20:25 Wednesday, July 28, 2010
data
Obs treat
block
y
1 Seedling
1 34.4
2 Seedling
2 35.9
3 Seedling
3 36.0
4 Seedling
4 34.1
5 Early_Bloom
1 33.3
6 Early_Bloom
2 31.9
7 Early_Bloom
3 34.9
8 Early_Bloom
4 37.1
9 Full_Bloom
1 34.4
10 Full_Bloom
2
.
11 Full_Bloom
3 34.5
12 Full_Bloom
4 33.1
13 Full_Bloom_P
1 36.8
14 Full_Bloom_P
2 36.6
15 Full_Bloom_P
3 37.0
16 Full_Bloom_P
4 36.4
17 Ripening
1 36.3
18 Ripening
2 34.9
19 Ripening
3 35.9
20 Ripening
4 37.1
21 uninoculated
1 36.4
22 uninoculated
2 37.3
23 uninoculated
3
24 uninoculated
4 36.7
.
1
20:25 Wednesday, July 28, 2010
data
The MEANS Procedure
Analysis Variable : y
treat
N
Obs
Mean
Sum Corrected SS N
Early_Bloom
4 34.3000000 137.2000000
14.9600000
4
Full_Bloom
4 34.0000000 102.0000000
1.2200000
3
Full_Bloom_P
4 36.7000000 146.8000000
0.2000000
4
Ripening
4 36.0500000 144.2000000
2.5100000
4
Seedling
4 35.1000000 140.4000000
2.9400000
4
uninoculated
4 36.8000000 110.4000000
0.4200000
3
2
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Class Level Information
Class Levels Values
treat
6 Early_Bloom Full_Bloom Full_Bloom_P Ripening Seedling uninoculated
block
4 1234
Number of Observations Read
24
Number of Observations Used
22
3
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Matrix Element Representation
Dependent Variable: y
Effect
Representation
Intercept
Intercept
block
1
block 1
block
2
block 2
block
3
block 3
block
4
block 4
treat
Early_Bloom
Dummy001
treat
Full_Bloom
Dummy002
treat
Full_Bloom_P
Dummy003
treat
Ripening
Dummy004
treat
Seedling
Dummy005
treat
uninoculated
Dummy006
4
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
X'X Generalized Inverse (g2)
Intercept
block 1
block 2
Intercept
0.4494047619 -0.166666667
-0.181547619
block 1
Dummy001
Dummy002
0 -0.334821429
-0.357142857
-0.166666667 0.3333333333 0.1666666667 0.1666666667
0
-3.59336E-17
block 2
-0.181547619 0.1666666667 0.3779761905 0.1636904762
0 0.0044642857 0.0714285714
block 3
-0.110119048 0.1666666667 0.1636904762 0.3779761905
0 -0.066964286
block 4
0
0
block 3 block 4
-0.110119048
0
0
-2.77246E-17
0
-0.071428571
0
0
Dummy001
-0.334821429
-2.77246E-17 0.0044642857 -0.066964286
0 0.6004464286 0.3571428571
Dummy002
-0.357142857
-3.59336E-17 0.0714285714 -0.071428571
0 0.3571428571 0.7142857143
Dummy003
-0.334821429
-2.77246E-17 0.0044642857 -0.066964286
0 0.3504464286 0.3571428571
Dummy004
-0.334821429
-2.77246E-17 0.0044642857 -0.066964286
0 0.3504464286 0.3571428571
Dummy005
-0.334821429
-2.77246E-17 0.0044642857 -0.066964286
0 0.3504464286 0.3571428571
Dummy006
0
y
0
37.214880952 -0.483333333
0
0
-0.761309524 0.2029761905
0
0
0
0 -2.654464286
-3.121428571
X'X Generalized Inverse (g2)
Dummy003
Dummy004
Intercept
-0.334821429
-0.334821429
-0.334821429
0 37.214880952
block 1
-2.77246E-17
-2.77246E-17
-2.77246E-17
0
-0.483333333
block 2
0.0044642857 0.0044642857 0.0044642857
0
-0.761309524
block 3
-0.066964286
-0.066964286
-0.066964286
0 0.2029761905
block 4
0
0
0
0
0
Dummy001 0.3504464286 0.3504464286 0.3504464286
0
-2.654464286
Dummy002 0.3571428571 0.3571428571 0.3571428571
0
-3.121428571
Dummy003 0.6004464286 0.3504464286 0.3504464286
0
-0.254464286
Dummy004 0.3504464286 0.6004464286 0.3504464286
0
-0.904464286
Dummy005 0.3504464286 0.3504464286 0.6004464286
0
-1.854464286
Dummy006
y
Dummy005 Dummy006
y
0
0
0
0
0
-0.254464286
-0.904464286
-1.854464286
0
19.37202381
5
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Dependent Variable: y
Source
DF
Sum of
Squares Mean Square F Value
Model
8 28.06797619
3.50849702
Error
13 19.37202381
1.49015568
Corrected Total
21 47.44000000
R-Square Coeff Var Root MSE
0.591652 3.438646
Source DF
Pr > F
2.35 0.0820
y Mean
1.220719 35.50000
Type I SS Mean Square F Value
Pr > F
block
3
0.99166667
0.33055556
0.22 0.8795
treat
5 27.07630952
5.41526190
3.63 0.0282
Source DF
Type III SS Mean Square F Value
Pr > F
block
3
2.87797619
0.95932540
0.64 0.6005
treat
5 27.07630952
5.41526190
3.63 0.0282
Parameter
Estimate
Standard
Error t Value Pr > |t|
Intercept
37.21488095 B 0.81834165
45.48 <.0001
block
1
-0.48333333 B 0.70478263
-0.69 0.5049
block
2
-0.76130952 B 0.75049541
-1.01 0.3289
block
3
0.20297619 B 0.75049541
0.27 0.7911
block
4
0.00000000 B
.
