options pagesize=65 linesize=65;
data one;
es=.50      ; *Effect size for largest and smallest mean;
alpha=.05   ; *Type I error rate;
j=6         ; *Number of levels for the the between-subjects factor
               for which es is define. j is limited to 6 or less;
tpower=.70  ; *Target power;
maxn= 2000  ; *Maximum sample size for calculations;
prod=1      ; *product of number of levels of the other factors. Equals 1
               for a single factor design and equals the number of level in
               the other factor for a two-factor design;
rho=.50      ; *correlation between covariate and dependent variable. 
               Equal to zero if there is no covriate;
prob=1-alpha;
df1=j-1;
if j =3 then do;
  do i = 1 to 2;
    if i = 1 then do;
      config='minimum range and equally spaced                      ';
      mu1 = .00;
      mu2 = es/2;
      mu3 = es;
      gm=(mu1 + mu2 + mu3)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x1 cval power mu1 mu2 mu3;
                 do over x1;
                  x1=round(x1,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x2 cval power mu1 mu2 mu3;
                 do over x2;
                  x2=round(x2,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 2 then do;
      config='maximum range, one extreme mean, and two extreme means';
      mu1 = .00;
      mu2 = es;
      mu3 = es;
      gm=(mu1 + mu2 + mu3)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x3 cval power mu1 mu2 mu3;
                 do over x3;
                  x3=round(x3,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x4 cval power mu1 mu2 mu3;
                 do over x4;
                  x1=round(x4,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
  end;
end;
if j=4 then do;
  do i = 1 to 4;
    if i = 1 then do;
      config='minimum range   ';
      mu1 = .00;
      mu2 = es/2;
      mu3 = es/2;
      mu4 = es;
      gm=(mu1 + mu2 + mu3 + mu4)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2);
         do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x5 cval power mu1 mu2 mu3 mu4;
                 do over x5;
                  x5=round(x5,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x6 cval power mu1 mu2 mu3 mu4;
                 do over x6;
                  x6=round(x6,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 2 then do;
      config='maximum range and two extreme means  ';
      mu1 = .00;
      mu2 = .00;
      mu3 = es;
      mu4 = es;
      gm=(mu1 + mu2 + mu3 + mu4)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x7 cval power mu1 mu2 mu3 mu4;
                 do over x7;
                  x7=round(x7,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x8 cval power mu1 mu2 mu3 mu4;
                 do over x8;
                  x8=round(x8,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 3 then do;
      config='equally spaced  ';
      mu1 = .00;
      mu2 = es/3;
      mu3 = 2*es/3;
      mu4 = es;
      gm=(mu1 + mu2 + mu3 + mu4)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x9 cval power mu1 mu2 mu3 mu4;
                 do over x9;
                  x9=round(x9,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x10 cval power mu1 mu2 mu3 mu4;
                 do over x10;
                  x10=round(x10,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 4 then do;
      config='one extreme mean';
      mu1=0;
      mu2=es;
      mu3=es;
      mu4=es;
      gm=(mu1 + mu2 + mu3 + mu4)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x11 cval power mu1 mu2 mu3 mu4;
                 do over x11;
                  x11=round(x11,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x12 cval power mu1 mu2 mu3 mu4;
                 do over x12;
                  x12=round(x12,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
  end;
end;
if j=5 then do;
  do i = 1 to 4;
    if i = 1 then do;
      config='minimum range                             ';
      mu1 = .00;
      mu2 = es/2;
      mu3 = es/2;
      mu4 = es/2;
      mu5 = es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2);
         do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x13 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x13;
                  x13=round(x13,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x14 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x14;
                  x14=round(x14,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 2 then do;
      config='maximum range and two extreme means';
      mu1 = .00;
      mu2 = .00;
      mu3 = .00;
      mu4 =  es;
      mu5 =  es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x15 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x15;
                  x15=round(x15,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x16 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x16;
                  x16=round(x16,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 3 then do;
      config='equally spaced                            ';
      mu1 = .00;
      mu2 = es/4;
      mu3 = es/2;
      mu4 =  3*es/4;
      mu5 =  es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x17 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x17;
                  x17=round(x17,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x18 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x18;
                  x18=round(x18,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 4 then do;
      config='one extreme mean                          ';
      mu1=0;
      mu2=es;
      mu3=es;
      mu4=es;
      mu5=es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2);
           do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x19 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x19;
                  x19=round(x19,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x20 cval power mu1 mu2 mu3 mu4 mu5;
                 do over x20;
