20:25 Wednesday, July 28, 2010
data
Obs treatment
block
y
1 Early_Bloom
1 33.3
2 Early_Bloom
2 31.9
3 Early_Bloom
3 34.9
4 Early_Bloom
4 37.1
5 Full_Bloom
1 34.4
6 Full_Bloom
2 34.0
7 Full_Bloom
3 34.5
8 Full_Bloom
4 33.1
9 Full_Bloom_P
1 36.8
10 Full_Bloom_P
2 36.6
11 Full_Bloom_P
3 37.0
12 Full_Bloom_P
4 36.4
13 Ripening
1 36.3
14 Ripening
2 34.9
15 Ripening
3 35.9
16 Ripening
4 37.1
17 Seedling
1 34.4
18 Seedling
2 35.9
19 Seedling
3 36.0
20 Seedling
4 34.1
21 Uninoculated
1 36.4
22 Uninoculated
2 37.3
23 Uninoculated
3 37.7
24 Uninoculated
4 36.7
1
20:25 Wednesday, July 28, 2010
data
The MEANS Procedure
Analysis Variable : y
treatment
N
Obs
Mean
Sum Corrected SS
Early_Bloom
4 34.3000000 137.2000000
14.9600000
Full_Bloom
4 34.0000000 136.0000000
1.2200000
Full_Bloom_P
4 36.7000000 146.8000000
0.2000000
Ripening
4 36.0500000 144.2000000
2.5100000
Seedling
4 35.1000000 140.4000000
2.9400000
Uninoculated
4 37.0250000 148.1000000
1.0275000
2
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
Class Level Information
Class
Levels Values
block
4 1234
treatment
6 Early_Bloom Full_Bloom Full_Bloom_P Ripening Seedling Uninoculated
Number of Observations Read
24
Number of Observations Used
24
3
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
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
treatment
Early_Bloom
Dummy001
treatment
Full_Bloom
Dummy002
treatment
Full_Bloom_P Dummy003
treatment
Ripening
Dummy004
treatment
Seedling
Dummy005
treatment
Uninoculated
Dummy006
4
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
X'X Generalized Inverse (g2)
Intercept
Intercept
block 1
block 2
0.375 -0.166666667
-0.166666667
block 3 block 4 Dummy001 Dummy002
-0.166666667
0
-0.25
-0.25
block 1
-0.166666667 0.3333333333 0.1666666667 0.1666666667
0
0
0
block 2
-0.166666667 0.1666666667 0.3333333333 0.1666666667
0
0
0
block 3
-0.166666667 0.1666666667 0.1666666667 0.3333333333
0
0
0
block 4
0
0
0
0
0
0
0
Dummy001
-0.25
0
0
0
0
0.5
0.25
Dummy002
-0.25
0
0
0
0
0.25
0.5
Dummy003
-0.25
0
0
0
0
0.25
0.25
Dummy004
-0.25
0
0
0
0
0.25
0.25
Dummy005
-0.25
0
0
0
0
0.25
0.25
Dummy006
0
0
0
0
0
0
0
37.245833333 -0.483333333
-0.65
0.25
0
-2.725
-3.025
y
X'X Generalized Inverse (g2)
Dummy003 Dummy004 Dummy005 Dummy006
Intercept
y
-0.25
-0.25
-0.25
block 1
0
0
0
0
-0.483333333
block 2
0
0
0
0
-0.65
block 3
0
0
0
0
0.25
block 4
0
0
0
0
0
Dummy001
0.25
0.25
0.25
0
-2.725
Dummy002
0.25
0.25
0.25
0
-3.025
Dummy003
0.5
0.25
0.25
0
-0.325
Dummy004
0.25
0.5
0.25
0
-0.975
Dummy005
0.25
0.25
0.5
0
-1.925
Dummy006
0
0
0
0
0
-0.325
-0.975
-1.925
0
19.71625
y
0 37.245833333
5
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
Dependent Variable: y
Source
Sum of
Squares Mean Square F Value
DF
Model
8 34.79333333
4.34916667
Error
15 19.71625000
1.31441667
Corrected Total
23 54.50958333
R-Square Coeff Var Root MSE
0.638298 3.226870
Source
DF
Pr > F
3.31 0.0219
y Mean
1.146480 35.52917
Type I SS Mean Square F Value
Pr > F
block
3
3.14125000
1.04708333
0.80 0.5147
treatment
5 31.65208333
6.33041667
4.82 0.0080
Source
DF
Type III SS Mean Square F Value
Pr > F
block
3
3.14125000
1.04708333
0.80 0.5147
treatment
5 31.65208333
6.33041667
4.82 0.0080
Parameter
Estimate
Standard
Error t Value Pr > |t|
Intercept
37.24583333 B 0.70207282
53.05 <.0001
block
1
-0.48333333 B 0.66192061
-0.73 0.4765
block
2
-0.65000000 B 0.66192061
-0.98 0.3417
block
3
0.25000000 B 0.66192061
0.38 0.7110
block
4
0.00000000 B
.
