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489 lines
16 KiB
ObjectPascal
489 lines
16 KiB
ObjectPascal
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unit KWANOVAUnit;
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{$mode objfpc}{$H+}
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interface
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uses
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Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
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StdCtrls, Buttons, MainUnit, OutPutUnit, FunctionsLib,
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Globals, DataProcs, Math;
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type
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{ TKWAnovaFrm }
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TKWAnovaFrm = class(TForm)
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AlphaEdit: TEdit;
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Label4: TLabel;
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Label5: TLabel;
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MWUChk: TCheckBox;
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ResetBtn: TButton;
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CancelBtn: TButton;
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ComputeBtn: TButton;
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ReturnBtn: TButton;
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GrpEdit: TEdit;
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DepEdit: TEdit;
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GrpIn: TBitBtn;
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GrpOut: TBitBtn;
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DepIn: TBitBtn;
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DepOut: TBitBtn;
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Label1: TLabel;
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Label2: TLabel;
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Label3: TLabel;
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VarList: TListBox;
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procedure ComputeBtnClick(Sender: TObject);
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procedure DepInClick(Sender: TObject);
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procedure DepOutClick(Sender: TObject);
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procedure FormShow(Sender: TObject);
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procedure GrpInClick(Sender: TObject);
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procedure GrpOutClick(Sender: TObject);
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procedure ResetBtnClick(Sender: TObject);
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private
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{ private declarations }
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public
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{ public declarations }
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end;
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var
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KWAnovaFrm: TKWAnovaFrm;
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implementation
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{ TKWAnovaFrm }
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procedure TKWAnovaFrm.ResetBtnClick(Sender: TObject);
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VAR i : integer;
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begin
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GrpEdit.Text := '';
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DepEdit.Text := '';
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AlphaEdit.Text := '0.05';
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GrpIn.Visible := true;
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GrpOut.Visible := false;
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DepIn.Visible := true;
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DepOut.Visible := false;
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MWUChk.Checked := false;
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VarList.Items.Clear;
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for i := 1 to NoVariables do
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VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
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end;
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procedure TKWAnovaFrm.FormShow(Sender: TObject);
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begin
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ResetBtnClick(self);
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end;
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procedure TKWAnovaFrm.DepInClick(Sender: TObject);
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VAR index : integer;
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begin
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index := VarList.ItemIndex;
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DepEdit.Text := VarList.Items.Strings[index];
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VarList.Items.Delete(index);
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DepIn.Visible := false;
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DepOut.Visible := true;
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end;
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procedure TKWAnovaFrm.ComputeBtnClick(Sender: TObject);
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label cleanup, Check1, Check2;
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var
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i, j, k, m, ind_var, dep_var, min_grp, max_grp, group, total_n : integer;
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NoTies, NoTieGroups, nogroups, NoSelected, npairs, n1, n2 : integer;
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largestn : integer;
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ColNoSelected : IntdyneVec;
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group_count : IntDyneVec;
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score, t, SumT, Avg, Probchi, H, CorrectedH, value : double;
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Correction, Temp, TieSum, alpha, U, U2, SD, z, prob : double;
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Ranks, X : DblDyneMat;
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RankSums : DblDyneVec;
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cellstring, outline : string;
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begin
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// Check for data
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if (NoVariables < 1) then
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begin
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ShowMessage('ERROR! You must have grid data!');
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exit;
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end;
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// allocate space
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SetLength(ColNoSelected,NoVariables);
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SetLength(Ranks,NoCases,2);
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SetLength(X,NoCases,2);
