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algol<
begin
_____
integer n,p,g,i,j,sum,k;
_______
real m,s,a,h,T,l;
____
procedure writesp(x);
_________
  value x; integer x;
  _____    _______
    for x:=x step -1 until 1 do writechar(0);
    ___      ____    _____   __
procedure chi square test (n,m,s,a,h,k,g,T,X) ;
_________
value a,n,m,s ; integer n,k,g; real a,h,m,s,T ; array X ;
_____           _______        ____             _____
comment
_______
This procedure performs the chi-square test of the hypothesis
that the observations X=X[1:n] are from a normal population.
The observations are grouped such that there are at least
k observations in each class.
parameters:
n    the number of observations
m    the sample mean
s    the sample dispersion
a    is the upper limit of the first class
h    the length of the classes
k    minimal number of observations in each class
g    is equal 1 if output of the computations are wanted
T    the value of the test criterion
X    the observations.
At the exit the value of g is the number of classes which are used  ;
begin  integer i,j,q,v,r,y,l ; real W,B ; boolean out;
_____  _______                 ____       _______
real procedure Psi(z) ; value z; real z;
____ _________          _____    ____
Psi:=1-1/(1+0.07052308⨯B⨯z + 0.04228201⨯(B⨯z)∧2 + 0.00927053⨯(B⨯z)∧3+
                                             |                    |
0.00015201⨯(B⨯z)∧4 + 0.00027657⨯(B⨯z)∧5 + 0.00004306⨯(B⨯z)∧6)∧16 ;
                |                    |                    |  |
  B:=1/sqrt(2) ;  if k<0 then k:=0 ;
                  __     ____
  if h_0 then begin writetext(|< the length of the classes is too small|);
  __  <  ____ _____           <                                        >
  h:=10∧(-8)  end ;
       |      ___
  for i:=n-1 step -1 until 1 do
  ___        ____    _____   __
  for j:=1   step  1 until i do
  ___        ____    _____   __
  if X[j]>X[j+1] then begin W:=X[j] ; X[j]:=X[j+1] ; X[j+1]:=W end ;
  __             ____ _____                                    ___
  comment  The elements of X have been ordered ;
  _______
  q:=entier((X[n]-a)/h) + 1 ; l:=q+1 ;
  comment  l is the total number of classes ;
  _______
  begin  integer array on[1:l] ; array F[0:l],cl,U[1:l] ;
  _____  _______ _____           _____
    T:=a ; v:=y:=r:=0 ; i:=1 ;
    ONCE:  j:=0 ;
    AGAIN: i:=i-1 ;
    for i:=i+1 while X[i]<T do j:=j+1 ;
    ___        _____        __
    T:=T + h ; r:=r + 1 ;
    if j<k ∧ r<q then go to AGAIN ;
    __           ____ __ __
    y:=y+1 ; v:=v+j ; cl[y]:=T-h ; on[y]:=j ;
    if r<q then go to ONCE ;
    __     ____ __ __
    comment  cl[i] are the class limits. on[i] is the observed number
    _______
    in the class (cl[i-1] - cl[i]). All classes, except possibly the
    last two, contain at least k elements ;
    v:=n-v ; r:=j+v ;
    if r<k then begin y:=y-2 ; on[y+1]:=on[y+1]+r end else
    __     ____ _____                             ___ ____
    if j<k ∨ v<k then begin y:=y-1 ; on[y+1]:=r end
    __           ____ _____                     ___
    else  on[y+1]:=v ;
    ____
    comment  Each of the last two classes contains now at least k elements ;
    _______
    T:=F[0]:=0 ;
    for i:=1 step 1 until y do
    ___      ____   _____   __
    begin
    _____
      W:=(cl[i] - m)/s ;
      if W<0 then F[i]:=.5 - .5⨯Psi(-W) else F[i]:=.5 + .5⨯Psi(W) ;
      __     ____                       ____
      W:=F[i-1]:=n⨯(F[i] - F[i-1]) ;
      W:=U[i]:=if W_0 then 0 else (on[i] - W)∧2/W ;
               __  <  ____   ____            |
      T:=T + W
    end i ;
    ___
    W:=F[y]:=n⨯(1-F[y]) ;
    W:=U[y+1]:=if W_0.00000001 then 0 else (on[y+1] - W)∧2/W ;
               __  <           ____   ____              |
    T:=T + W ;
    comment
    _______
    In the class (cl[i-1] - cl[i]) are grouped on[i] observations,
    the corresponding theoretical number is F[i-1].
    U[i]=(on[i] - F[i-1])∧2/F[i-1]. T=Sum(U[i]) is the value of
                         |
    the test criterion  ;
    if g=1 then
    __     ____
    begin
    _____
      out:=|-dd dd dd.dd|;
           <            >
      writetext(|<       Class  limits        Observed number  Theor. number
                <
 _on_cn_∧_|) ;
 (__-__)|2>
        _
      writecr;
      writetext(|<            cl                     on             cn
                <
   cn|);
     >
      writecr;
      writesp(15);
      write(out,cl[1]);
      writesp(3);
      write(out,on[1]);
      writesp(3);
      write(out,F[0]);
      writesp(3);
      write(out,U[1]);
      writecr;
      for i:=2 step 1 until y do
      ___      ____   _____   __
        begin
        _____
          write(out,cl[i-1]);
          writesp(3);
          write(out,cl[i]);
          writesp(3);
          write(out,on[i]);
          writesp(3);
          write(out,F[i-1]);
          writesp(3);
          write(out,U[i]);
          writecr;
        end
        ___
      write(out,cl[y]);
      writesp(30);
      write(out,on[y+1]);
      writesp(3);
      write(out,F[y]);
      writesp(3);
      write(out,U[y+1]);
      writecr;
      writetext(|<_chi_square=_|);
                < ,   ,       ,>
      write(out,T);
      writecr;
      writetext(|<_degrees_of_freedom_|);
                < ,       ,  ,       ,>
      write(|pddd|,y-2);
            <    >
    end if output of results is wanted;
    ___
    g:=y+1;
  end
  ___
end chi square test;
___
select(8);writecr;p:=0;
nextdatagroup:for n:=read integer while n|0 do
              ___                 _____  =  __
 begin
 _____
  writechar(11);
 g:=1;p:=p+1;
 m:=read real;s:=read real;a:=read real;h:=read real;k:=readinteger;
  begin
  _____
  real array A[1:n];sum:=0;
  ____ _____
  writetext(|<sample number:|);write(|ddd|,p);
            <               >        <   >
  writecr;
  for i:=1 step 1 until n do
  ___      ____   _____   __
   begin
   _____
   A[i]:=read real;sum:=sum+1;
   if A[i]=0 then
   __        ____
    begin
    _____
    writetext(|<input error:too few elements in the datagroup.|);
              <                                               >
    writecr;writecr;writecr;go to nextdatagroup;
                            __ __
    end
    ___
   end;
   ___
  for l:=read real while l|0 do
  ___              _____  =  __
   begin
   _____
   sum:=sum+1;
   writetext(|<input error:too many elements in the datagroup.|);
             <                                                >
   writecr;
   end;writecr;writecr;
   ___
  if sum>n then go to nextdatagroup;
  __       ____ __ __
  chi square test(n,m,s,a,h,k,g,T,A);
  writecr;
  writetext(|<level of significance:|);
            <                       >
  writecr;writecr;writecr;
  end
  ___
 end
 ___
end;t<
___