1
*******************************************************;
2
*** Example of CRD with 2 levels of error
***;
3
*** From Snedecor & Cochran, 1980 (pg 248)
***;
4
*******************************************************;
5
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
6
DATA CALCIUM; INFILE CARDS MISSOVER;
7
INPUT PLANT LEAF SAMPLE CALCIUM;
8
TITLE1 'CALCIUM CONCENTRATION IN TURNIP LEAVES';
9
TITLE2 '4 PLANTS, 3 LEAVES AND 2
SAMPLES OF 100 MG PER LEAF';
10
CARDS;
NOTE: The data set WORK.CALCIUM has 24
observations and 4 variables.
NOTE: DATA statement used:
real
time 0.06
seconds
cpu
time
0.06 seconds
10 !
RUN;
35
;
36
PROC PRINT; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There were 24 observations read from the
data set WORK.CALCIUM.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
real
time 0.03
seconds
cpu
time
0.02 seconds
CALCIUM CONCENTRATION IN TURNIP LEAVES
4 PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER
LEAF
RAW DATA LISTING
Obs PLANT
LEAF SAMPLE CALCIUM
1
1 1
1
3.28
2
1 1
2 3.09
3
1 2
1
3.52
4
1 2
2
3.48
5
1 3
1
2.88
6
1 3
2
2.80
7
2 1
1
2.46
8
2 1
2
2.44
9
2 2
1
1.87
10
2 2
2
1.92
11
2 3
1
2.19
12
2 3
2
2.19
13
3 1
1
2.77
14
3 1
2
2.66
15
3 2
1
3.74
16
3 2
2
3.44
17
3 3
1
2.55
18
3 3
2
2.55
19
4 1
1
3.78
20
4 1
2
3.87
21
4 2
1
4.07
22
4 2
2
4.12
23
4 3
1
3.31
24
4 3
2
3.31
37
PROC MIXED DATA=CALCIUM cl covtest; CLASSES PLANT LEAF SAMPLE;
38
TITLE3 'Analysis OF Variance with PROC MIXED - Nested Error';
39
MODEL CALCIUM = / htype=1 DDFM=Satterthwaite outp=ResidDataP;
40
RANDOM PLANT LEAF(PLANT);
41
RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 24
observations and 11 variables.
NOTE: The PROCEDURE MIXED printed page 2.
NOTE: PROCEDURE MIXED used:
real
time 0.16
seconds
cpu
time
0.16 seconds
41
! QUIT;
CALCIUM CONCENTRATION IN TURNIP LEAVES
4 PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER
LEAF
Analysis OF Variance with PROC MIXED - Nested
Error
The Mixed Procedure
Model Information
Data Set
WORK.CALCIUM
Dependent Variable
CALCIUM
Covariance Structure Variance
Components
Estimation Method
REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
PLANT
4 1 2 3 4
LEAF
3 1 2 3
SAMPLE
2 1 2
Dimensions
Covariance Parameters
3
Columns in X
1
Columns in Z
16
Subjects
1
Max Obs Per Subject
24
Observations Used
24
Observations Not Used
0
Total Observations
24
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 49.90596741
1
1
2.17294242 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate
Error
Value Pr Z
Alpha
Lower Upper
PLANT
0.3652 0.3440
1.06
0.1442 0.05
0.1042
10.1188
LEAF(PLANT) 0.1611
0.08220 1.96
0.0250 0.05
0.07253 0.6127
Residual 0.006654
0.002717 2.45
0.0072 0.05
0.003422 0.01813
Fit Statistics
-2 Res Log Likelihood
2.2
AIC (smaller is better)
8.2
AICC (smaller is better)
9.4
BIC (smaller is better)
6.3
42
PROC MIXED DATA=CALCIUM cl covtest method=type1;
43
CLASSES PLANT LEAF SAMPLE;
44
TITLE3 'Analysis OF Variance with Type I SS - Nested Error';
45
MODEL CALCIUM = / htype=1 DDFM=Satterthwaite outp=ResidDataP;
46
RANDOM PLANT LEAF(PLANT);
47 RUN;
NOTE: The data set WORK.RESIDDATAP has 24
observations and 11 variables.
