Biserial correlation coefficient. Applicative program.

Costescu, Mihai Radu

Considerand ca variabila dihotomica poate lua valorile A si B, formula de calcul al coeficientului de corelatie biserial este:

r = [[bar.x].sub.1] --[[bar.x].sub.2]/s * pq/y

unde:

[[bar.x].sub.1] = media valorilor variabilei continue pentru subiectii care au caracteristica A a variabilei dihotomice;

[[bar.x].sub.2] = media valorilor variabilei continue pentru subiectii care au caracteristica B a variabilei dihotomice;

s = abaterea standard a variabilei continue pe intreg lotul de subiecti;

pq/y = valoare care se ia dintr-un tabel special in functie de p, sau de q.

procedure coef_corel_biserial(pq_y:real;var r:real);
   type vect=array[1..50] of real;
   var v,n1,n2:vect;
      n:integer;
      media1,media2,med_tot,s:real;
   procedure citire(k:integer;var x:vect);
      var i:integer;
      begin
      for i:=1 to k do
      begin
      write('Varianta',i:3,' : ');
      readln(x[i]);
      end;
   end;
function media(k:integer;v,x:vect):real;
   var nt,suma:real;
      i:integer;
   begin
      suma:=0;
      nt:=0;
      for i:=1 to k do
      begin
      suma:= suma+v[i]*x[i];
      nt:=nt+x[i];
      end;
      media:=suma/nt;
   end;
function media_total(k:integer;v,x,y:vect):real;
   var nt,suma:real;
      i:integer;
   begin
      suma:=0;
      nt:=0;
      for i:=1 to k do
      begin
      suma:= suma+v[i]*(x[i]+y[i]);
      nt:=nt+x[i]+y[i];
      end;
      media_total:=suma/nt;
   end;
function ab_med_patrat(k:integer;med_total:real;v,x,y:vect):real;
   var nt,suma:real;
      i:integer;
   begin
      suma:=0;
      nt:=0;
      for i:=1 to k do
      begin
      suma:=suma+sqr(v[i]-med_total)*(x[i]+y[i]);
      nt:=nt+x[i]+y[i];
      end;
      ab_med_patrat:=sqrt(suma/nt);
   end;
begin {procedure coef_corel_biserial}
   write('Introduceti numarul de variante al variabilei continue n=');
      readln(n);
      writeln('Introduceti variantele variabilei continue');
      citire(n,v);
      writeln('Introduceti numerele corespunzatoare variantelor care
      poarta caracteristica A a variantei dihotomice');
      citire(n,n1);
      writeln('Introduceti numerele corespunzatoare variantelor care
      poarta caracteristica B a variantei dihotomice');
      citire(n,n2);
      write('Introduceti valoarea pq/y = ');
      readln(pq_y);
      media1:=media(n,v,n1);
      media2:=media(n,v,n2);
      med_tot:=media_total(n,v,n1,n2);
      s:=ab_med_patrat(n,med_tot,v,n1,n2);
      r:=(media1-media2)/s*pq_y;
   writeln('Coeficientul de corelatie biserial r = ',r:6:4);
end;

Bibliografie

1. Costescu, Mihai-Radu, Statistic Methods Applied in Social Sciences, Liberty Press and Publishing House, Panciova, 2007

2. Costescu, Mihai-Radu, Costel, Ionascu, Electronic Information Processing, Universitaria Press, Craiova, 2001