.
.
treat
Early_Bloom
-2.65446429 B 0.94591683
-2.81 0.0149
treat
Full_Bloom
-3.12142857 B 1.03169613
-3.03 0.0097
treat
Full_Bloom_P
-0.25446429 B 0.94591683
-0.27 0.7921
treat
Ripening
-0.90446429 B 0.94591683
-0.96 0.3564
treat
Seedling
-1.85446429 B 0.94591683
-1.96 0.0717
treat
uninoculated
0.00000000 B
.
.
.
Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations.
Terms whose estimates are followed by the letter 'B' are not uniquely estimable.
6
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Observation
Observed
Predicted
Residual
1
34.40000000 34.87708333 -0.47708333
2
35.90000000 34.59910714
1.30089286
3
36.00000000 35.56339286
0.43660714
4
34.10000000 35.36041667 -1.26041667
5
33.30000000 34.07708333 -0.77708333
6
31.90000000 33.79910714 -1.89910714
7
34.90000000 34.76339286
0.13660714
8
37.10000000 34.56041667
2.53958333
9
34.40000000 33.61011905
0.78988095
. 33.33214286
.
11
34.50000000 34.29642857
0.20357143
12
33.10000000 34.09345238 -0.99345238
13
36.80000000 36.47708333
0.32291667
14
36.60000000 36.19910714
0.40089286
15
37.00000000 37.16339286 -0.16339286
16
36.40000000 36.96041667 -0.56041667
17
36.30000000 35.82708333
18
34.90000000 35.54910714 -0.64910714
19
35.90000000 36.51339286 -0.61339286
20
37.10000000 36.31041667
21
36.40000000 36.73154762 -0.33154762
22
37.30000000 36.45357143
0.84642857
. 37.41785714
.
10 *
23 *
24
0.47291667
0.78958333
36.70000000 37.21488095 -0.51488095
* Observation was not used in this analysis
Sum of Residuals
0.00000000
Sum of Squared Residuals
19.37202381
Sum of Squared Residuals - Error SS
-0.00000000
First Order Autocorrelation
0.10853759
Durbin-Watson D
1.75749067
7
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
y
Level of
treat
N
Early_Bloom
4 34.3000000 2.23308456
Full_Bloom
3 34.0000000 0.78102497
Full_Bloom_P
4 36.7000000 0.25819889
Ripening
4 36.0500000 0.91469485
Seedling
4 35.1000000 0.98994949
uninoculated
3 36.8000000 0.45825757
Mean
Std Dev
y
Level of
block
N
Mean
Std Dev
1
6 35.2666667 1.41938954
2
5 35.3200000 2.10760528
3
5 35.6600000 0.98640762
4
6 35.7500000 1.71551741
8
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Least Squares Means
treat
y LSMEAN
Standard
Error Pr > |t|
Early_Bloom
34.3000000 0.6103597 <.0001
Full_Bloom
33.8330357 0.7226477 <.0001
Full_Bloom_P 36.7000000 0.6103597 <.0001
Ripening
36.0500000 0.6103597 <.0001
Seedling
35.1000000 0.6103597 <.0001
uninoculated
36.9544643 0.7226477 <.0001
block
y LSMEAN
Standard
Error Pr > |t|
1
35.2666667 0.4983566 <.0001
2
34.9886905 0.5611453 <.0001
3
35.9529762 0.5611453 <.0001
4
35.7500000 0.4983566 <.0001
9
20:25 Wednesday, July 28, 2010
data
RCBD Block and Treat fixed effects
GLM ANOVA table
2 missing obs
The GLM Procedure
Dependent Variable: y
Parameter
Estimate
Standard
Error t Value Pr > |t|
T1 vs T2
0.46696429 0.94591683
0.49 0.6298
T1 vs T4
-0.80000000 0.86317891
-0.93 0.3709
10