NOTE: The PROCEDURE MIXED printed page 3.
NOTE: PROCEDURE MIXED used:
real
time 0.15
seconds
cpu
time
0.15 seconds
47
! QUIT;
CALCIUM CONCENTRATION IN TURNIP LEAVES
4 PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER
LEAF
Analysis OF Variance with Type I SS - Nested
Error
The Mixed Procedure
Model Information
Data Set
WORK.CALCIUM
Dependent Variable
CALCIUM
Covariance Structure
Variance Components
Estimation Method
Type 1
Residual Variance Method Factor
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
PLANT
4 1 2 3 4
LEAF
3 1 2 3
SAMPLE
2 1 2
Dimensions
Covariance Parameters
3
Columns in X
1
Columns in Z
16
Subjects
1
Max Obs Per Subject
24
Observations Used
24
Observations Not Used
0
Total Observations
24
Type 1 Analysis of Variance
Sum of
Error
Source DF
Squares Mean Square Expected Mean Square
Error Term DF
PLANT 3
7.560346 2.520115 Var(Residual) + 2
Var(LEAF(PLANT)) MS(LEAF(PLANT))
8
+
6 Var(PLANT)
LEAF(PLANT) 8
2.630200 0.328775 Var(Residual) + 2
Var(LEAF(PLANT)) MS(Residual)
12
Residual 12
0.079850 0.006654 Var(Residual)
.
.
Type 1 Analysis of Variance
Source
F Value Pr > F
PLANT
7.67 0.0097
LEAF(PLANT)
49.41 <.0001
Residual
. .
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate
Error
Value Pr Z
Alpha
Lower Upper
PLANT
0.3652 0.3440
1.06
0.2884 0.05
-0.3091 1.0395
LEAF(PLANT) 0.1611
0.08220 1.96
0.0501 0.05 -0.00006
0.3222
Residual 0.006654
0.002717 2.45
0.0072 0.05 0.003422
0.01813
Fit Statistics
-2 Res Log Likelihood
2.2
AIC (smaller is better)
8.2
AICC (smaller is better)
9.4
BIC (smaller is better)
6.3
48 proc univariate
data=ResidDataP plot
normal; var resid;
49
TITLE3 'Univariate analysis for PROC MIXED - Nested Error';
50
run;
NOTE: The PROCEDURE UNIVARIATE printed page 4.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.03
seconds
cpu
time
0.03 seconds
CALCIUM
CONCENTRATION IN TURNIP LEAVES
4
PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER LEAF
Univariate
analysis for PROC MIXED - Nested Error
The
UNIVARIATE Procedure
Variable: Resid
Moments
N
24 Sum Weights
24
Mean
0 Sum Observations
0
Std
Deviation 0.05933696
Variance
0.00352087
Skewness
0.380389 Kurtosis
2.28744979
Uncorrected
SS 0.08098011 Corrected SS
0.08098011
Coeff
Variation
. Std Error Mean
0.01211211
Basic Statistical Measures
Location
Variability
Mean 0.00000 Std
Deviation
0.05934
Median -0.00677
Variance
0.00352
Mode -0.00829 Range
0.30000
Interquartile Range 0.05477
NOTE:
The mode displayed is the smallest of 3 modes with a count of 2.