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// Get column numbers of the independent and dependent variables
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ind_var := 0;
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dep_var := 0;
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for i := 1 to NoVariables do
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begin
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cellstring := GrpEdit.Text;
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if (cellstring = OS3MainFrm.DataGrid.Cells[i,0]) then ind_var := i;
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cellstring := DepEdit.Text;
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if (cellstring = OS3MainFrm.DataGrid.Cells[i,0]) then dep_var := i;
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end;
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ColNoSelected[0] := ind_var;
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ColNoSelected[1] := dep_var;
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//get minimum and maximum group codes
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total_n := 0;
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NoSelected := 2;
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min_grp := 10000; //atoi(MainForm.Grid.Cells[ind_var,1].c_str);
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max_grp := -10000;
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for i := 1 to NoCases do
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begin
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if (not GoodRecord(i,NoSelected,ColNoSelected)) then continue;
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group := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ind_var,i])));
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if (group < min_grp) then min_grp := group;
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if (group > max_grp) then max_grp := group;
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total_n := total_n + 1;
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end;
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nogroups := max_grp - min_grp + 1;
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NoTieGroups := 0;
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SumT := 0.0;
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H := 0.0;
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// Initialize arrays
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SetLength(RankSums,nogroups);
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SetLength(group_count,nogroups);
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for i := 0 to nogroups-1 do
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begin
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group_count[i] := 0;
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RankSums[i] := 0.0;
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end;
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// Setup for printer output
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OutPutFrm.RichEdit.Clear;
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OutPutFrm.RichEdit.Lines.Add('Kruskal - Wallis One-Way Analysis of Variance');
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OutPutFrm.RichEdit.Lines.Add('See pages 184-194 in S. Siegel: Nonparametric Statistics for the Behavioral Sciences');
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OutPutFrm.RichEdit.Lines.Add('');
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// Get data
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for i := 1 to NoCases do
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begin
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if (not GoodRecord(i,NoSelected,ColNoSelected)) then continue;
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score := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[dep_var,i]));
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group := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ind_var,i])));
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group := group - min_grp + 1;
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if (group > nogroups) then
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begin
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ShowMessage('ERROR! Group codes must be sequential like 1 and 2!');
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goto cleanup;
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end;
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group_count[group-1] := group_count[group-1] + 1;
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X[i-1,0] := score;
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X[i-1,1] := group;
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end;
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//Sort all scores in ascending order
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for i := 1 to total_n - 1 do
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begin
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for j := i + 1 to total_n do
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begin
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if (X[i-1,0] > X[j-1,0]) then
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begin
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Temp := X[i-1,0];
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X[i-1,0] := X[j-1,0];
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X[j-1,0] := Temp;
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Temp := X[i-1,1];
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X[i-1,1] := X[j-1,1];
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X[j-1,1] := Temp;
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end;
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end;
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end;
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// Store ranks
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for i := 0 to total_n-1 do
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begin
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Ranks[i,0] := i+1;
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Ranks[i,1] := X[i,1];
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end;
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//Check for ties in ranks - replace with average rank and calculate
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//T for each tie and sum of the T's
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i := 1;
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while i < total_n do
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begin
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j := i + 1;
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TieSum := 0;
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NoTies := 0;
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while (j < total_n) do
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begin
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if (X[j-1,0] > X[i-1,0]) then goto Check1;
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if (X[j-1,0] = X[i-1,0]) then // match
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begin
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TieSum := TieSum + round(Ranks[j-1,0]);
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NoTies := NoTies + 1;
