OBS FACTORA FACTORB RESPONSE
1 -1 -1 28
2 -1 -1 25
3 -1 -1 27
4 1 -1 36
5 1 -1 32
6 1 -1 32
7 -1 1 18
8 -1 1 19
9 -1 1 23
10 1 1 31
11 1 1 30
12 1 1 29
note: This is just a listing of the data. This is how you should
enter the data into your .dat file. If you want to be able to
determine factor effects then you must use -1 and +1 to denote the low
and high levels of a particular factor.
General Linear Models Procedure
Dependent Variable: RESPONSE
Source DF Sum of Squares F Value Pr > F
Model 3 291.66666667 24.82 0.0002
Error 8 31.33333333
Corrected Total 11 323.00000000
R-Square C.V. RESPONSE Mean
0.902993 7.196571 27.5000000
note: For the above F Value, the "full" model contains the overall
mean, factorA effect, factorB effect, and the interaction effect. The
"reduced" model contains just the overall mean.
Source DF Type III SS F Value Pr > F
FACTORA 1 208.33333333 53.19 0.0001
FACTORB 1 75.00000000 19.15 0.0024
FACTORB*FACTORA 1 8.33333333 2.13 0.1828
note: The above Type III F Values (and pvalues) correspond to the
Analysis of Variance table on page 295 of the textbook. The above
output was obtained from the GLM procedure using the CLASS statement.
There is no factor effects output here.
General Linear Models Procedure
Dependent Variable: RESPONSE
Source DF Sum of Squares F Value Pr > F
Model 3 291.66666667 24.82 0.0002
Error 8 31.33333333
Corrected Total 11 323.00000000
R-Square C.V. RESPONSE Mean
0.902993 7.196571 27.5000000
Source DF Type III SS F Value Pr > F
FACTORA 1 208.33333333 53.19 0.0001
FACTORB 1 75.00000000 19.15 0.0024
FACTORA*FACTORB 1 8.33333333 2.13 0.1828
T for H0: Pr > |T| Std Error of
Parameter Estimate Parameter=0 Estimate
INTERCEPT 27.50000000 48.14 0.0001 0.57130455
FACTORA 4.16666667 7.29 0.0001 0.57130455
FACTORB -2.50000000 -4.38 0.0024 0.57130455
FACTORA*FACTORB
0.83333333 1.46 0.1828 0.57130455
note: The above Type III F Values (and pvalues) correspond to the
Analysis of Variance table on page 295 of the textbook. The above
output was obtained from the GLM procedure without using the CLASS
statement. The factor effects (divided by 2) are output here.
note: Since the interaction term is not significant, we will drop this
from the model and fit the refined model (which contains just the main
effects).
General Linear Models Procedure
Dependent Variable: RESPONSE
Source DF Sum of Squares F Value Pr > F
Model 2 283.33333333 32.14 0.0001
Error 9 39.66666667
Corrected Total 11 323.00000000
R-Square C.V. RESPONSE Mean
0.877193 7.634119 27.5000000
Source DF Type III SS F Value Pr > F
FACTORA 1 208.33333333 47.27 0.0001
FACTORB 1 75.00000000 17.02 0.0026
Observation Observed Predicted Residual
Value Value
1 28.00000000 25.83333333 2.16666667
2 25.00000000 25.83333333 -0.83333333
3 27.00000000 25.83333333 1.16666667
4 36.00000000 34.16666667 1.83333333
5 32.00000000 34.16666667 -2.16666667
6 32.00000000 34.16666667 -2.16666667
7 18.00000000 20.83333333 -2.83333333
8 19.00000000 20.83333333 -1.83333333
9 23.00000000 20.83333333 2.16666667
10 31.00000000 29.16666667 1.83333333
11 30.00000000 29.16666667 0.83333333
12 29.00000000 29.16666667 -0.16666667
T tests (LSD) for variable: RESPONSE
Alpha= 0.05 df= 9 MSE= 4.407407
Critical Value of T= 2.26
Least Significant Difference= 2.7419
Means with the same letter are not significantly different.
T Grouping Mean N FACTORA
A 31.667 6 1
B 23.333 6 -1
T tests (LSD) for variable: RESPONSE
Alpha= 0.05 df= 9 MSE= 4.407407
Critical Value of T= 2.26
Least Significant Difference= 2.7419
Means with the same letter are not significantly different.
T Grouping Mean N FACTORB
A 30.000 6 -1
B 25.000 6 1
Plot of EXPECTED*RESID='*'. Plot of STDRESID*FIT='*'.
-+--------+--------+- -+-----+-----+-----+-
2 + + 2 +-------------------+
| | | |
| | | |
EXPECTED | * | STDRESID | * * * * |
| | | |
| * | | * * |
| * | | |
0 + * * + 0 + * +
| * | | |
| * | | * |
| * | | |
| | | * * |
| * | | * |
| | | |
-2 + + -2 +-------------------+
-+--------+--------+- -+-----+-----+-----+-
-5 0 5 20 25 30 35
RESID FIT
NOTE: 3 obs hidden. NOTE: 1 obs hidden.
W:Normal 0.887 Pr<W 0.104
Plot of STDRESID*FACTORA='*'. Plot of STDRESID*FACTORB='*'.
---+------------+--- ---+------------+---
2 +------------------+ 2 +------------------+
| | | |
| | | |
STDRESID | * * | STDRESID | * * |
| | | |
| * * | | * * |
| | | |
0 + * + 0 + * +
| | | |
| * | | * |
| | | |
| * * | | * * |
| * | | * |
| | | |
-2 +------------------+ -2 +------------------+
---+------------+--- ---+------------+---
-1 1 -1 1
FACTORA FACTORB
NOTE: 3 obs hidden. NOTE: 3 obs hidden.