Potato Clones
1900
1800
1700
1600
1500
1400
1300
1200
titer
1100
1000
900
800
700
600
500
400
300
200
100
0
1
2
3
4
5
6
7
8
9
10
11
12
clone
type
cult
etb
odd
par
res
susc
13
clone means vs observations
1900
1800
1700
1600
1500
1400
1300
1200
titer
1100
1000
900
800
700
600
500
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Mean_titer
type
cult
etb
odd
par
res
susc
clone mean vs variance
SD
600
500
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Mean_titer
type
cult
etb
odd
par
res
susc
clone mean vs variance
var
400000
300000
200000
100000
0
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Mean_titer
type
cult
etb
odd
par
res
susc
clone mean vs variance
cv
90
80
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Mean_titer
type
cult
etb
odd
par
res
susc
Yandell cloning data
ANOVA table - homogeneity of variance test
The GLM Procedure
Class Level Information
Class Levels Values
clone
rep
13 1 2 3 4 5 6 7 8 9 10 11 12 13
5 12345
Number of Observations Read 64
Number of Observations Used 64
17:38 Thursday, September 11, 2008 6
Yandell cloning data
ANOVA table - homogeneity of variance test
The GLM Procedure
Dependent Variable: titer
Source
DF
Sum of
Squares Mean Square F Value Pr > F
Model
12 13844104.69
Error
51
Corrected Total
63 16753509.44
2909404.75
1153675.39
20.22 <.0001
57047.15
R-Square Coeff Var Root MSE titer Mean
0.826341
Source DF
clone
37.44209
238.8455
637.9063
Type I SS Mean Square F Value Pr > F
12 13844104.69
1153675.39
20.22 <.0001
Source DF Type III SS Mean Square F Value Pr > F
clone
12
13844104.69
1153675.39
20.22 <.0001
17:38 Thursday, September 11, 2008 7
Yandell cloning data
ANOVA table - homogeneity of variance test
The GLM Procedure
17:38 Thursday, September 11, 2008 8
Yandell cloning data
ANOVA table - homogeneity of variance test
17:38 Thursday, September 11, 2008 9
The GLM Procedure
Brown and Forsythe's Test for Homogeneity of titer Variance
ANOVA of Absolute Deviations from Group Medians
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
clone
12
679400
56616.6
1.76
0.0809
Error
51
1639324
32143.6
Source
Bartlett's Test for Homogeneity of
titer Variance
Source DF Chi-Square Pr > ChiSq
clone
12
42.7104
<.0001
Yandell cloning data
ANOVA table - homogeneity of variance test
The GLM Procedure
titer
Level of
clone
N
Mean
Std Dev
1
5 1358.20000 225.616267
2
5
44.60000
32.469986
3
4 1789.25000
48.917447
4
5
264.80000 111.335978
5
5
428.00000 150.103298
6
5
645.40000 339.847466
7
5
876.20000 593.932404
8
5
279.20000
9
5
287.80000 253.182148
10
5
746.40000 133.008646
11
5
406.20000 169.090804
12
5 1068.20000 134.021267
13
5
97.801840
328.80000 180.304465
17:38 Thursday, September 11, 2008 10
Yandell cloning data
ANOVA table - homogeneity of variance test
extreme observations - outliers
Obs clone rep titer code type resid StudentResid pred
34
7
5 1660 g
cult
783.8
3.66896 876.2
17:38 Thursday, September 11, 2008 11
ANOVA table - homogeneity of variance test
Residual checking
4
3
StudentResid
2
1
0
-1
-2
-3
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
pred
clone
1
8
2
9
3
10
4
11
5
12
6
13
7
Yandell cloning data
ANOVA table - homogeneity of variance test
Residual normality test
17:38 Thursday, September 11, 2008 13
The CAPABILITY Procedure
Variable: StudentResid
Moments
N
64 Sum Weights
Mean
64
4.61E-16 Sum Observations 2.9504E-14
Std Deviation
Skewness
1.0060175 Variance
1.01207122
0.35509779 Kurtosis
2.88124685
Uncorrected SS 63.7604866 Corrected SS
63.7604866
