Potato Clones
Obs clone rep titer code
6
2
1
32 b
7
2
2
12 b
8
2
3
25 b
9
2
4
61 b
10
2
5
93 b
20
5
1
529 e
21
5
2
396 e
22
5
3
629 e
23
5
4
261 e
24
5
5
325 e
30
7
1 1361 g
31
7
2
363 g
32
7
3
418 g
33
7
4
579 g
34
7
5 1660 g
09:18 Thursday, August 28, 2008
type
etb
etb
etb
etb
etb
par
par
par
par
par
cult
cult
cult
cult
cult
1
1700
1600
1500
1400
1300
1200
1100
titer
1000
900
800
700
600
500
400
300
200
100
0
2
3
4
5
6
clone
clone
2
5
7
7
Potato Clones
09:18 Thursday, August 28, 2008
Obs clone n Mean_titter n
SD
var
1
2 5
44.6 5 32.470
1054.3
2
5 5
428.0 5 150.103 22531.0
3
7 5
876.2 5 593.932 352755.7
3
ANOVA table
Homogeneity of variance test
The GLM Procedure
Class Level
Information
Class Levels Values
clone
3 2 5 7
rep
5 1 2 3 4 5
Number of Observations Read 15
Number of Observations Used 15
09:18 Thursday, August 28, 2008
4
ANOVA table
Homogeneity of variance test
09:18 Thursday, August 28, 2008
The GLM Procedure
Dependent Variable: titer
Source
DF
Model
2
Error
12
Corrected Total 14
Sum of
Squares Mean Square F Value Pr > F
1732395.600 866197.800
6.90 0.0101
1505364.000 125447.000
3237759.600
R-Square Coeff Var Root MSE titer Mean
0.535060 78.77780 354.1850
449.6000
Source DF
Type I SS Mean Square F Value Pr > F
clone
2 1732395.600 866197.800
6.90 0.0101
Source DF Type III SS Mean Square F Value Pr > F
clone
2 1732395.600 866197.800
6.90 0.0101
5
ANOVA table
Homogeneity of variance test
The GLM Procedure
09:18 Thursday, August 28, 2008
6
ANOVA table
Homogeneity of variance test
09:18 Thursday, August 28, 2008
The GLM Procedure
Brown and Forsythe's Test for Homogeneity of titer Variance
ANOVA of Absolute Deviations from Group Medians
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
clone
2
499759
249879
3.40
0.0675
Error
12
881222
73435.2
7
ANOVA table
Homogeneity of variance test
The GLM Procedure
titer
Level of
clone
N
Mean
Std Dev
2
5 44.600000 32.469986
5
5 428.000000 150.103298
7
5 876.200000 593.932404
09:18 Thursday, August 28, 2008
8
ANOVA table
Homogeneity of variance test
The GLM Procedure
Bartlett's Test for Homogeneity
of titer Variance
Source
clone
DF Chi-Square Pr > ChiSq
2
19.6636
<.0001
09:18 Thursday, August 28, 2008
9
ANOVA table
Homogeneity of variance test
The GLM Procedure
titer
Level of
clone
N
Mean
Std Dev
2
5 44.600000 32.469986
5
5 428.000000 150.103298
7
5 876.200000 593.932404
09:18 Thursday, August 28, 2008
10
Homogeneity of variance test
3
StudentResid
2
1
0
-1
-2
0
100
200
300
400
500
600
pred
clone
2
5
7
700
800
900
Mixed Model with common residual variance
12
09:18 Thursday, August 28, 2008
The Mixed Procedure
Data Set
Model Information
WORK.A
Dependent Variable
titer
Covariance Structure
Diagonal
Estimation Method
REML
Residual Variance Method
Profile
Fixed Effects SE Method
Model-Based
Degrees of Freedom Method Residual
Class Level
Information
Class Levels Values
clone
3 2 5 7
rep
5 1 2 3 4 5
Dimensions
Covariance Parameters
1
Columns in X
4
Columns in Z
0
Subjects
1
Max Obs Per Subject
15
Number of Observations
Number of Observations Read
15
Number of Observations Used
15
Number of Observations Not Used
0
Mixed Model with common residual variance
13
09:18 Thursday, August 28, 2008
The Mixed Procedure
Covariance
Parameter
Estimates
Cov Parm Estimate
Residual
125447
Fit Statistics
-2 Res Log Likelihood
179.8
AIC (smaller is better)
181.8
AICC (smaller is better) 182.2
BIC (smaller is better)
182.2
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
clone
2 12
6.90 0.0101
Least Squares Means
Standard
Effect clone Estimate
Error DF t Value Pr > |t| Alpha
clone
clone
clone
2
5
7
44.6000
428.00
876.20
158.40 12
158.40 12
158.40 12
0.28
2.70
5.53
0.7831
0.0192
0.0001
Lower
Upper
0.05 -300.52 389.72
0.05 82.8840 773.12
0.05 531.08 1221.32
Mixed Model with common residual variance
14
09:18 Thursday, August 28, 2008
The Mixed Procedure
Differences of Least Squares Means
Standard
Effect clone _clone Estimate
Error DF t Value Pr > |t| Alpha
clone
clone
clone
2
2
5
5
7
7
-383.40
-831.60
-448.20
224.01 12
224.01 12
224.01 12
-1.71
-3.71
-2.00
0.1127
0.0030
0.0686
Lower
Upper
0.05 -871.47 104.67
0.05 -1319.67 -343.53
0.05 -936.27 39.8677
Mixed Model with common residual variance
The Mixed Procedure
15
09:18 Thursday, August 28, 2008
Mixed Model with separate residual variance
Residual variance within each clone
16
09:18 Thursday, August 28, 2008