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t 0
Pr > |t| 1.0000
Sign M
-3
Pr >= |M| 0.3075
Signed
Rank S -6
Pr >= |S| 0.8681
Tests
for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk W
0.942796 Pr < W
0.1882
Kolmogorov-Smirnov D
0.144029 Pr > D >0.1500
Cramer-von
Mises W-Sq 0.115831
Pr > W-Sq 0.0676
Anderson-Darling A-Sq
0.644916 Pr > A-Sq 0.0849
Quantiles
(Definition 5)
Quantile Estimate
100%
Max 0.16275988
99%
0.16275988
95%
0.09563256
90%
0.05005051
75%
Q3 0.03032897
50% Median -0.00677133
25%
Q1 -0.02444381
10%
-0.05994949
5%
-0.09436744
1%
-0.13724012
0%
Min -0.13724012
Extreme Observations
-------Lowest------
------Highest------
Value
Obs
Value
Obs
-0.1372401 16
0.0340483 22
-0.0943674 2
0.0485837 20
-0.0599495 14
0.0500505 13
-0.0463500 6
0.0956326 1
-0.0414163 19
0.1627599 15
Stem Leaf
# Boxplot
Normal Probability Plot
1 6
1 0
0.175+
*
1 0
1 |
|
+++++++++
0 55
2 |
|
+++*++*+
0 12333
5 +--+--+
0.025+
++++****+**
-0 43211111100
11
*-----* |
**+****+*+ **
-0 965
3 |
| +*++*+++
-1 4
1 0
-0.125+++++++*++
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by 10**-1
-2 -1
0 +1
+2
51
proc sort data=calcium; by plant leaf; run;
NOTE: There were 24 observations read from the
data set WORK.CALCIUM.
NOTE: The data set WORK.CALCIUM has 24
observations and 4 variables.
NOTE: PROCEDURE SORT used:
real
time 0.04
seconds
cpu
time
0.04 seconds
52
OPTIONS PS=45 LS=88;
53
proc means data=calcium noprint; by plant leaf; var calcium;
54
output out=next1 n=n mean=mean var=var; run;
NOTE: There were 24 observations read from the
data set WORK.CALCIUM.
NOTE: The data set WORK.NEXT1 has 12 observations
and 7 variables.
NOTE: PROCEDURE MEANS used:
real
time 0.04
seconds
cpu
time
0.04 seconds
55
proc plot data=next1; plot var*mean;
56
TITLE3 'Variance/Mean plot for PROC MIXED - Nested Error';
57
run;
57
! OPTIONS PS=256 LS=111;
NOTE: There were 12 observations read from the
data set WORK.NEXT1.
NOTE: The PROCEDURE PLOT printed page 5.
NOTE: PROCEDURE PLOT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
CALCIUM CONCENTRATION IN TURNIP LEAVES
4 PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER
LEAF
Variance/Mean plot for PROC MIXED - Nested Error
Plot of var*mean. Legend: A = 1 obs, B = 2 obs, etc.
var |
0.05 +
|
|
|
A
|
|
0.04 +
|
|
|
|
|
0.03 +
|
|
|
|
|
0.02 +
|
A
|
|
|
|
0.01 +
|
|
A
|
|
A
A
|
A
A
0.00
+
A A A
A A
|
--+------------+------------+------------+------------+------------+------------+--
1.5
2.0 2.5
3.0 3.5
4.0 4.5
mean
59
PROC GLM DATA=CALCIUM; CLASSES PLANT LEAF SAMPLE;
60
TITLE3 'Analysis OF Variance with GLM - Nested Error';
61
MODEL CALCIUM = PLANT LEAF(PLANT);
62
TEST H=PLANT E=LEAF(PLANT) / HTYPE=1 ETYPE=1;
63
RANDOM PLANT LEAF(PLANT);
64
RUN;
NOTE: TYPE I EMS not available without the E1
option.
64
! QUIT;
NOTE: The PROCEDURE GLM printed pages 6-8.
