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{ ******************************************************************
Non-parametric tests
****************************************************************** }
unit unonpar;
interface
uses
utypes;
procedure Mann_Whitney(N1, N2 : Integer;
X1, X2 : PVector;
var U, Eps : Float);
{ ------------------------------------------------------------------
Mann-Whitney test
------------------------------------------------------------------ }
procedure Wilcoxon(X, Y : PVector;
Lb, Ub : Integer;
var Ndiff : Integer;
var T, Eps : Float);
{ ------------------------------------------------------------------
Wilcoxon test
------------------------------------------------------------------ }
procedure Kruskal_Wallis(Ns : Integer;
N : PIntVector;
X : PMatrix;
var H : Float;
var DoF : Integer);
{ ------------------------------------------------------------------
Kruskal-Wallis test
------------------------------------------------------------------ }
implementation
procedure Ranks(Ns : Integer;
N : PIntVector;
X : PMatrix;
Sr : PVector;
var Corr : Float);
{ ------------------------------------------------------------------
Compute ranks for non-parametric tests
------------------------------------------------------------------
Sr = sum of ranks for each sample
Corr = correction for ties = Sum k(k^2 - 1) k = nb of ties
------------------------------------------------------------------ }
var
I, J, I1, J1, NI, NE : Integer;
Y, Z, R : Float;
begin
if Ns < 2 then
begin
SetErrCode(MatErrDim);
Exit
end;
SetErrCode(MatOk);
Corr := 0.0;
for I := 1 to Ns do
Sr^[I] := 0;
for I := 1 to Ns do
for J := 1 to N^[I] do
begin
Y := X^[J]^[I];
NE := 0; { Nb of values = Y }
NI := 0; { Nb of values < Y }
for I1 := 1 to Ns do
for J1 := 1 to N^[I1] do
begin
Z := X^[J1]^[I1];
if Z < Y then Inc(NI) else if Z = Y then Inc(NE);
end;
R := NI + Succ(NE) / 2; { Mean rank of Y }
Sr^[I] := Sr^[I] + R; { Sum of ranks for sample I }
if NE > 1 then
Corr := Corr + NE * (Sqr(NE) - 1);
end;
end;
procedure Mann_Whitney(N1, N2 : Integer;
X1, X2 : PVector;
var U, Eps : Float);
var
Nmax, I : Integer;
N : PIntVector;
X : PMatrix;
Sr : PVector;
Sum, Prod, Corr : Float;
U1, U2, MU, VU : Float;
begin
if N1 > N2 then Nmax := N1 else Nmax := N2;
DimIntVector(N, 2);
DimVector(Sr, 2);
DimMatrix(X, Nmax, 2);
N^[1] := N1;
N^[2] := N2;
for I := 1 to N1 do { Copy X1 into first column of X }
X^[I]^[1] := X1^[I];
for I := 1 to N2 do { Copy X2 into second column of X }
X^[I]^[2] := X2^[I];
Ranks(2, N, X, Sr, Corr);
Sum := N1 + N2;
Prod := N1 * N2;
U1 := Prod + N1 * (N1 + 1) / 2 - Sr^[1];
U2 := Prod + N2 * (N2 + 1) / 2 - Sr^[2];
if U1 > U2 then U := U2 else U := U1;
MU := Prod / 2;
VU := Prod * ((Sum + 1) - Corr / Sum / (Sum - 1)) / 12;
Eps := (U - MU) / Sqrt(VU);
DelIntVector(N, 2);
DelVector(Sr, 2);
DelMatrix(X, Nmax, 2);
end;
procedure Wilcoxon(X, Y : PVector;
Lb, Ub : Integer;
var Ndiff : Integer;
var T, Eps : Float);
var
J, J1, J2, N : Integer;
Diff, MT, VT, Corr : Float;
D : PMatrix;
ND : PIntVector;
Sr : PVector;
begin
N := Ub - Lb + 1;
DimMatrix(D, N, 2);
DimIntVector(ND, 2);
DimVector(Sr, 2);
J1 := 0; J2 := 0;
for J := Lb to Ub do
begin
Diff := X^[J] - Y^[J];
if Diff < 0 then
begin
Inc(J1);
D^[J1]^[1] := Abs(Diff); { Negative difference }
end
else if Diff > 0 then
begin
Inc(J2);
D^[J2]^[2] := Diff; { Positive difference }
end;
end;
ND^[1] := J1; { Nb of negative differences }
ND^[2] := J2; { Nb of positive differences }
Ndiff := J1 + J2; { Nb of non-null differences }
Ranks(2, ND, D, Sr, Corr);
if Sr^[1] > Sr^[2] then T := Sr^[2] else T := Sr^[1];
MT := N * (N + 1) / 4;
VT := MT * (2 * N + 1) / 6 - Corr / 48;
Eps := (T - MT) / Sqrt(VT);
DelMatrix(D, N, 2);
DelIntVector(ND, 2);
DelVector(Sr, 2);
end;
procedure Kruskal_Wallis(Ns : Integer;
N : PIntVector;
X : PMatrix;
var H : Float;
var DoF : Integer);
var
I, NT : Integer;
S, Corr : Float;
Sr : PVector;
begin
DimVector(Sr, Ns);
Ranks(Ns, N, X, Sr, Corr);
S := 0.0; NT := 0;
for I := 1 to Ns do
begin
S := S + Sqr(Sr^[I]) / N^[I];
NT := NT + N^[I];
end;
H := 12 * S / NT / (NT + 1) - 3 * (NT + 1);
H := H / (1 - Corr / NT / (Sqr(NT) - 1));
DoF := Pred(Ns);
DelVector(Sr, Ns);
end;
end.
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