Data from Table 21.1, page 466
data table21_1; input a b c recall @@; datalines; 1 1 1 7 2 1 1 6 3 1 1 10 1 1 1 7 2 1 1 8 3 1 1 8 1 1 1 9 2 1 1 7 3 1 1 8 1 1 1 10 2 1 1 9 3 1 1 6 1 1 1 9 2 1 1 9 3 1 1 8 1 2 1 7 2 2 1 6 3 2 1 7 1 2 1 8 2 2 1 8 3 2 1 7 1 2 1 9 2 2 1 8 3 2 1 6 1 2 1 10 2 2 1 9 3 2 1 9 1 2 1 10 2 2 1 9 3 2 1 9 1 3 1 7 2 3 1 3 3 3 1 2 1 3 1 7 2 3 1 5 3 3 1 3 1 3 1 10 2 3 1 3 3 3 1 4 1 3 1 7 2 3 1 6 3 3 1 5 1 3 1 9 2 3 1 5 3 3 1 5 1 1 2 10 2 1 2 6 3 1 2 9 1 1 2 8 2 1 2 9 3 1 2 10 1 1 2 9 2 1 2 8 3 1 2 7 1 1 2 7 2 1 2 7 3 1 2 7 1 1 2 8 2 1 2 10 3 1 2 9 1 2 2 7 2 2 2 6 3 2 2 8 1 2 2 8 2 2 2 7 3 2 2 8 1 2 2 9 2 2 2 9 3 2 2 6 1 2 2 9 2 2 2 9 3 2 2 9 1 2 2 11 2 2 2 10 3 2 2 9 1 3 2 6 2 3 2 6 3 3 2 6 1 3 2 7 2 3 2 8 3 3 2 5 1 3 2 8 2 3 2 6 3 3 2 7 1 3 2 9 2 3 2 9 3 3 2 8 1 3 2 9 2 3 2 8 3 3 2 9 ; run;
Table 21.2, page 468 and Table 21.6, page 479. Group and Marginal, and Analysis of Variance for a three-factor design
proc glm data = table21_1; class a b c; model recall = a|b|c/ss3; lsmeans a|b|c; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
a 3 1 2 3
b 3 1 2 3
c 2 1 2
Number of observations 90
Dependent Variable: recall
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 17 155.6000000 9.1529412 4.85 <.0001
Error 72 136.0000000 1.8888889
Corrected Total 89 291.6000000
R-Square Coeff Var Root MSE recall Mean
0.533608 18.08380 1.374369 7.600000
Source DF Type III SS Mean Square F Value Pr > F
a 2 26.86666667 13.43333333 7.11 0.0015
b 2 64.86666667 32.43333333 17.17 <.0001
a*b 4 14.66666667 3.66666667 1.94 0.1128
c 1 14.40000000 14.40000000 7.62 0.0073
a*c 2 8.60000000 4.30000000 2.28 0.1100
b*c 2 16.20000000 8.10000000 4.29 0.0174
a*b*c 4 10.00000000 2.50000000 1.32 0.2695
Least Squares Means
recall
a LSMEAN
1 8.36666667
2 7.30000000
3 7.13333333
b LSMEAN
1 8.16666667
2 8.23333333
3 6.40000000
recall
a b LSMEAN
1 1 8.40000000
1 2 8.80000000
1 3 7.90000000
2 1 7.90000000
2 2 8.10000000
2 3 5.90000000
3 1 8.20000000
3 2 7.80000000
3 3 5.40000000
recall
c LSMEAN
1 7.20000000
2 8.00000000
recall
a c LSMEAN
1 1 8.40000000
1 2 8.33333333
2 1 6.73333333
2 2 7.86666667
3 1 6.46666667
3 2 7.80000000
recall
b c LSMEAN
1 1 8.06666667
1 2 8.26666667
2 1 8.13333333
2 2 8.33333333
3 1 5.40000000
3 2 7.40000000
recall
a b c LSMEAN
1 1 1 8.40000000
1 1 2 8.40000000
1 2 1 8.80000000
1 2 2 8.80000000
1 3 1 8.00000000
1 3 2 7.80000000
2 1 1 7.80000000
2 1 2 8.00000000
2 2 1 8.00000000
2 2 2 8.20000000
2 3 1 4.40000000
2 3 2 7.40000000
3 1 1 8.00000000
3 1 2 8.40000000
3 2 1 7.60000000
3 2 2 8.00000000
3 3 1 3.80000000
3 3 2 7.00000000