NOTE: PROCEDURE GLM used:
real
time 0.08
seconds
cpu
time
0.08 seconds
CALCIUM CONCENTRATION IN TURNIP LEAVES
4 PLANTS, 3 LEAVES AND 2 SAMPLES OF 100 MG PER
LEAF
Analysis OF Variance with GLM - Nested Error
The GLM Procedure
Class
Level Information
Class
Levels Values
PLANT
4 1 2 3 4
LEAF
3 1 2 3
SAMPLE
2 1 2
Number of observations 24
Dependent Variable: CALCIUM
Sum of
Source
DF Squares
Mean Square F Value
Pr > F
Model
11 10.19054583
0.92641326 139.22
<.0001
Error
12 0.07985000
0.00665417
Corrected Total
23 10.27039583
R-Square Coeff Var
Root MSE CALCIUM Mean
0.992225 2.708195
0.081573 3.012083
Source
DF Type I SS
Mean Square F Value
Pr > F
PLANT
3 7.56034583
2.52011528 378.73
<.0001
LEAF(PLANT)
8 2.63020000
0.32877500 49.41
<.0001
Source
DF Type III SS Mean
Square F Value
Pr > F
PLANT
3 7.56034583
2.52011528 378.73
<.0001
LEAF(PLANT)
8 2.63020000
0.32877500 49.41
<.0001
Tests of Hypotheses Using the Type I MS for
LEAF(PLANT) as an Error Term
Source
DF Type I SS
Mean Square F Value
Pr > F
PLANT
3 7.56034583
2.52011528 7.67
0.0097
Source
Type III Expected Mean Square
PLANT
Var(Error) + 2
Var(LEAF(PLANT)) + 6 Var(PLANT)
LEAF(PLANT)
Var(Error) + 2 Var(LEAF(PLANT))
66
**EXAMPLE 3****************************************************;
67
*** Example of nested design with unequal number
***;
68
*** From Snedecor & Cochran, 1967 (pg 293)
***;
69
***************************************************************;
70
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
71
DATA WHEAT; INFILE CARDS MISSOVER;
72
INPUT YIELD FIELD FARM DISTRICT $;
73
TITLE1 'Wheat yields (g / 0.00009 acre)';
74
TITLE2 'CRD with unequal experimental and sampling units)';
75
CARDS;
NOTE: The data set WORK.WHEAT has 36 observations
and 4 variables.
NOTE: DATA statement used:
real
time 0.03
seconds
cpu
time
0.03 seconds
75
! RUN;
112
;
113
PROC PRINT; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There were 36 observations read from the
data set WORK.WHEAT.
NOTE: The PROCEDURE PRINT printed page 9.
NOTE: PROCEDURE PRINT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
Wheat yields (g / 0.00009 acre)
CRD with unequal number of experimental and
sampling units)
RAW DATA LISTING
Obs YIELD
FIELD FARM DISTRICT
1 23 1
1 A
2 19 2
1 A
3 31 1
2 A
4 37 2
2 A
5 33 1
1 B
6 29 2
1 B
7 29 1
2 B
8 36 1
1 C
9 29 2
1 C
10
33 3
1
C
11
11 1
1
D
12
21 2
1
D
13
23 1
2
D
14
18 2
2
D
15
33 1
3
D
16
23 1
4
D
17
26 1
5
D
18
39 1
6
D
19
20 1
7
D
20
24 1
8
D
21
36 1
9
D
22
25 1
1
E
23
33 2
1
E
24
28 1
1
F
25
31 2
1
F
26
25 1
2
F
27
42 2
2
F
28
32 1
3
F
29
36 2
3
F
30
41 1
4
F
31
35 1
5
F
32 16
1 6
F
33
30 1
7
F
34
40 1
8
F
35
32 1
9
F
36
44 1
10
F
114
PROC MIXED DATA=WHEAT cl COVTEST; CLASSES FIELD FARM DISTRICT;
115
TITLE3 'ANOVA with PROC MIXED - unequal sized nested Errors';
116
MODEL YIELD = / htype=1 DDFM=Satterthwaite outp=ResidDataP;
117
RANDOM DISTRICT FARM(DISTRICT);
118
RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 36
observations and 11 variables.
NOTE: The PROCEDURE MIXED printed page 10.
