/*
Example SAS code for mixed effect ANOVA */
Option
ps=45
ls=80
nodate nonumber;
DATA
ta7_4;
input
method day Y;
Lines;
1
1
142.3
1
1
144.0
1
2
134.9
1
2
146.3
1
3
148.6
1
3
156.5
1
4
152.0
1
4
151.4
2
1
142.9
2
1
147.4
2
2
125.9
2
2
127.6
2
3
135.5
2
3
138.9
2
4
142.9
2
4
142.3
;
Proc
GLM;
class
method day;
Model
Y=method day method*day ;
random
day method*day/test;
output
out=out7_4
r=resid p=pred;
contrast
'method1-method2'
method 1
-1
/ E=method*day;
run;
/*
partial output
The SAS System
The GLM Procedure
Class Level Information
Class
Levels
Values
method
2 1
2
day
4 1 2 3
4
Number of Observations Read
16
Number of Observations Used
16
The SAS System
The GLM Procedure
Dependent
Variable: Y
Sum of
Source
DF
Squares Mean
Square F Value Pr > F
Model
7
945.697500
135.099643
9.37
0.0026
Error
8
115.340000
14.417500
Corrected Total
15
1061.037500
R-Square
Coeff Var Root MSE Y
Mean
0.891295
2.665290
3.797038 142.4625
Source
DF
Type I
method
1
329.4225000
329.4225000 22.85 0.0014
day
3
431.4425000
143.8141667
9.97
0.0044
method*day
3
184.8325000
61.6108333
4.27
0.0446
Source
method
1
329.4225000
329.4225000 22.85 0.0014
day
3 431.4425000 143.8141667 9.97 0.0044
method*day
3
184.8325000
61.6108333
4.27
0.0446
The SAS System
The GLM Procedure
Source
Type III Expected Mean Square
method
Var(Error) + 2 Var(method*day) + Q(method)
day
Var(Error) + 2 Var(method*day) + 4 Var(day)
method*day
Var(Error) + 2 Var(method*day)
The
SAS System
The GLM Procedure
Tests of Hypotheses for Mixed Model Analysis of
Variance
Dependent
Variable: Y
Source
method
1
329.422500
329.422500 5.35 0.1038
day
3
431.442500
143.814167
2.33
0.2522
Error
3
184.832500
61.610833
Error: MS(method*day)
Source
method*day
3
184.832500
61.610833
4.27
0.0446
Error: MS(Error)
8
115.340000
14.417500
Note:
SAS uses the unrestricted model for hypothesis test above. For the restricted
model, use MSB/MSE (instead of MSB/MSAB) to test the significance of the
variance component for the random factor.
The SAS System
Dependent
Variable: Y
Tests of Hypotheses Using the Type
III MS for method*day as an Error Term
Contrast
method1-method2 1 329.4225000 329.4225000 5.35 0.1038