Coeff Variation 2.18224E17 Std Error Mean
0.12575219
Basic Statistical Measures
Location
Mean
Variability
0.000000 Std Deviation
1.00602
Median 0.008426 Variance
1.01207
Mode
6.42326
. Range
Interquartile Range 0.99986
Tests for Location: Mu0=0
Test
Statistic
Student's t
t
Sign
M
Signed Rank S
p Value
3.67E-15 Pr > |t|
1.0000
0 Pr >= |M| 1.0000
-14 Pr >= |S|
0.9263
Yandell cloning data
ANOVA table - homogeneity of variance test
Residual normality test
The CAPABILITY Procedure
Variable: StudentResid
Quantiles (Definition 5)
Quantile
Estimate
100% Max
3.668962576
99%
3.668962576
95%
1.433320159
90%
1.100969632
75% Q3
0.462482142
50% Median
0.008425788
25% Q1
-0.537378035
10%
-1.075692268
5%
-1.391191219
1%
-2.754296478
0% Min
-2.754296478
Extreme Observations
Lowest
Highest
Value Obs
Value Obs
-2.75429648
38 1.33689170
36
-2.40228578
47 1.43332016
16
-2.14483115
48 1.67954041
57
-1.39119122
49 2.26934557
46
-1.24139943
60 3.66896258
50
17:38 Thursday, September 11, 2008 14
ANOVA table - homogeneity of variance test
Residual normality test
40
35
30
25
P
e
r
c 20
e
n
t
15
10
5
0
-2.5
-1.5
-0.5
0.5
1.5
StudentResid
Curve:
Normal(Mu=46E-17 Sigma=1.006)
2.5
3.5
Yandell cloning data
ANOVA table - homogeneity of variance test
Residual normality test
17:38 Thursday, September 11, 2008 16
The CAPABILITY Procedure
Fitted Normal Distribution for StudentResid
Parameters for Normal
Distribution
Parameter Symbol Estimate
Mean
Mu
4.61E-16
Std Dev
Sigma
1.006018
Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
DF
p Value
Kolmogorov-Smirnov D
0.0928020
Pr > D
Cramer-von Mises
W-Sq
0.1347628
Pr > W-Sq
0.039
Anderson-Darling
A-Sq
0.8712849
Pr > A-Sq
0.024
Chi-Square
Chi-Sq 15.3594394
4 Pr > Chi-Sq
0.004
Quantiles for Normal
Distribution
Quantile
Percent Observed Estimated
1.0
-2.75430
-2.340347
5.0
-1.39119
-1.654752
10.0
-1.07569
-1.289263
25.0
-0.53738
-0.678548
50.0
0.00843
0.000000
75.0
0.46248
0.678548
90.0
1.10097
1.289263
95.0
1.43332
1.654752
99.0
3.66896
2.340347
>0.150
ANOVA table - homogeneity of variance test
Residual normality test
4
3
2
S
t
u
d
e
n
t
R
e
s
i
d
1
0
-1
-2
-3
-3
-2
-1
0
1
Normal Quantiles
Normal Line:
Mu=0, Sigma=1
2
3
Yandell cloning data
Fitting one-way linear model with proc mixed
The Mixed Procedure
Model Information
Data Set
WORK.A
Dependent Variable
titer
Covariance Structure
Diagonal
Estimation Method
Type 3
Residual Variance Method
Factor
Fixed Effects SE Method
Model-Based
Degrees of Freedom Method Residual
Class Level Information
Class Levels Values
clone
rep
13 1 2 3 4 5 6 7 8 9 10 11 12 13
5 12345
Dimensions
Covariance Parameters
1
Columns in X
14
Columns in Z
0
Subjects
1
Max Obs Per Subject
64
Number of Observations
Number of Observations Read
64
Number of Observations Used
64
Number of Observations Not Used
0
17:38 Thursday, September 11, 2008 18
Yandell cloning data
Fitting one-way linear model with proc mixed
17:38 Thursday, September 11, 2008 19
The Mixed Procedure
Type 3 Analysis of Variance
Source
Sum of
Error
DF Squares Mean Square Expected Mean Square Error Term
DF F Value Pr > F
clone
12 13844105
Residual
51
2909405
1153675 Var(Residual) + Q(clone)
57047 Var(Residual)
MS(Residual)
.
Covariance
Parameter
Estimates
Cov Parm Estimate
Residual
57047
Fit Statistics
-2 Res Log Likelihood
724.0
AIC (smaller is better)
726.0
AICC (smaller is better) 726.0
BIC (smaller is better)
727.9
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF F Value Pr > F
clone
12
51
20.22 <.0001
51
.
20.22 <.0001
.
.
