* power.sas;
* Doing sample size power calculations using SAS functions for 1-way 
* ANOVA, 6 treatments, alpha=0.05, sigma=25, and Delta=50;
options ls=78 nocenter nodate;
;
data power;
  r=6; alpha=0.05; DELTA=50; sigma2=25**2;
  do n=2 to 20;
    F95 = finv(0.95,r-1,r*(n-1));
    nc = n*DELTA**2/(2*sigma2); * nc = n*[2*(delta/2)]^2/sigma^2;
    power = 1 - probf(F95,r-1,r*(n-1),nc);
    phi=sqrt(nc/r);
    output;
    end;
;
proc print;
  var n power F95 phi nc;
  title 'Power in one-way ANOVA';
;
proc plot;
  plot power*n;




Power in one-way ANOVA                                                       1

Obs     n     power       F95        phi      nc

  1     2    0.15142    4.38737    0.81650     4
  2     3    0.28888    3.10588    1.00000     6
  3     4    0.43221    2.77285    1.15470     8
  4     5    0.56514    2.62065    1.29099    10
  5     6    0.67879    2.53355    1.41421    12
  6     7    0.77012    2.47717    1.52753    14
  7     8    0.84000    2.43769    1.63299    16
  8     9    0.89135    2.40851    1.73205    18
  9    10    0.92784    2.38607    1.82574    20
 10    11    0.95302    2.36827    1.91485    22
 11    12    0.96996    2.35381    2.00000    24
 12    13    0.98110    2.34183    2.08167    26
 13    14    0.98829    2.33174    2.16025    28
 14    15    0.99284    2.32313    2.23607    30
 15    16    0.99568    2.31569    2.30940    32
 16    17    0.99742    2.30920    2.38048    34
 17    18    0.99848    2.30349    2.44949    36
 18    19    0.99911    2.29843    2.51661    38
 19    20    0.99949    2.29391    2.58199    40
Power in one-way ANOVA                                                       2

             Plot of power*n.  Legend: A = 1 obs, B = 2 obs, etc.

      power |
            |
        1.0 +                                         A  A  A  A  A  A
            |                                   A  A
            |                             A  A
            |
            |                          A
        0.9 +                       A
            |
            |
            |                    A
            |
        0.8 +
            |                 A
            |
            |
            |
        0.7 +
            |              A
            |
            |
            |
        0.6 +
            |
            |           A
            |
            |
        0.5 +
            |
            |
            |        A
            |
        0.4 +
            |
            |
            |
            |
        0.3 +
            |     A
            |
            |
            |
        0.2 +
            |
            |  A
            |
            |
        0.1 +
            |
            ---+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--
               2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20

                                          n