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LazStats: Minor refactoring of MannWhitUUnit
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7813 8e941d3f-bd1b-0410-a28a-d453659cc2b4
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wp_xxyyzz
@ -53,7 +53,7 @@ implementation
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uses
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Math,
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Utils;
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Utils, MatrixUnit, GridProcs;
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{ TMannWhitUForm }
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@ -74,17 +74,15 @@ var
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Ranks: DblDyneMat = nil;
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X: DblDyneMat = nil;
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RankSums: DblDyneVec = nil;
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i, j, ind_var, dep_var, min_grp, max_grp, group, total_n : integer;
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NoTies, NoTieGroups, n1, n2, nogroups, largestn : integer;
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NoSelected : integer;
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TieSum, score, t, SumT, Avg, z, prob, U, U2, SD, Temp : double;
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cellstring, outline : string;
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i, j, ind_var, dep_var, min_grp, max_grp, group, total_n: integer;
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NoTies, NoTieGroups, n1, n2, nogroups, largestn: integer;
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TieSum, score, t, SumT, Avg, z, prob, U, U2, SD: double;
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outline: string;
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lReport: TStrings;
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begin
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total_n := 0;
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NoTieGroups := 0;
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NoSelected := 2;
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SumT := 0.0;
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// Check for data
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@ -94,38 +92,30 @@ begin
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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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// 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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if ind_var = 0 then
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ind_var := GetVariableIndex(OS3MainFrm.DataGrid, GrpEdit.Text);
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dep_var := GetVariableIndex(OS3MainFrm.DataGrid, DepEdit.Text);
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if ind_var = -1 then
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begin
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ErrorMsg('No group variable.');
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exit;
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end;
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if dep_var = 0 then
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if dep_var = -1 then
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begin
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ErrorMsg('No dependent variable.');
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exit;
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end;
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SetLength(ColNoSelected, 2);
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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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min_grp := MaxInt;
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max_grp := -MaxInt;
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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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if (not GoodRecord(OS3MainFrm.DataGrid, i, 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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@ -144,121 +134,115 @@ begin
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RankSums[i] := 0.0;
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end;
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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(OS3mainFrm.DataGrid, i, 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 > 2) then
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begin
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ErrorMsg('Group codes must be 1 and 2!');
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exit;
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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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Exchange(X[i-1, 0], X[j-1, 0]);
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Exchange(X[i-1, 1], X[j-1, 1]);
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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
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break;
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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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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 := 0 to total_n-1 do
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begin
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group := round(Ranks[i, 1]);
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RankSums[group-1] := RankSums[group-1] + Ranks[i, 0];
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end;
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// Calculate U for larger and smaller groups
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n1 := group_count[0];
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n2 := group_count[1];
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if (n1 > n2) then
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U := n1 * n2 + n1 * (n1 + 1) / 2.0 - RankSums[0]
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else
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U := n1 * n2 + n2 * (n2 + 1) / 2.0 - RankSums[1];
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U2 := n1 * n2 - U;
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SD := n1 * n2 * (n1 + n2 + 1) / 12.0;
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SD := sqrt(SD);
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if (U2 > U) then
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z := (U2 - n1 * n2 / 2) / SD
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else
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z := (U - n1 * n2 / 2) / SD;
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prob := 1.0 - probz(z);
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// Setup for printer output
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lReport := TStringList.Create;
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try
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lReport.Add('MANN-WHITNEY U TEST');
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lReport.Add('See pages 116-127 in S. Siegel: Nonparametric Statistics for the Behavioral Sciences');
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lReport.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 > 2) then
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begin
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ErrorMsg('Group codes must be 1 and 2!');
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exit;
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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 := 1 to total_n do
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begin
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Ranks[i-1,0] := i;
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Ranks[i-1,1] := X[i-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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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
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break;
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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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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 U for larger and smaller groups
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n1 := group_count[0];
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n2 := group_count[1];
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if (n1 > n2) then
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U := n1 * n2 + n1 * (n1 + 1) / 2.0 - RankSums[0]
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else
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U := n1 * n2 + n2 * (n2 + 1) / 2.0 - RankSums[1];
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U2 := n1 * n2 - U;
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SD := n1 * n2 * (n1 + n2 + 1) / 12.0;
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SD := sqrt(SD);
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if (U2 > U) then
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z := (U2 - n1 * n2 / 2) / SD
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else
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z := (U - n1 * n2 / 2) / SD;
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prob := 1.0 - probz(z);
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// Report results
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lReport.Add(' Score Rank Group');
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lReport.Add('');
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for i := 1 to total_n do
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lReport.Add('%10.2f %10.2f %10.0f', [X[i-1,0], Ranks[i-1,0], Ranks[i-1,1]]);
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for i := 0 to total_n-1 do
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lReport.Add('%10.2f %10.2f %10.0f', [X[i,0], Ranks[i,0], Ranks[i,1]]);
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lReport.Add('');
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lReport.Add('Sum of Ranks in each Group');
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lReport.Add('Group Sum No. in Group');
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for i := 1 to nogroups do
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lReport.Add('%3d %10.2f %5d', [i+min_grp-1, RankSums[i-1], group_count[i-1]]);
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for i := 0 to noGroups-1 do
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lReport.Add('%3d %10.2f %5d', [i+min_grp, RankSums[i], group_count[i]]);
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lReport.Add('');
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lReport.Add('No. of tied rank groups: %10d', [NoTieGroups]);
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if (n1 > n2) then
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