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end;
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j := j + 1;
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end;
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Check1:
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if (NoTies > 0) then //At least one tie found
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begin
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TieSum := TieSum + Ranks[i-1,0];
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NoTies := NoTies + 1;
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Avg := TieSum / NoTies;
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for j := i to i + NoTies - 1 do Ranks[j-1,0] := Avg;
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t := Power(NoTies,3) - NoTies;
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SumT := SumT + t;
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NoTieGroups := NoTieGroups + 1;
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i := i + (NoTies - 1);
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end;
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i := i + 1;
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end; // next i
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// Calculate sum of ranks in each group
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for i := 1 to total_n do
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begin
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group := round(Ranks[i-1,1]);
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RankSums[group-1] := RankSums[group-1] + Ranks[i-1,0];
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end;
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// Calculate statistics
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for j := 0 to nogroups-1 do H := H + (RankSums[j] * RankSums[j] / (group_count[j]));
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H := H * (12.0 / ( total_n * (total_n + 1)) );
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H := H - (3.0 * (total_n + 1));
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Correction := 1.0 - ( SumT / (Power(total_n,3) - total_n) );
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CorrectedH := H / Correction;
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k := max_grp - min_grp;
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Probchi := 1.0 - chisquaredprob(H, k);
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// Report results
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OutPutFrm.RichEdit.Lines.Add(' Score Rank Group');
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OutPutFrm.RichEdit.Lines.Add('');
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for i := 1 to total_n do
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begin
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outline := format('%10.2f %10.2f %10.0f',
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[X[i-1,0], Ranks[i-1,0], Ranks[i-1,1]]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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end;
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OutPutFrm.RichEdit.Lines.Add('');
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OutPutFrm.RichEdit.Lines.Add('Sum of Ranks in each Group');
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OutPutFrm.RichEdit.Lines.Add('Group Sum No. in Group');
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for i := 1 to nogroups do
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begin
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outline := format('%3d %10.2f %5d', [i+min_grp-1, RankSums[i-1],group_count[i-1]]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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end;
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OutPutFrm.RichEdit.Lines.Add('');
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outline := format('No. of tied rank groups = %3d',[NoTieGroups]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Statistic H uncorrected for ties = %8.4f',[H]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Correction for Ties = %6.4f',[Correction]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Statistic H corrected for ties = %8.4f',[CorrectedH]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Corrected H is approx. chi-square with %3d D.F. and probability = %6.4f',[k,Probchi]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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OutPutFrm.ShowModal;
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OutPutFrm.RichEdit.Clear;
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if not MWUChk.Checked then goto cleanup;
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// do Mann-Whitney U tests on group pairs
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alpha := StrToFloat(AlphaEdit.Text);
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npairs := nogroups * (nogroups - 1) div 2;
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alpha := alpha / npairs;
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outline := format('New alpha for %d paired comparisons = %5.3f',[npairs, alpha]);
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ShowMessage(outline);
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for i := 1 to nogroups - 1 do
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begin
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for j := i + 1 to nogroups do
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begin
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// Setup for printer output
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OutPutFrm.RichEdit.Clear;
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OutPutFrm.RichEdit.Lines.Add('Mann-Whitney U Test');
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OutPutFrm.RichEdit.Lines.Add('See pages 116-127 in S. Siegel: Nonparametric Statistics for the Behavioral Sciences');
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OutPutFrm.RichEdit.Lines.Add('');
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outline := format('Comparison of group %d with group %d',[i,j]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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group_count[0] := 0;
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group_count[1] := 0;
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RankSums[0] := 0;
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RankSums[1] := 0;
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total_n := 0;
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for k := 1 to NoCases do
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begin
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if (not GoodRecord(k,NoSelected,ColNoSelected)) then continue;
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score := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[dep_var,k]));
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value := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[ind_var,k]));
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if round(value) = i then
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begin
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X[total_n,0] := score;
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X[total_n,1] := value;
