Printout of Factorial Data 1
09:57 Tuesday, October 28, 2003
Obs a b rep yield
1 0 0 1 12
2 0 0 2 15
3 0 0 3 14
4 0 0 4 13
5 0 1 1 19
6 0 1 2 22
7 0 1 3 23
8 0 1 4 21
9 1 0 1 29
10 1 0 2 27
11 1 0 3 33
12 1 0 4 30
13 1 1 1 32
14 1 1 2 35
15 1 1 3 38
16 1 1 4 37
ANOVA assuming A and B are fixed effects 2
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Class Level Information
Class Levels Values
rep 4 1 2 3 4
a 2 0 1
b 2 0 1
Number of observations 16
ANOVA assuming A and B are fixed effects 3
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 1149.000000 191.500000 82.07 <.0001
Error 9 21.000000 2.333333
Corrected Total 15 1170.000000
R-Square Coeff Var Root MSE yield Mean
0.982051 6.110101 1.527525 25.00000
Source DF Anova SS Mean Square F Value Pr > F
rep 3 32.5000000 10.8333333 4.64 0.0317
a 1 930.2500000 930.2500000 398.68 <.0001
b 1 182.2500000 182.2500000 78.11 <.0001
a*b 1 4.0000000 4.0000000 1.71 0.2229
ANOVA assuming A and B are fixed effects 4
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
t Tests (LSD) for yield
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error
rate.
Alpha 0.05
Error Degrees of Freedom 9
Error Mean Square 2.333333
Critical Value of t 2.26216
Least Significant Difference 1.7278
Means with the same letter are not significantly different.
t Grouping Mean N a
A 32.6250 8 1
B 17.3750 8 0
ANOVA assuming A and B are fixed effects 5
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
t Tests (LSD) for yield
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error
rate.
Alpha 0.05
Error Degrees of Freedom 9
Error Mean Square 2.333333
Critical Value of t 2.26216
Least Significant Difference 1.7278
Means with the same letter are not significantly different.
t Grouping Mean N b
A 28.3750 8 1
B 21.6250 8 0
ANOVA assuming A and B are fixed effects 6
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Level of Level of ------------yield------------
a b N Mean Std Dev
0 0 4 13.5000000 1.29099445
0 1 4 21.2500000 1.70782513
1 0 4 29.7500000 2.50000000
1 1 4 35.5000000 2.64575131
ANOVA assuming A and B are random effects 7
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Class Level Information
Class Levels Values
rep 4 1 2 3 4
a 2 0 1
b 2 0 1
Number of observations 16
ANOVA assuming A and B are random effects 8
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Dependent Variable: yield
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 1149.000000 191.500000 82.07 <.0001
Error 9 21.000000 2.333333
Corrected Total 15 1170.000000
R-Square Coeff Var Root MSE yield Mean
0.982051 6.110101 1.527525 25.00000
Source DF Anova SS Mean Square F Value Pr > F
rep 3 32.5000000 10.8333333 4.64 0.0317
a 1 930.2500000 930.2500000 398.68 <.0001
b 1 182.2500000 182.2500000 78.11 <.0001
a*b 1 4.0000000 4.0000000 1.71 0.2229
Tests of Hypotheses Using the Anova MS for a*b as an Error Term
Source DF Anova SS Mean Square F Value Pr > F
a 1 930.2500000 930.2500000 232.56 0.0417
b 1 182.2500000 182.2500000 45.56 0.0936
ANOVA assuming A and B are random effects 9
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
t Tests (LSD) for yield
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error
rate.
Alpha 0.05
Error Degrees of Freedom 1
Error Mean Square 4
Critical Value of t 12.70620
Least Significant Difference 12.706
Means with the same letter are not significantly different.
t Grouping Mean N a
A 32.625 8 1
B 17.375 8 0
ANOVA assuming A and B are random effects 10
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
t Tests (LSD) for yield
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error
rate.
Alpha 0.05
Error Degrees of Freedom 1
Error Mean Square 4
Critical Value of t 12.70620
Least Significant Difference 12.706
Means with the same letter are not significantly different.
t Grouping Mean N b
A 28.375 8 1
A
A 21.625 8 0
ANOVA assuming A and B are random effects 11
09:57 Tuesday, October 28, 2003
The ANOVA Procedure
Level of Level of ------------yield------------
a b N Mean Std Dev
0 0 4 13.5000000 1.29099445
0 1 4 21.2500000 1.70782513
1 0 4 29.7500000 2.50000000
1 1 4 35.5000000 2.64575131