdjChiSqr := AdjChiSqr / (AFrequencies[0,2] * AFrequencies[1,2] * AFrequencies[2,0] * AFrequencies[2,1]);
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.GetColProportions(const AFrequencies: IntDyneMat;
|
||||
out AProportions: DblDyneMat);
|
||||
var
|
||||
numRows, numCols: Integer;
|
||||
i, j: Integer;
|
||||
begin
|
||||
MatSize(AFrequencies, numRows, numCols); // totals in last row/col
|
||||
SetLength(AProportions, numRows, numCols);
|
||||
for j := 0 to numCols-1 do
|
||||
begin
|
||||
for i := 0 to numRows-1 do // Do not process the totals row
|
||||
begin
|
||||
if AFrequencies[numRows-1, j] > 0.0 then
|
||||
AProportions[i, j] := AFrequencies[i, j] / AFrequencies[numRows-1, j]
|
||||
else
|
||||
AProportions[i, j] := 0.0;
|
||||
end;
|
||||
if AFrequencies[numRows-1, j] > 0.0 then
|
||||
AProportions[numRows-1,j] := 1.0
|
||||
else
|
||||
AProportions[numRows-1,j] := 0.0;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.GetRowProportions(const AFrequencies: IntDyneMat;
|
||||
out AProportions: DblDyneMat);
|
||||
var
|
||||
numRows, numCols: Integer;
|
||||
i, j: Integer;
|
||||
begin
|
||||
MatSize(AFrequencies, numRows, numCols); // totals in last row/col
|
||||
SetLength(AProportions, numRows, numCols);
|
||||
for i := 0 to numRows-1 do
|
||||
begin
|
||||
for j := 0 to numCols-1 do // do not touch the totals column here
|
||||
begin
|
||||
if AFrequencies[i, numCols-1] > 0.0 then
|
||||
AProportions[i, j] := AFrequencies[i, j] / AFrequencies[i, numCols-1]
|
||||
else
|
||||
AProportions[i-1, j-1] := 0.0;
|
||||
end;
|
||||
if AFrequencies[i, numCols-1] > 0.0 then
|
||||
AProportions[i, numCols-1] := 1.0
|
||||
else
|
||||
AProportions[i, numCols-1] := 0.0;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.GetTotalProportions(const AFrequencies: IntDyneMat;
|
||||
out AProportions: DblDyneMat);
|
||||
var
|
||||
numRows, numCols, numCases: Integer;
|
||||
i, j: Integer;
|
||||
begin
|
||||
MatSize(AFrequencies, numRows, numCols); // totals in last row/col
|
||||
numCases := AFrequencies[numRows-1, numCols-1];
|
||||
|
||||
SetLength(AProportions, numRows, numCols);
|
||||
for i := 0 to numRows-1 do
|
||||
for j := 0 to numCols-1 do
|
||||
AProportions[i, j] := AFrequencies[i, j] / numCases;
|
||||
AProportions[numRows-1, numCols-1] := 1.0;
|
||||
end;
|
||||
|
||||
|
||||
procedure TChiSqrFrm.InputGrpClick(Sender: TObject);
|
||||
begin
|
||||
case InputGrp.ItemIndex of
|
||||
|
||||
@ -14,6 +14,8 @@ type
|
||||
TDblMatrix = DblDyneMat;
|
||||
TDblVector = DblDyneVec;
|
||||
|
||||
TIntMatrix = IntDyneMat;
|
||||
|
||||
EMatrix = class(Exception);
|
||||
|
||||
// Vectors
|
||||
@ -79,6 +81,7 @@ function MatNumRows(A: TDblMatrix): Integer;
|
||||
function MatRowMeans(A: TDblMatrix): TDblVector;
|
||||
function MatRowVector(A: TDblMatrix; ARowIndex: Integer): TDblVector;
|
||||
procedure MatSize(A: TDblMatrix; out n, m: Integer);
|
||||
procedure MatSize(A: TIntMatrix; out n, m: Integer);
|
||||
function MatTransposed(A: TDblMatrix): TDblMatrix;
|
||||
|
||||
function SubMatrix(A: TDblMatrix; i1,j1, i2,j2: Integer): TDblMatrix;
|
||||
@ -699,6 +702,13 @@ begin
|
||||
end;
|
||||
|
||||
|
||||
procedure MatSize(A: TIntMatrix; out n, m: Integer);
|
||||
begin
|
||||
n := Length(A);
|
||||
m := Length(A[0]);
|
||||
end;
|
||||
|
||||
|
||||
function MatTransposed(A: TDblMatrix): TDblMatrix;
|
||||
var
|
||||
n, m, i, j: Integer;
|
||||
|
||||
Reference in New Issue
Block a user