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group_count[0] := group_count[0] + 1;
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total_n := total_n + 1;
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end;
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if round(value) = j then
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begin
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X[total_n,0] := score;
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X[total_n,1] := value;
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group_count[1] := group_count[1] + 1;
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total_n := total_n + 1;
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end;
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end; // next case k
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//Sort all scores in ascending order
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for k := 1 to total_n - 1 do
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begin
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for m := k + 1 to total_n do
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begin
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if (X[k-1,0] > X[m-1,0]) then
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begin
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Temp := X[k-1,0];
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X[k-1,0] := X[m-1,0];
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X[m-1,0] := Temp;
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Temp := X[k-1,1];
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X[k-1,1] := X[m-1,1];
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X[m-1,1] := Temp;
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end;
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end;
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end;
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// get ranks for these two groups
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for k := 1 to total_n do
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begin
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Ranks[k-1,0] := k;
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Ranks[k-1,1] := X[k-1,1];
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end;
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//Check for ties in ranks - replace with average rank and calculate
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//T for each tie and sum of the T's
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NoTieGroups := 0;
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k := 1;
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while k < total_n do
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begin
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m := k + 1;
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TieSum := 0;
|
||
|
|
NoTies := 0;
|
||
|
|
while (m < total_n) do
|
||
|
|
begin
|
||
|
|
if (X[m-1,0] > X[k-1,0]) then goto Check2;
|
||
|
|
if (X[m-1,0] = X[k-1,0]) then // match
|
||
|
|
begin
|
||
|
|
TieSum := TieSum + round(Ranks[m-1,0]);
|
||
|
|
NoTies := NoTies + 1;
|
||
|
|
end;
|
||
|
|
m := m + 1;
|
||
|
|
end;
|
||
|
|
Check2:
|
||
|
|
if (NoTies > 0) then //At least one tie found
|
||
|
|
begin
|
||
|
|
TieSum := TieSum + Ranks[k-1,0];
|
||
|
|
NoTies := NoTies + 1;
|
||
|
|
Avg := TieSum / NoTies;
|
||
|
|
for m := k to k + NoTies - 1 do Ranks[m-1,0] := Avg;
|
||
|
|
t := Power(NoTies,3) - NoTies;
|
||
|
|
SumT := SumT + t;
|
||
|
|
NoTieGroups := NoTieGroups + 1;
|
||
|
|
k := k + (NoTies - 1);
|
||
|
|
end;
|
||
|
|
k := k + 1;
|
||
|
|
end; // next k
|
||
|
|
|
||
|
|
// Calculate sum of ranks in each group
|
||
|
|
for k := 1 to total_n do
|
||
|
|
begin
|
||
|
|
group := round(Ranks[k-1,1]);
|
||
|
|
RankSums[group-1] := RankSums[group-1] + Ranks[k-1,0];
|
||
|
|
end;
|
||
|
|
|
||
|
|
//Calculate U for larger and smaller groups
|
||
|
|
n1 := group_count[0];
|
||
|
|
n2 := group_count[1];
|
||
|
|
if (n1 > n2) then
|
||
|
|
begin
|
||
|
|
group := i-1;
|
||
|
|
U := (n1 * n2) + ((n1 * (n1 + 1)) / 2.0) - RankSums[group];
|
||
|
|
end
|
||
|
|
else
|
||
|
|
begin
|
||
|
|
group := j - 1;
|
||
|
|
U := (n1 * n2) + ((n2 * (n2 + 1)) / 2.0) - RankSums[group];
|
||
|
|
end;
|
||
|
|
U2 := (n1 * n2) - U;
|
||
|
|
SD := (n1 * n2 * (n1 + n2 + 1)) / 12.0;
|
||
|
|
SD := sqrt(SD);
|
||
|
|
if (U2 > U) then z := (U2 - (n1 * n2 / 2)) / SD
|
||
|
|
else z := (U - (n1 * n2 / 2)) / SD;
|
||
|
|
prob := 1.0 - probz(z);
|
||
|
|
|
||
|
|
//Report results
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(' Score Rank Group');
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('');
|
||
|
|
for k := 1 to total_n do
|
||
|
|
begin
|
||
|
|
outline := format('%10.2f %10.2f %10.0f',
|
||
|
|
[X[k-1,0], Ranks[k-1,0], Ranks[k-1,1]]);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
end;
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('');
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('Sum of Ranks in each Group');
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('Group Sum No. in Group');
|
||
|
|
group := i - 1;
|
||
|
|
outline := format('%3d %10.3f %5d', [i, RankSums[group],group_count[0]]);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
group := j - 1;
|
||
|
|
outline := format('%3d %10.3f %5d', [j, RankSums[group],group_count[1]]);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('');
|
||
|
|
outline := format('No. of tied rank groups = %3d',[NoTieGroups]);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
if (n1 > n2) then largestn := n1
|
||
|
|
else largestn := n2;
|
||
|
|
if (largestn < 20) then
|
||
|
|
outline := format('Statistic U = %8.4f',[U])
|
||
|
|
else
|
||
|
|
begin
|
||
|
|
if (U > U2) then outline := format('Statistic U = %8.4f',[U])
|
||
|
|
else outline := format('Statistic U = %8.4f',[U2]);
|
||
|
|
end;
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
outline := format('z Statistic (corrected for ties) = %8.4f, Prob. > z = %6.4f',
|
||
|
|
[z, prob]);
|
||
|
|
OutPutFrm.RichEdit.Lines.Add(outline);
|
||
|
|
if (n2 < 20) then
|
||
|
|
begin
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('z test is approximate. Use tables of exact probabilities in Siegel.');
|
||
|
|
OutPutFrm.RichEdit.Lines.Add('(Table J or K, pages 271-277)');
|
||
|
|
end;
|
||
|
|
OutPutFrm.ShowModal;
|
||
|
|
end; // next group j
|
||
|
|
end; // next group i
|
||
|
|
cleanup:
|
||
|
|
group_count := nil;
|
||
|
|
RankSums := nil;
|
||
|
|
X := nil;
|
||
|
|
Ranks := nil;
|
||
|
|
ColNoSelected := nil;
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TKWAnovaFrm.DepOutClick(Sender: TObject);
|
||
|
|
begin
|
||
|
|
VarList.Items.Add(DepEdit.Text);
|
||
|
|
DepEdit.Text := '';
|
||
|
|
DepIn.Visible := true;
|
||
|
|
DepOut.Visible := false;
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TKWAnovaFrm.GrpInClick(Sender: TObject);
|
||
|
|
VAR index : integer;
|
||
|
|
begin
|
||
|
|
index := VarList.ItemIndex;
|
||
|
|
GrpEdit.Text := VarList.Items.Strings[index];
|
||
|
|
VarList.Items.Delete(index);
|
||
|
|
GrpIn.Visible := false;
|
||
|
|
GrpOut.Visible := true;
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TKWAnovaFrm.GrpOutClick(Sender: TObject);
|
||
|
|
begin
|
||
|
|
VarList.Items.Add(GrpEdit.Text);
|
||
|
|
GrpEdit.Text := '';
|
||
|
|
GrpIn.Visible := true;
|
||
|
|
GrpOut.Visible := false;
|
||
|
|
end;
|
||
|
|
|
||
|
|
initialization
|
||
|
|
{$I kwanovaunit.lrs}
|
||
|
|
|
||
|
|
end.
|
||
|
|
|