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Program 9

OPTIONS LS=80 NODATE PAGENO=1;
TITLE 'Example 10, Y603';
DATA nested;
     INPUT treat b score @@;
LABEL treat='Treatment levels, 1=games, 2=arts'
      b    ='levels of factor B, the nested factor';
CARDS;
1 1 3 1 1 6 1 1 3 1 1 3
1 2 1 1 2 2 1 2 2 1 2 2
1 3 5 1 3 6 1 3 5 1 3 6
1 4 2 1 4 3 1 4 4 1 4 3
2 5 7 2 5 8 2 5 7 2 5 6
2 6 4 2 6 5 2 6 4 2 6 3
2 7 7 2 7 8 2 7 9 2 7 8
2 8 10 2 8 10 2 8 9 2 8 11
;
PROC GLM;
     CLASS treat b;
     MODEL score=treat b(treat);
     TEST H=treat E=b(treat);
TITLE2 'The correct analysis of a nested design';
PROC GLM;
     CLASS treat;
     MODEL score=treat;
TITLE2 'The incorrect analysis of a nested design';
RUN;
                                 Example 10, Y603                               1
                    The correct analysis of a nested design
            
                        General Linear Models Procedure
                            Class Level Information
            
                       Class    Levels    Values
            
                       TREAT         2    1 2
            
                       B             8    1 2 3 4 5 6 7 8
            
                    Number of observations in data set = 32
            
                                Example 10, Y603                               2
                    The correct analysis of a nested design
                        General Linear Models Procedure
            
Dependent Variable: SCORE
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F
            
Model                    7     217.00000000     31.00000000     40.22     0.0001
            
Error                   24      18.50000000      0.77083333
            
Corrected Total         31     235.50000000
            
                  R-Square             C.V.        Root MSE           SCORE Mean
            
                  0.921444         16.33435       0.8779711            5.3750000
            
Source                  DF        Type I SS     Mean Square   F Value     Pr > F
            
TREAT                    1     112.50000000    112.50000000    145.95     0.0001
B(TREAT)                 6     104.50000000     17.41666667     22.59     0.0001
            
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
            
TREAT                    1     112.50000000    112.50000000    145.95     0.0001
B(TREAT)                 6     104.50000000     17.41666667     22.59     0.0001
            
Tests of Hypotheses using the Type III MS for B(TREAT) as an error term
            
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
            
TREAT                    1     112.50000000    112.50000000      6.46     0.0440
            
            
                                Example 10, Y603                               3
                   The incorrect analysis of a nested design
            
                        General Linear Models Procedure
                            Class Level Information
            
                           Class    Levels    Values
            
                           TREAT         2    1 2
            
            
                    Number of observations in data set = 32
            
            
                                Example 10, Y603                               4
                   The incorrect analysis of a nested design
            
                        General Linear Models Procedure
            
Dependent Variable: SCORE
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F
            
Model                    1     112.50000000    112.50000000     27.44     0.0001
            
Error                   30     123.00000000      4.10000000
            
Corrected Total         31     235.50000000
            
                  R-Square             C.V.        Root MSE           SCORE Mean
            
                  0.477707         37.67155       2.0248457            5.3750000
            
            
Source                  DF        Type I SS     Mean Square   F Value     Pr > F
            
TREAT                    1     112.50000000    112.50000000     27.44     0.0001
            
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
            
TREAT                    1     112.50000000    112.50000000     27.44     0.0001
            



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