NOTE: PROCEDURE MIXED used:
real
time 0.16
seconds
cpu
time
0.14 seconds
118
! QUIT;
Wheat yields (g / 0.00009 acre)
CRD with unequal number of experimental and
sampling units)
ANOVA with PROC MIXED - unequal sized nested
Errors
The Mixed Procedure
Model Information
Data Set
WORK.WHEAT
Dependent Variable
YIELD
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
FIELD
3 1 2 3
FARM
10 1 2 3 4 5 6 7 8 9 10
DISTRICT
6 A B C D E F
Dimensions
Covariance Parameters
3
Columns in X
1
Columns in Z
31
Subjects
1
Max Obs Per Subject
36
Observations Used
36
Observations Not Used
0
Total Observations
36
Iteration History
Iteration
Evaluations -2 Res Log Like
Criterion
0
1 246.55907914
1
3 243.48928235
0.00694802
2
2 242.71561388
0.00192010
3
1 242.51666454
0.00017057
4
1
242.50058397 0.00000150
5
1 242.50044987
0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate
Error
Value Pr Z
Alpha
Lower Upper
DISTRICT
6.3148 9.1543
0.69 0.2452
0.05
1.2289 9022.02
FARM(DISTRICT) 26.0928
18.6720 1.40
0.0811 0.05
9.2820 223.79
Residual 29.8395
13.2217
2.26 0.0120
0.05
14.6468 90.6929
Fit Statistics
-2 Res Log Likelihood
242.5
AIC (smaller is better)
248.5
AICC (smaller is better) 249.3
BIC (smaller is better)
247.9
119
PROC MIXED DATA=WHEAT cl COVTEST method=TYPE1;
120
CLASSES FIELD FARM DISTRICT;
121
TITLE3 'ANOVA with Type I SS - unequal sized nested Errors';
122
MODEL YIELD = / htype=1 DDFM=Satterthwaite outp=ResidDataP;
123
RANDOM DISTRICT FARM(DISTRICT);
124
RUN;
NOTE: Estimated G matrix is not positive
definite.
NOTE: The data set WORK.RESIDDATAP has 36
observations and 11 variables.
NOTE: The PROCEDURE MIXED printed page 11.
NOTE: PROCEDURE MIXED used:
real
time 0.17
seconds
cpu
time
0.17 seconds
124
! QUIT;
Wheat yields (g / 0.00009 acre)
CRD with unequal number of experimental and
sampling units)
ANOVA with Type I SS - unequal sized nested
Errors
The Mixed Procedure
Model
Information
Data Set
WORK.WHEAT
Dependent Variable
YIELD
Covariance Structure
Variance Components
Estimation Method
Type 1
Residual Variance Method Factor
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
FIELD
3 1 2 3
FARM
10 1 2 3 4 5 6 7 8 9 10
DISTRICT
6 A B C D E F
Dimensions
Covariance Parameters
3
Columns in X
1
Columns in Z
31
Subjects
1
Max Obs Per Subject
36
Observations Used
36
Observations Not Used
0
Total Observations
36
Type 1 Analysis of Variance
Sum of
Source
DF Squares
Mean Square Expected Mean Square
DISTRICT
5 461.422106 92.284421
Var(Residual) + 1.965 Var(FARM(DISTRICT))
+ 5.3778 Var(DISTRICT)
FARM(DISTRICT) 19
1349.383450 71.020182 Var(Residual) +
1.2899 Var(FARM(DISTRICT))
Residual
11 310.166667 28.196970
Var(Residual)
Type 1 Analysis of Variance
Error
Source Error Term
DF F Value Pr > F
DISTRICT 1.5234
MS(FARM(DISTRICT)) - 0.5234
MS(Residual) 13.729
0.99
0.4601
FARM(DISTRICT) MS(Residual)
11 2.52 0.0597
Residual .
. .
.
