Data from Table 18.3, page 407
data table18_3; input s a b recall ; datalines; 1 1 1 1 1 1 2 1 1 1 3 2 1 1 4 2 1 2 1 1 1 2 2 2 1 2 3 2 1 2 4 3 1 3 1 1 1 3 2 2 1 3 3 2 1 3 4 3 2 1 1 2 2 1 2 2 2 1 3 3 2 1 4 4 2 2 1 2 2 2 2 3 2 2 3 4 2 2 4 5 2 3 1 3 2 3 2 3 2 3 3 3 2 3 4 5 3 1 1 2 3 1 2 3 3 1 3 3 3 1 4 3 3 2 1 3 3 2 2 4 3 2 3 3 3 2 4 4 3 3 1 2 3 3 2 3 3 3 3 3 3 3 4 4 4 1 1 0 4 1 2 1 4 1 3 0 4 1 4 2 4 2 1 1 4 2 2 2 4 2 3 2 4 2 4 3 4 3 1 2 4 3 2 2 4 3 3 2 4 3 4 3 5 1 1 1 5 1 2 1 5 1 3 2 5 1 4 2 5 2 1 1 5 2 2 1 5 2 3 2 5 2 4 3 5 3 1 1 5 3 2 1 5 3 3 2 5 3 4 2 6 1 1 1 6 1 2 2 6 1 3 3 6 1 4 3 6 2 1 2 6 2 2 3 6 2 3 3 6 2 4 5 6 3 1 2 6 3 2 3 6 3 3 4 6 3 4 4 7 1 1 1 7 1 2 1 7 1 3 2 7 1 4 3 7 2 1 2 7 2 2 1 7 2 3 2 7 2 4 3 7 3 1 1 7 3 2 1 7 3 3 2 7 3 4 3 8 1 1 1 8 1 2 1 8 1 3 2 8 1 4 3 8 2 1 1 8 2 2 2 8 2 3 2 8 2 4 3 8 3 1 2 8 3 2 2 8 3 3 3 8 3 4 4 ; run;
Table 18.4, page 408. Summary of the Analysis of Variance of a two-factor within-subject design from the data in Table 18.3
NOTE: The model appears to have blown-up (no error sums of squares and F-values) at first glance, however, the designation of correct error terms is required (see Keppel page 404-405 for discussion) and is done through the test command in SAS.
proc glm data = table18_3; class s a b; model recall = s|a|b /ss3; test h = a e = a*s; test h = b e = b*s; test h = a*b e = a*s*b; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
s 8 1 2 3 4 5 6 7 8
a 3 1 2 3
b 4 1 2 3 4
Number of observations 96
Dependent Variable: recall
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 95 107.8333333 1.1350877 . .
Error 0 0.0000000 .
Corrected Total 95 107.8333333
R-Square Coeff Var Root MSE recall Mean
1.000000 . . 2.291667
Source DF Type III SS Mean Square F Value Pr > F
s 7 39.16666667 5.59523810 . .
a 2 8.33333333 4.16666667 . .
s*a 14 5.33333333 0.38095238 . .
b 3 42.08333333 14.02777778 . .
s*b 21 6.58333333 0.31349206 . .
a*b 6 0.66666667 0.11111111 . .
s*a*b 42 5.66666667 0.13492063 . .
Tests of Hypotheses Using the Type III MS for s*a as an Error Term
Source DF Type III SS Mean Square F Value Pr > F
a 2 8.33333333 4.16666667 10.94 0.0014
Tests of Hypotheses Using the Type III MS for s*b as an Error Term
Source DF Type III SS Mean Square F Value Pr > F
b 3 42.08333333 14.02777778 44.75 <.0001
Tests of Hypotheses Using the Type III MS for s*a*b as an Error Term
Source DF Type III SS Mean Square F Value Pr > F
a*b 6 0.66666667 0.11111111 0.82 0.5582
Table 18.8, page 413. The analysis of the simple effects of the trials factor B for words with positive emotional value (level a2)
proc glm data = table18_3; where a =2; class b s ; model recall = b s/ss3; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
b 4 1 2 3 4
s 8 1 2 3 4 5 6 7 8
Number of observations 32
Dependent Variable: recall
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 10 33.25000000 3.32500000 14.70 <.0001
Error 21 4.75000000 0.22619048
Corrected Total 31 38.00000000
R-Square Coeff Var Root MSE recall Mean
0.875000 19.02379 0.475595 2.500000
Source DF Type III SS Mean Square F Value Pr > F
b 3 16.75000000 5.58333333 24.68 <.0001
s 7 16.50000000 2.35714286 10.42 <.0001