Design and Analysis, Fourth Edition, by Keppel and Wickens Chapter 17: Further Within-Subject Topics | SAS Textbook Examples

Data from Table 17.2, page 387

data table17_2;
input s a p y;
datalines;
1 1 1 8
1 2 2 12
1 3 3 9
2 2 1 13
2 3 2 14
2 1 3 8
3 3 1 6
3 1 2 9
3 2 3 15
4 1 1 0
4 3 2 12
4 2 3 18
5 2 1 14
5 1 2 13
5 3 3 19
6 3 1 7
6 2 2 18
6 1 3 12
; 
run;

Table 17.2, page 387. The analysis of a within-subject design, accounting for the counterbalanced factor, using proc glm

proc glm data = table17_2;
  class a p s;
  model y = a p s/ss3;
run; 
quit;

The GLM Procedure

      Class Level Information
Class         Levels    Values
a                  3    1 2 3
p                  3    1 2 3
s                  6    1 2 3 4 5 6

Number of observations    18

Dependent Variable: y
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        9     315.1666667      35.0185185       3.72    0.0390
Error                        8      75.3333333       9.4166667
Corrected Total             17     390.5000000

R-Square     Coeff Var      Root MSE        y Mean
0.807085      26.68399      3.068659      11.50000

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            2     134.3333333      67.1666667       7.13    0.0167
p                            2     111.0000000      55.5000000       5.89    0.0267
s                            5      69.8333333      13.9666667       1.48    0.2950

The same analysis using proc mixed.

proc mixed data = table17_2;
  class a p s;
  model y = a p;
  repeated/ subject = s type = cs;
run; quit;

The Mixed Procedure

                  Model Information
Data Set                     WORK.TABLE17_2
Dependent Variable           y
Covariance Structure         Compound Symmetry
Subject Effect               s
Estimation Method            REML
Residual Variance Method     Profile
Fixed Effects SE Method      Model-Based
Degrees of Freedom Method    Between-Within

             Class Level Information
Class    Levels    Values
a             3    1 2 3
p             3    1 2 3
s             6    1 2 3 4 5 6

            Dimensions
Covariance Parameters             2
Columns in X                      7
Columns in Z                      0
Subjects                          6
Max Obs Per Subject               3
Observations Used                18
Observations Not Used             0
Total Observations               18

                     Iteration History
Iteration    Evaluations    -2 Res Log Like       Criterion
        0              1        76.12071787
        1              1        75.87580396      0.00000000
                   Convergence criteria met.

 Covariance Parameter Estimates
Cov Parm     Subject    Estimate
CS           s            1.5167
Residual                  9.4167

           Fit Statistics
-2 Res Log Likelihood            75.9
AIC (smaller is better)          79.9
AICC (smaller is better)         81.1
BIC (smaller is better)          79.5

  Null Model Likelihood Ratio Test
    DF    Chi-Square      Pr > ChiSq
     1          0.24          0.6207

        Type 3 Tests of Fixed Effects
              Num     Den
Effect         DF      DF    F Value    Pr > F
a               2       8       7.13    0.0167
p               2       8       5.89    0.0267