* ch17eg2.sas, using pseudo-random to illustrate Tukey's method analysis 
* of factor effects in a one-way ANOVA, and specifically the graphical
* presentation of the results for equal sample sizes;
options ls=76;
;
data mine;
 do A=1 to 4;
  do rep=1 to 5;
    y = 10.5 + 2*A + 3*rannor(555);
    y=round(y,0.01);
    output;
 end; end;
;
proc print; 
 var A rep y;
 title 'Tukey''s methods of multiple comparisons, including graphical';
 title2 'display of the results, is illustrated using pseudo-random data.';
;
proc glm; 
 class A;
 model Y = A;
 means A / Tukey alpha=0.05;
 title3 '(The option "cldiff" would give Confidence Limits for DIFFerences.)';
 
        Tukey's methods of multiple comparisons, including graphical       1
      display of the results, is illustrated using pseudo-random data.
                                            15:55 Thursday, January 15, 2009

                          Obs    A    rep      y

                            1    1     1     10.27
                            2    1     2     13.83
                            3    1     3     15.90
                            4    1     4     16.17
                            5    1     5     15.18
                            6    2     1     14.47
                            7    2     2     13.83
                            8    2     3     19.99
                            9    2     4     18.45
                           10    2     5     12.98
                           11    3     1     17.13
                           12    3     2     16.32
                           13    3     3     23.41
                           14    3     4     13.20
                           15    3     5     16.71
                           16    4     1     21.08
                           17    4     2     17.51
                           18    4     3     23.25
                           19    4     4     21.06
                           20    4     5     17.05
        Tukey's methods of multiple comparisons, including graphical       2
      display of the results, is illustrated using pseudo-random data.
    (The option "cldiff" would give Confidence Limits for DIFFerences.)
                                            15:55 Thursday, January 15, 2009

                             The GLM Procedure

                          Class Level Information
 
                      Class         Levels    Values

                      A                  4    1 2 3 4 


                  Number of Observations Read          20
                  Number of Observations Used          20
        Tukey's methods of multiple comparisons, including graphical       3
      display of the results, is illustrated using pseudo-random data.
    (The option "cldiff" would give Confidence Limits for DIFFerences.)
                                            15:55 Thursday, January 15, 2009

                             The GLM Procedure
 
Dependent Variable: y   

                                     Sum of
 Source                    DF       Squares   Mean Square  F Value  Pr > F

 Model                      3    87.9230550    29.3076850     3.24  0.0498

 Error                     16   144.5852400     9.0365775                 

 Corrected Total           19   232.5082950                               


             R-Square     Coeff Var      Root MSE        y Mean

             0.378150      17.79857      3.006090      16.88950


 Source                    DF     Type I SS   Mean Square  F Value  Pr > F

 A                          3   87.92305500   29.30768500     3.24  0.0498


 Source                    DF   Type III SS   Mean Square  F Value  Pr > F

 A                          3   87.92305500   29.30768500     3.24  0.0498
        Tukey's methods of multiple comparisons, including graphical       4
      display of the results, is illustrated using pseudo-random data.
    (The option "cldiff" would give Confidence Limits for DIFFerences.)
                                            15:55 Thursday, January 15, 2009

                             The GLM Procedure
 
                 Tukey's Studentized Range (HSD) Test for y

   NOTE: This test controls the Type I experimentwise error rate, but it 
           generally has a higher Type II error rate than REGWQ.


                Alpha                                   0.05
                Error Degrees of Freedom                  16
                Error Mean Square                   9.036577
                Critical Value of Studentized Range  4.04609
                Minimum Significant Difference        5.4394


         Means with the same letter are not significantly different.
 
 
              Tukey Grouping          Mean      N    A

                           A        19.990      5    4
                           A                          
                      B    A        17.354      5    3
                      B    A                          
                      B    A        15.944      5    2
                      B                               
                      B             14.270      5    1