Yandell cloning data
Fitting one-way linear model with proc mixed
extreme observations - outliers
17:38 Thursday, September 11, 2008 20
Obs clone rep titer code type Pred StdErrPred DF Alpha Lower Upper Resid StudentResid PearsonResid
34
7
5 1660 g
cult
876.2
106.815
51
0.05 661.760 1090.64
783.8
3.66896
3.28162
Fitting one-way linear model with proc mixed
Residual checking
4
3
Studentized Residual
2
1
0
-1
-2
-3
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Predicted
code
a
h
b
i
c
j
d
k
e
l
f
m
g
Yandell cloning data
Fitting one-way linear model with proc mixed
Residual Normality checking
17:38 Thursday, September 11, 2008 22
The CAPABILITY Procedure
Variable: StudentResid (Studentized Residual)
Moments
N
64 Sum Weights
64
Mean
7.481E-16 Sum Observations 4.7878E-14
Std Deviation
1.0060175 Variance
1.01207122
0.35509779 Kurtosis
2.88124685
Skewness
Uncorrected SS 63.7604866 Corrected SS
63.7604866
Coeff Variation 1.34476E17 Std Error Mean
0.12575219
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std Deviation
1.00602
Median
0.00843 Variance
1.01207
Mode
-0.53738 Range
6.42326
Interquartile Range 0.99986
Tests for Location: Mu0=0
Test
Statistic
Student's t
t
Sign
M
Signed Rank S
p Value
5.95E-15 Pr > |t|
1.0000
0 Pr >= |M| 1.0000
-14 Pr >= |S|
0.9263
Yandell cloning data
Fitting one-way linear model with proc mixed
Residual Normality checking
The CAPABILITY Procedure
Variable: StudentResid (Studentized Residual)
Quantiles (Definition 5)
Quantile
Estimate
100% Max
3.668962576
99%
3.668962576
95%
1.433320159
90%
1.100969632
75% Q3
0.462482142
50% Median
0.008425788
25% Q1
-0.537378035
10%
-1.075692268
5%
-1.391191219
1%
-2.754296478
0% Min
-2.754296478
Extreme Observations
Lowest
Highest
Value Obs
Value Obs
-2.75429648
38 1.33689170
36
-2.40228578
47 1.43332016
16
-2.14483115
48 1.67954041
57
-1.39119122
49 2.26934557
46
-1.24139943
60 3.66896258
50
17:38 Thursday, September 11, 2008 23
Fitting one-way linear model with proc mixed
Residual Normality checking
40
35
30
25
P
e
r
c 20
e
n
t
15
10
5
0
-2.5
-1.5
-0.5
0.5
1.5
Studentized Residual
Curve:
Normal(Mu=75E-17 Sigma=1.006)
2.5
3.5
Yandell cloning data
Fitting one-way linear model with proc mixed
Residual Normality checking
17:38 Thursday, September 11, 2008 25
The CAPABILITY Procedure
Fitted Normal Distribution for StudentResid
Parameters for Normal
Distribution
Parameter Symbol Estimate
Mean
Mu
7.48E-16
Std Dev
Sigma
1.006018
Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
DF
p Value
Kolmogorov-Smirnov D
0.0928020
Pr > D
Cramer-von Mises
W-Sq
0.1347628
Pr > W-Sq
0.039
Anderson-Darling
A-Sq
0.8712849
Pr > A-Sq
0.024
Chi-Square
Chi-Sq 15.3594394
4 Pr > Chi-Sq
0.004
Quantiles for Normal
Distribution
Quantile
Percent Observed Estimated
1.0
-2.75430
-2.340347
5.0
-1.39119
-1.654752
10.0
-1.07569
-1.289263
25.0
-0.53738
-0.678548
50.0
0.00843
0.000000
75.0
0.46248
0.678548
90.0
1.10097
1.289263
95.0
1.43332
1.654752
99.0
3.66896
2.340347
>0.150
Fitting one-way linear model with proc mixed
Residual Normality checking
4
3
S
t
u
d
e
n
t
i
z
e
d
2
1
R 0
e
s
i
d -1
u
a
l
-2
-3
-3
-2
-1
0
1
Normal Quantiles
Normal Line:
Mu=0, Sigma=1
2
3
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
The Mixed Procedure
Model Information
Data Set
WORK.A
Dependent Variable
titer
Covariance Structure
Variance Components
Subject Effect
rep(clone)
Group Effect
type
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
13 1 2 3 4 5 6 7 8 9 10 11 12 13
rep
5 12345
type
6 cult etb odd par res susc
Dimensions
Covariance Parameters
6
Columns in X
14
Columns in Z
0
Subjects
Max Obs Per Subject
64
1
17:38 Thursday, September 11, 2008 27
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
The Mixed Procedure
Number of Observations
Number of Observations Read
64
Number of Observations Used
64
Number of Observations Not Used
0
