Design and Analysis, Fourth Edition, by Keppel and Wickens Chapter 14: The General Linear Model | SAS Textbook Examples

Data from Table 14.2, page 299

data table14_2;
input a b scores;
datalines;
1 1 16
1 1 12
1 1 9
1 1 14
1 1 17
2 1 21
2 1 20
2 1 19
2 1 15
2 1 17
2 1 22
3 1 8
3 1 18
3 1 12
1 2 9
1 2 6
1 2 15
1 2 11
1 2 12
1 2 8
1 2 14
2 2 22
2 2 19
2 2 24
2 2 25
2 2 19
2 2 19
2 2 14
2 2 26
2 2 21
3 2 8
3 2 10
3 2 14
3 2 7
3 2 5
3 2 11
3 2 8
;
run;

Evaluating the simple effect of Factor A across the levels of B , bottom of page 307

proc glm data = table14_2;
  class a b;
  model scores = a|b/ ss3;
  lsmeans a*b/slice = b;
run;
quit;

The GLM Procedure

   Class Level Information
Class         Levels    Values
a                  3    1 2 3
b                  2    1 2

Number of observations    37

Dependent Variable: scores
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        5      824.975032      164.995006      14.48    <.0001
Error                       31      353.295238       11.396621
Corrected Total             36     1178.270270

R-Square     Coeff Var      Root MSE    scores Mean
0.700158      22.83508      3.375888       14.78378

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            2     599.6950907     299.8475454      26.31    <.0001
b                            1      18.8946868      18.8946868       1.66    0.2074
a*b                          2      57.6943170      28.8471585       2.53    0.0959

Least Squares Means

                scores
a    b          LSMEAN
1    1      13.6000000
1    2      10.7142857
2    1      19.0000000
2    2      21.0000000
3    1      12.6666667
3    2       9.0000000

Least Squares Means

               a*b Effect Sliced by b for scores
                     Sum of
b        DF         Squares     Mean Square    F Value    Pr > F
1         2      114.990476       57.495238       5.04    0.0127
2         2      690.484472      345.242236      30.29    <.0001

Main effect contrasts in a two-factor design, page 308-309

NOTE: The rationale for doing a main effect contrast (without consideration of the other factor) is that the interaction between the two factors is statistically non-significant.

proc glm data = table14_2;
  class a b;
  model scores = a|b/ ss3;
  contrast 'a1 - a3' a -1 0 1;
  contrast 'a1 - 2a2 + a3 ' a 1 -2 1;
run; 
quit;

The GLM Procedure

   Class Level Information
Class         Levels    Values
a                  3    1 2 3
b                  2    1 2

Number of observations    37

Dependent Variable: scores
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        5      824.975032      164.995006      14.48    <.0001
Error                       31      353.295238       11.396621
Corrected Total             36     1178.270270

R-Square     Coeff Var      Root MSE    scores Mean
0.700158      22.83508      3.375888       14.78378

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            2     599.6950907     299.8475454      26.31    <.0001
b                            1      18.8946868      18.8946868       1.66    0.2074
a*b                          2      57.6943170      28.8471585       2.53    0.0959

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
a1 - a3                      1       8.5585825       8.5585825       0.75    0.3928
a1 - 2a2 + a3                1     599.5857143     599.5857143      52.61    <.0001

(NOTE! t^2 = F, so .87^2 = .75, and (-7.25)^2 = 52.56)