Covariance Parameter Estimates
Standard
Z
Cov Parm Estimate
Error
Value Pr Z Alpha
Lower Upper
DISTRICT -0.2137
3.7702
-0.06 0.9548 0.05
-7.6031 7.1757
FARM(DISTRICT) 33.1988
24.0001 1.38
0.1666 0.05 -13.8405
80.2380
Residual 28.1970
13.3949 2.11
0.0176 0.05
14.1499
81.2859
Fit Statistics
-2 Res Log Likelihood
243.6
AIC (smaller is better)
249.6
AICC (smaller is better) 250.4
BIC (smaller is better)
249.0
125
proc univariate data=ResidDataP plot normal; var resid;
126
TITLE3 'Univariate analysis for PROC MIXED - unequal nested Errors';
127
run;
NOTE: The PROCEDURE UNIVARIATE printed page 12.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.03
seconds
cpu
time
0.03 seconds
Wheat
yields (g / 0.00009 acre)
CRD
with unequal number of experimental and sampling units)
Univariate
analysis for PROC MIXED - unequal nested Errors
The
UNIVARIATE Procedure
Variable: Resid
Moments
N
36 Sum Weights
36
Mean
0 Sum Observations
0
Std
Deviation 4.11793027
Variance
16.9573497
Skewness
-0.059663 Kurtosis
-0.1028235
Uncorrected
SS 593.50724 Corrected
SS 593.50724
Coeff
Variation
. Std Error Mean
0.68632171
Basic Statistical Measures
Location
Variability
Mean 0.00000 Std
Deviation
4.11793
Median -0.07467
Variance
16.95735
Mode .
Range
18.79915
Interquartile Range 5.91856
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t 0
Pr > |t| 1.0000
Sign M
0
Pr >= |M| 1.0000
Signed
Rank S
1
Pr >= |S| 0.9877
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk W
0.994152 Pr < W
0.9994
Kolmogorov-Smirnov D
0.053846 Pr > D >0.1500
Cramer-von
Mises W-Sq 0.015867
Pr > W-Sq >0.2500
Anderson-Darling A-Sq
0.114678 Pr > A-Sq >0.2500
Quantiles
(Definition 5)
Quantile Estimate
100%
Max 9.647650
99%
9.647650
95%
6.590515
90%
4.753452
75%
Q3 3.042826
50%
Median -0.074667
25%
Q1 -2.875738
10%
-5.310128
5%
-7.352350
1%
-9.151499
0%
Min -9.151499
Extreme
Observations
------Lowest-----
-----Highest-----
Value
Obs Value
Obs
-9.15150 11
4.24802 4
-7.35235 26
4.75345 34
-6.26893 32
5.21272 30
-5.31013 14
6.59052 36
-4.62705 2
9.64765 27
Stem Leaf
# Boxplot
Normal Probability Plot
8 6
1 |
9+
+*+++
6 6
1 |
|
++*++
4 02282
5 |
|
**+*+*
2 45838
5 +-----+
3+
*****
0 280145
6 |
+ | |
*****
-0 88657643
8 *-----* |
******
-2 207
3 +-----+
-3+
+***+
-4 3662
4 |
| +*+***
-6 43
2
| |
++*+*
-8 2
1 |
-9+ +++*+
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
-2
-1 0
+1 +2
128
proc sort data=WHEAT; by district farm; run;
NOTE: There were 36 observations read from the
data set WORK.WHEAT.
NOTE: The data set WORK.WHEAT has 36 observations
and 4 variables.
NOTE: PROCEDURE SORT used:
real
time 0.03
seconds
cpu
time
0.03 seconds
128
!
OPTIONS PS=45 LS=88;
129
proc means data=WHEAT noprint; by district farm; var yield;
130 output
out=next2 n=n mean=mean var=var;
run;
NOTE: There were 36 observations read from the
data set WORK.WHEAT.
NOTE: The data set WORK.NEXT2 has 25 observations
and 7 variables.
NOTE: PROCEDURE MEANS used:
real
time 0.04
seconds
cpu time
0.04 seconds
131
proc plot data=next2; plot var*mean;
132
TITLE3 'Variance/Mean plot for PROC MIXED - unequal nested Errors';
133
run; OPTIONS PS=256 LS=111;
NOTE: There were 25 observations read from the
data set WORK.NEXT2.