.
.
treatment Early_Bloom
-2.72500000 B 0.81068387
-3.36 0.0043
treatment Full_Bloom
-3.02500000 B 0.81068387
-3.73 0.0020
treatment Full_Bloom_P
-0.32500000 B 0.81068387
-0.40 0.6941
treatment Ripening
-0.97500000 B 0.81068387
-1.20 0.2477
treatment Seedling
-1.92500000 B 0.81068387
-2.37 0.0313
treatment 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
RCBD Analysis of Variance
The GLM Procedure
Observation
Observed
Predicted
Residual
1 33.30000000 34.03750000 -0.73750000
2 31.90000000 33.87083333 -1.97083333
3 34.90000000 34.77083333
0.12916667
4 37.10000000 34.52083333
2.57916667
5 34.40000000 33.73750000
0.66250000
6 34.00000000 33.57083333
0.42916667
7 34.50000000 34.47083333
0.02916667
8 33.10000000 34.22083333 -1.12083333
9 36.80000000 36.43750000
0.36250000
10 36.60000000 36.27083333
0.32916667
11 37.00000000 37.17083333 -0.17083333
12 36.40000000 36.92083333 -0.52083333
13 36.30000000 35.78750000
0.51250000
14 34.90000000 35.62083333 -0.72083333
15 35.90000000 36.52083333 -0.62083333
16 37.10000000 36.27083333
0.82916667
17 34.40000000 34.83750000 -0.43750000
18 35.90000000 34.67083333
1.22916667
19 36.00000000 35.57083333
0.42916667
20 34.10000000 35.32083333 -1.22083333
21 36.40000000 36.76250000 -0.36250000
22 37.30000000 36.59583333
0.70416667
23 37.70000000 37.49583333
0.20416667
24 36.70000000 37.24583333 -0.54583333
Sum of Residuals
0.00000000
Sum of Squared Residuals
19.71625000
Sum of Squared Residuals - Error SS
-0.00000000
First Order Autocorrelation
0.09483241
Durbin-Watson D
1.76763738
7
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
y
Level of
block
N
Mean
Std Dev
1
6 35.2666667 1.41938954
2
6 35.1000000 1.96061215
3
6 36.0000000 1.21326007
4
6 35.7500000 1.71551741
y
Level of
treatment
N
Early_Bloom
4 34.3000000 2.23308456
Full_Bloom
4 34.0000000 0.63770422
Full_Bloom_P
4 36.7000000 0.25819889
Ripening
4 36.0500000 0.91469485
Seedling
4 35.1000000 0.98994949
Uninoculated
4 37.0250000 0.58523500
Mean
Std Dev
8
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
Least Squares Means
block
y LSMEAN
Standard
Error Pr > |t|
1
35.2666667 0.4680485 <.0001
2
35.1000000 0.4680485 <.0001
3
36.0000000 0.4680485 <.0001
4
35.7500000 0.4680485 <.0001
treatment
y LSMEAN
Standard
Error Pr > |t|
Early_Bloom
34.3000000 0.5732401 <.0001
Full_Bloom
34.0000000 0.5732401 <.0001
Full_Bloom_P 36.7000000 0.5732401 <.0001
Ripening
36.0500000 0.5732401 <.0001
Seedling
35.1000000 0.5732401 <.0001
Uninoculated
37.0250000 0.5732401 <.0001
9
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
The GLM Procedure
Dependent Variable: y
Parameter
Estimate
Standard
Error t Value Pr > |t|
T1 vs T2
0.30000000 0.81068387
0.37 0.7165
T1 vs T4
-0.80000000 0.81068387
-0.99 0.3394
10
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
Obs _NAME_ block treatment
LSMEAN STDERR
1 y
1
35.2667
0.46805
2 y
2
35.1000
0.46805
3 y
3
36.0000
0.46805
4 y
4
35.7500
0.46805
5 y
. Early_Bloom
34.3000
0.57324
6 y
. Full_Bloom
34.0000
0.57324
7 y
. Full_Bloom_P
36.7000
0.57324
8 y
. Ripening
36.0500
0.57324
9 y
. Seedling
35.1000
0.57324
. Uninoculated
37.0250
0.57324
10 y
11
20:25 Wednesday, July 28, 2010
RCBD Analysis of Variance
LSMEAN MEAN
40
30
20
10
0
Early_Bloom
Full_Bloom
Full_Bloom_P
treatment
Ripening
Seedling
Uninoculated
12