* ch17eg.sas, using pseudo-random to illustrate Tukey's method for 
* pairwise comparison of factor effects in a one-way ANOVA, including
* the graphical presentation of the results;
options ls=78 nodate;
;
data pseudo;
 do A=1 to 4;
  do rep=1 to 5;
    y = 10.5 + 2*(A-2)**2 + 1.3*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, illustrated using pseudo-random data.';
;
proc glm; 
 class A;
 model Y = A;
 means A / Tukey alpha=0.10;
 title3 '(The option "cldiff" would give Confidence Limits for DIFFerences.)';

         Tukey's methods of multiple comparisons, including graphical        1
        display of the results, illustrated using pseudo-random data.

                           Obs    A    rep      y

                             1    1     1     11.53
                             2    1     2     13.08
                             3    1     3     13.97
                             4    1     4     14.09
                             5    1     5     13.66
                             6    2     1     10.49
                             7    2     2     10.21
                             8    2     3     12.88
                             9    2     4     12.21
                            10    2     5      9.84
                            11    3     1     12.77
                            12    3     2     12.42
                            13    3     3     15.49
                            14    3     4     11.07
                            15    3     5     12.59
                            16    4     1     19.62
                            17    4     2     18.07
                            18    4     3     20.56
                            19    4     4     19.61
                            20    4     5     17.87
         Tukey's methods of multiple comparisons, including graphical        2
        display of the results, illustrated using pseudo-random data.
     (The option "cldiff" would give Confidence Limits for DIFFerences.)

                              The GLM Procedure

                           Class Level Information
 
                       Class         Levels    Values

                       A                  4    1 2 3 4 


                         Number of observations    20



         Tukey's methods of multiple comparisons, including graphical        3
        display of the results, illustrated using pseudo-random data.
     (The option "cldiff" would give Confidence Limits for DIFFerences.)

                              The GLM Procedure
 
Dependent Variable: y   

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

Model                       3    182.6008150     60.8669383     35.87   <.0001

Error                      16     27.1476400      1.6967275                   

Corrected Total            19    209.7484550                                  


              R-Square     Coeff Var      Root MSE        y Mean

              0.870570      9.237208      1.302585      14.10150


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

A                           3    182.6008150     60.8669383     35.87   <.0001


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

A                           3    182.6008150     60.8669383     35.87   <.0001
         Tukey's methods of multiple comparisons, including graphical        4
        display of the results, illustrated using pseudo-random data.
     (The option "cldiff" would give Confidence Limits for DIFFerences.)

                              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                                    0.1
                 Error Degrees of Freedom                  16
                 Error Mean Square                   1.696728
                 Critical Value of Studentized Range  3.52008
                 Minimum Significant Difference        2.0506


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

                          A       19.1460      5    4   
                                                        
                          B       13.2660      5    1   
                          B                             
                     C    B       12.8680      5    3   
                     C                                  
                     C            11.1260      5    2