NOTE: The PROCEDURE PLOT printed page 13.
NOTE: PROCEDURE PLOT used:
real
time 0.02
seconds
cpu
time
0.02 seconds
Wheat yields (g / 0.00009 acre)
CRD with unequal number of experimental and
sampling units)
Variance/Mean plot for PROC MIXED - unequal
nested Errors
Plot of var*mean. Legend: A = 1
obs, B = 2 obs, etc.
var |
150 +
|
A
|
|
|
125 +
|
|
|
|
100 +
|
|
|
|
75 +
|
|
|
|
50 + A
|
|
|
|
A
25 +
|
A
|
A
|
A
A
A A
|
A
0 +
|
---+------------+------------+------------+------------+------------+------------+--
15 20
25 30
35 40
45
mean
NOTE: 15 obs had missing values.
135
PROC GLM DATA=WHEAT; CLASSES FIELD FARM DISTRICT;
136
TITLE3 'ANOVA with GLM - unequal sized nested Errors';
137
MODEL YIELD = DISTRICT FARM(DISTRICT);
138
TEST H=DISTRICT E=FARM(DISTRICT) / HTYPE=1 ETYPE=1;
139
RANDOM DISTRICT FARM(DISTRICT) / TEST;
140
RUN;
NOTE: TYPE I EMS not available without the E1
option.
140
! QUIT;
NOTE: The PROCEDURE GLM printed pages 14-17.
NOTE: PROCEDURE GLM used:
real
time 0.08
seconds
cpu
time
0.08 seconds
Wheat yields (g / 0.00009 acre)
CRD with unequal number of experimental and
sampling units)
ANOVA with GLM - unequal sized nested Errors
The GLM Procedure
Class Level Information
Class
Levels Values
FIELD
3 1 2 3
FARM
10 1 2 3 4 5 6 7 8 9 10
DISTRICT
6 A B C D E F
Number of observations 36
Dependent Variable: YIELD
Sum
of
Source
DF Squares
Mean Square F Value
Pr > F
Model
24 1810.805556
75.450231 2.68
0.0459
Error
11 310.166667
28.196970
Corrected Total
35 2120.972222
R-Square Coeff Var
Root MSE YIELD Mean
0.853762 17.98334
5.310082 29.52778
Source
DF Type I SS
Mean Square F Value
Pr > F
DISTRICT
5
461.422106 92.284421
3.27
0.0471
FARM(DISTRICT)
19 1349.383450
71.020182 2.52
0.0597
Source
DF Type III SS Mean
Square F Value
Pr > F
DISTRICT
5
324.470997 64.894199
2.30
0.1158
FARM(DISTRICT)
19 1349.383450
71.020182 2.52
0.0597
Tests of Hypotheses Using the Type I MS for
FARM(DISTRICT) as an Error Term
Source
DF
Type I SS Mean Square F Value
Pr > F
DISTRICT
5 461.4221057
92.2844211 1.30
0.3056
Source
Type III Expected Mean Square
DISTRICT
Var(Error) + 1.8302
Var(FARM(DISTRICT)) + 5.0601 Var(DISTRICT)
FARM(DISTRICT)
Var(Error) + 1.2899
Var(FARM(DISTRICT))
Tests of Hypotheses for Random
Model Analysis of Variance
Dependent Variable: YIELD
Source
DF Type III SS Mean
Square F Value
Pr > F
DISTRICT
5 324.470997
64.894199 0.73
0.6126
Error
14.464 1286.672238
88.958186
Error: 1.4189*MS(FARM(DISTRICT))
- 0.4189*MS(Error)
Source
DF Type III SS Mean
Square F Value Pr > F
FARM(DISTRICT)
19 1349.383450
71.020182 2.52
0.0597
Error: MS(Error)
11 310.166667
28.196970
143
**EXAMPLE 4*****************************************************;
144
*** Example of RBD
***;
145
*** From Snedecor & Cochran, 1980 (pg 256)
***;
146
****************************************************************;
147
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
148
DATA SOYBEAN; INFILE CARDS MISSOVER;
149
INPUT treatment $ BLOCK FAILURES;
150
TITLE1 'FAILURES TO GERMINATE OF SOYBEAN PLANTS';
151
TITLE2 '4 TREATMENTS AND A CONTROL, 5 BLOCKS';
152
CARDS;
NOTE: The data set WORK.SOYBEAN has 25
observations and 3 variables.