                  x20=round(x20,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
  end;
end;
if j=6 then do;
  do i = 1 to 5;
    if i = 1 then do;
      config='minimum range    ';
      mu1 = .00;
      mu2 = es/2;
      mu3 = es/2;
      mu4 = es/2;
      mu5 = es/2;
      mu6 = es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5 + mu6)/j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2 + (mu6-gm)**2);
         do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x21 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x21;
                  x21=round(x21,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x22 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x22;
                  x22=round(x22,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 2 then do;
      config='maximum range    ';
      mu1 = .00;
      mu2 = .00;
      mu3 = .00;
      mu4 = es;
      mu5 = es;
      mu6 = es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5 + mu6)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2 + (mu6-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x23 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x23;
                  x23=round(x23,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x24 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x24;
                  x24=round(x24,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 3 then do;
      config='equally spaced   ';
      mu1 = .00;
      mu2 = .2*es;
      mu3 = .4*es;
      mu4 = .6*es;
      mu5 = .8*es;
      mu6 = es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5 + mu6)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2 + (mu6-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x25 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x25;
                  x25=round(x25,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x26 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x26;
                  x26=round(x26,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 4 then do;
      config='one extreme mean ';
      mu1=-0;
      mu2=es;
      mu3=es;
      mu4=es;
      mu5=es;
      mu6=es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5 + mu6)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2 + (mu6-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x27 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x27;
                  x27=round(x27,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x28 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x28;
                  x28=round(x28,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
    if i = 5 then do;
      config='two extreme means';
      mu1= 0;
      mu2= 0;
      mu3= es;
      mu4= es;
      mu5= es;
      mu6= es;
      gm=(mu1 + mu2 + mu3 + mu4 + mu5 + mu6)/ j;
      delta = ((mu1-gm)**2 + (mu2-gm)**2 + (mu3-gm)**2 + (mu4-gm)**2
      + (mu5-gm)**2 + (mu6-gm)**2);
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x29 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x29;
                  x29=round(x29,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x30 cval power mu1 mu2 mu3 mu4 mu5 mu6;
                 do over x30;
                  x30=round(x30,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
     end;
  end;
end;
if j =2 then do;
      mu1 = .00;
      mu2 = es;
      gm=(mu1 + mu2)/j;
      delta = (mu1-gm)**2 + (mu2-gm)**2;
        do n=2 to maxn;
           lambda=n*prod*delta/(1-rho**2);
           df2=j*prod*(n-1);if rho ^=0 then df2=df2-1;
           cval=finv(prob,df1,df2);
           power=1-probf(cval,df1,df2,lambda);
             if power lt tpower and n = maxn then do;
               comment = 'raise maxn  ';
               array x31 cval power mu1 mu2 mu3;
                 do over x31;
                  x31=round(x31,.01);
                 end;
               output;
             end;
             if power ge tpower then do;
               comment ='analysis ok';
               array x32 cval power mu1 mu2 mu3;
                 do over x32;
                  x32=round(x32,.01);
                 end;
               output;
               n=maxn;
             end;
        end;
    end;
data two;
set one; if j=2;
cell_n=n;
proc sort; by n;
proc print noobs;
title1 ' ';
title2 ' ';
var comment j prod es rho alpha tpower ;
proc print noobs;
title1 'origin is set so that smallest mean equals zero';
title2 'means are in standard deviation units';
var mu1 mu2 cell_n power ;
data three;
set one; if j=3;
cell_n=n;
proc sort; by n;
data threea;
set three;
if _n_=1;
proc print noobs;
title1 ' ';
title2 ' ';
var comment j prod es rho alpha tpower ;
proc print noobs data=three;
title1 'origin is set so that smallest mean equals zero';
title2 'means are in standard deviation units';
var config mu1 mu2 mu3 cell_n power ;
data four;
set one; if j=4;
cell_n=n;
proc sort; by n;
data foura;
set four;
if _n_=1;
proc print noobs;
title1 ' ';
title2 ' ';
var comment j prod es rho alpha tpower ;
proc print noobs data=four;
title1 'origin is set so that smallest mean equals zero';
title2 'means are in standard deviation units';
var config mu1 mu2 mu3 mu4 cell_n power ;
data five;
set one; if j=5;
cell_n=n;
proc sort; by n;
data fivea;
set five;
if _n_=1;
proc print noobs;
title1 ' ';
title2 ' ';
var comment j prod es rho alpha tpower ;
proc print noobs data=five;
title1 'origin is set so that smallest mean equals zero';
title2 'means are in standard deviation units';
var config mu1 mu2 mu3 mu4 mu5 cell_n power ;
data six;
set one; if j=6;
cell_n=n;
proc sort; by n;
data sixa;
set six;
if _n_=1;
proc print noobs;
title1 ' ';
title2 ' ';
var comment j prod es rho alpha tpower ;
proc print noobs data=six;
title1 'origin is set so that smallest mean equals zero';
title2 'means are in standard deviation units';
var config mu1 mu2 mu3 mu4 mu5 mu6 cell_n power ;
proc datasets;
delete one;
quit;
run;