The Mixed Procedure
Model Information
WORK.A
Data Set
Dependent Variable
titer
Covariance Structure
Variance Components
Subject Effect
Group Effect
rep(clone)
clone
Estimation Method
REML
Residual Variance Method
None
Fixed Effects SE Method
Model-Based
Degrees of Freedom Method Between-Within
Class Level
Information
Class Levels Values
clone
3 2 5 7
rep
5 1 2 3 4 5
Dimensions
Covariance Parameters
3
Columns in X
4
Columns in Z
0
Subjects
Max Obs Per Subject
15
1
Mixed Model with separate residual variance
Residual variance within each clone
17
09:18 Thursday, August 28, 2008
The Mixed Procedure
Number of Observations
Number of Observations Read
15
Number of Observations Used
15
Number of Observations Not Used
0
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0
1
179.75850219
1
1
157.91008159 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm Subject
Group
Estimate
Residual rep(clone) clone 2
1054.30
Residual rep(clone) clone 5
22531
Residual rep(clone) clone 7
352756
Fit Statistics
-2 Res Log Likelihood
157.9
AIC (smaller is better)
163.9
AICC (smaller is better) 166.9
BIC (smaller is better)
166.0
Mixed Model with separate residual variance
Residual variance within each clone
18
09:18 Thursday, August 28, 2008
The Mixed Procedure
Null Model Likelihood
Ratio Test
DF Chi-Square Pr > ChiSq
2
21.85
<.0001
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
clone
2 12
20.27 0.0001
Least Squares Means
Standard
Effect clone Estimate
Error DF t Value Pr > |t| Alpha
clone
clone
clone
2
5
7
44.6000
428.00
876.20
14.5210 12
67.1282 12
265.61 12
3.07
6.38
3.30
0.0097
<.0001
0.0064
2
2
5
5
7
7
-383.40
-831.60
-448.20
68.6809 12
266.01 12
273.97 12
-5.58
-3.13
-1.64
Upper
0.05 12.9614 76.2386
0.05 281.74 574.26
0.05 297.48 1454.92
Differences of Least Squares Means
Standard
Effect clone _clone Estimate
Error DF t Value Pr > |t| Alpha
clone
clone
clone
Lower
0.0001
0.0088
0.1278
Lower
Upper
0.05 -533.04 -233.76
0.05 -1411.19 -252.01
0.05 -1045.12 148.72
Mixed Model with separate residual variance
Residual variance within each clone
The Mixed Procedure
19
09:18 Thursday, August 28, 2008
Mixed Model with separate residual variance
Residual variance within each clone
20
09:18 Thursday, August 28, 2008
The Mixed Procedure
Model Information
WORK.A
Data Set
Dependent Variable
titer
Covariance Structure
Variance Components
Subject Effect
Group Effect
rep(clone)
clone
Estimation Method
REML
Residual Variance Method
None
Fixed Effects SE Method
Model-Based
Degrees of Freedom Method Satterthwaite
Class Level
Information
Class Levels Values
clone
3 2 5 7
rep
5 1 2 3 4 5
Dimensions
Covariance Parameters
3
Columns in X
4
Columns in Z
0
Subjects
Max Obs Per Subject
15
1
Mixed Model with separate residual variance
Residual variance within each clone
21
09:18 Thursday, August 28, 2008
The Mixed Procedure
Number of Observations
Number of Observations Read
15
Number of Observations Used
15
Number of Observations Not Used
0
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0
1
179.75850219
1
1
157.91008159 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm Subject
Group
Estimate
Residual rep(clone) clone 2
1054.30
Residual rep(clone) clone 5
22531
Residual rep(clone) clone 7
352756
Fit Statistics
-2 Res Log Likelihood
157.9
AIC (smaller is better)
163.9
AICC (smaller is better) 166.9
BIC (smaller is better)
166.0
Mixed Model with separate residual variance
Residual variance within each clone
22
09:18 Thursday, August 28, 2008
The Mixed Procedure
Null Model Likelihood
Ratio Test
DF Chi-Square Pr > ChiSq
2
21.85
<.0001
Type 3 Tests of Fixed Effects
Num Den
Effect DF
DF F Value Pr > F
clone
2 4.31
20.27 0.0064
Least Squares Means
Standard
Effect clone Estimate
Error DF t Value Pr > |t| Alpha
clone
clone
clone
2
5
7
44.6000
428.00
876.20
14.5210
67.1282
265.61
4
4
4
3.07
6.38
3.30
0.0372
0.0031
0.0300
Lower
0.05 4.2832 84.9168
0.05 241.62 614.38
0.05 138.74 1613.66
Differences of Least Squares Means
Standard
Effect clone _clone Estimate
Error
DF t Value Pr > |t| Alpha
clone
clone
clone
2
2
5
5
7
7
-383.40
-831.60
-448.20
68.6809 4.37
266.01 4.02
273.97 4.51
-5.58
-3.13
-1.64
Upper
0.0039
0.0350
0.1691
Lower
Upper
0.05 -567.83 -198.97
0.05 -1568.44 -94.7618
0.05 -1176.16
279.76
Mixed Model with separate residual variance
Residual variance within each clone
The Mixed Procedure
23
09:18 Thursday, August 28, 2008