Iteration History
Iteration Evaluations -2 Res Log Like
Criterion
0
1
723.96458474
1
1
694.58834681 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm Subject
Group
Estimate
Residual
rep(clone) type cult
202600
Residual
rep(clone) type etb
1054.30
Residual
rep(clone) type odd
17691
Residual
rep(clone) type par
57680
Residual
rep(clone) type res
18157
Residual
rep(clone) type susc
34432
17:38 Thursday, September 11, 2008 28
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
The Mixed Procedure
Fit Statistics
-2 Res Log Likelihood
694.6
AIC (smaller is better)
706.6
AICC (smaller is better) 708.5
BIC (smaller is better)
719.5
Null Model Likelihood Ratio
Test
DF Chi-Square Pr > ChiSq
5
29.38
<.0001
Type 3 Tests of Fixed Effects
Effect
clone
Num Den
DF DF F Value Pr > F
12
51
49.73 <.0001
17:38 Thursday, September 11, 2008 29
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual checking
3
Studentized Residual
2
1
0
-1
-2
-3
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Predicted
code
a
h
b
i
c
j
d
k
e
l
f
m
g
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
17:38 Thursday, September 11, 2008 31
The CAPABILITY Procedure
Variable: StudentResid (Studentized Residual)
Moments
N
64 Sum Weights
64
Mean
4.7289E-15 Sum Observations 3.0265E-13
Std Deviation
1.00595807 Variance
1.01195163
Skewness
0.00559096 Kurtosis
-0.0746158
Uncorrected SS 63.7529528 Corrected SS
63.7529528
Coeff Variation 2.12728E16 Std Error Mean
0.12574476
Basic Statistical Measures
Location
Mean
Variability
0.000000 Std Deviation
1.00596
Median 0.015162 Variance
1.01195
Mode
4.90099
. Range
Interquartile Range 1.41944
Tests for Location: Mu0=0
Test
Statistic
Student's t
t
Sign
M
Signed Rank S
p Value
3.76E-14 Pr > |t|
1.0000
0 Pr >= |M| 1.0000
-12 Pr >= |S|
0.9368
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
The CAPABILITY Procedure
Variable: StudentResid (Studentized Residual)
Quantiles (Definition 5)
Quantile
Estimate
100% Max
2.1618474992
99%
2.1618474992
95%
1.8374912960
90%
1.3295369008
75% Q3
0.6912304349
50% Median
0.0151622671
25% Q1
-0.7282112132
10%
-1.1381254465
5%
-1.3790041519
1%
-2.7391439511
0% Min
-2.7391439511
Extreme Observations
Lowest
Highest
Value Obs
Value Obs
-2.73914395
38 1.66654968
5
-1.91500697
24 1.83749130
45
-1.59788728
60 1.94688504
50
-1.37900415
12 1.95151490
23
-1.27474024
47 2.16184750
57
17:38 Thursday, September 11, 2008 32
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
35
30
25
P
e 20
r
c
e
n 15
t
10
5
0
-2.8
-2.0
-1.2
-0.4
0.4
Studentized Residual
Curve:
Normal(Mu=47E-16 Sigma=1.006)
1.2
2.0
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
17:38 Thursday, September 11, 2008 34
The CAPABILITY Procedure
Fitted Normal Distribution for StudentResid
Parameters for Normal
Distribution
Parameter Symbol Estimate
Mean
Mu
4.73E-15
Std Dev
Sigma
1.005958
Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
DF
p Value
Kolmogorov-Smirnov D
0.06175445
Pr > D
>0.150
Cramer-von Mises
W-Sq
0.03167710
Pr > W-Sq
>0.250
Anderson-Darling
A-Sq
0.22583433
Pr > A-Sq
>0.250
Chi-Square
Chi-Sq 4.60658088
4 Pr > Chi-Sq
0.330
Quantiles for Normal
Distribution
Quantile
Percent Observed Estimated
1.0
-2.73914
-2.340208
5.0
-1.37900
-1.654654
10.0
-1.13813
-1.289187
25.0
-0.72821
-0.678508
50.0
0.01516
0.000000
75.0
0.69123
0.678508
90.0
1.32954
1.289187
Yandell cloning data
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
The CAPABILITY Procedure
Fitted Normal Distribution for StudentResid
Quantiles for Normal
Distribution
Quantile
Percent Observed Estimated
95.0
1.83749
1.654654
99.0
2.16185
2.340208
17:38 Thursday, September 11, 2008 35
Fitting one-way linear model with proc mixed
separate residual variance for each type
Residual Normality checking
3
S
t
u
d
e
n
t
i
z
e
d
2
1
0
R
e
s
i -1
d
u
a
l
-2
-3
-3
-2
-1
0
1
Normal Quantiles
Normal Line:
Mu=0, Sigma=1
2
3