NOTE: DATA statement used:
real
time 0.03
seconds
cpu
time
0.03 seconds
152
! RUN;
178
;
179
PROC PRINT; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There were 25 observations read from the
data set WORK.SOYBEAN.
NOTE: The PROCEDURE PRINT printed page 18.
NOTE: PROCEDURE PRINT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
FAILURES TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
RAW DATA LISTING
Obs
treatment BLOCK FAILURES
1 CHECK
1 8
2 CHECK
2 10
3 CHECK
3 12
4 CHECK
4
13
5 CHECK
5 11
6 ARASAN
1 2
7 ARASAN
2 6
8 ARASAN
3 7
9 ARASAN
4 11
10 ARASAN
5 5
11 SPERGON
1
4
12 SPERGON
2
10
13 SPERGON
3 9
14 SPERGON
4 8
15 SPERGON
5
10
16 SEMESAN
1 3
17 SEMESAN
2 5
18 SEMESAN
3 9
19 SEMESAN
4
10
20 SEMESAN
5 6
21 FERMATE
1 9
22 FERMATE
2 7
23 FERMATE
3 5
24 FERMATE
4 5
25 FERMATE
5 3
180 PROC MIXED DATA=SOYBEAN
cl COVTEST; CLASSES treatment BLOCK;
181
TITLE3 'ANOVA with PROC MIXED - RBD without reps';
182
MODEL FAILURES = treatment /
htype=3 DDFM=Satterthwaite outp=ResidDataP;
183
RANDOM BLOCK;
184
lsmeans treatment / pdiff adjust=tukey;
185
RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 25
observations and 10 variables.
NOTE: The PROCEDURE MIXED printed page 19.
NOTE: PROCEDURE MIXED used:
real
time 0.20
seconds
cpu
time
0.20 seconds
185
! QUIT;
FAILURES TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
ANOVA with PROC MIXED - RBD without reps
The Mixed Procedure
Model Information
Data Set
WORK.SOYBEAN
Dependent Variable
FAILURES
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
treatment
5 ARASAN CHECK FERMATE SEMESAN
SPERGON
BLOCK
5 1 2 3 4 5
Dimensions
Covariance Parameters
2
Columns in X
6
Columns in Z
5
Subjects
1
Max Obs Per Subject
25
Observations Used
25
Observations Not Used
0
Total Observations
25
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 103.20192033
1
1 101.90681043
0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate
Error
Value Pr Z
Alpha
Lower Upper
BLOCK 1.4100
1.8032 0.78
0.2171 0.05
0.3075 430.52
Residual 5.4100
1.9127 2.83
0.0023 0.05
3.0008
12.5310
Fit Statistics
-2 Res Log Likelihood
101.9
AIC (smaller is better)
105.9
AICC (smaller is better) 106.6
BIC (smaller is better)
105.1
Type
3 Tests of Fixed Effects
Num Den
Effect
DF DF F Value
Pr > F
treatment
4 16
3.87
0.0219
Least Squares
Means
Standard
Effect treatment
Estimate Error
DF
t Value Pr > |t|
treatment
ARASAN 6.2000
1.1679
17.1 5.31
<.0001
treatment
CHECK 10.8000
1.1679
17.1 9.25
<.0001
treatment
FERMATE 5.8000
1.1679
17.1 4.97
0.0001
treatment
SEMESAN 6.6000
1.1679
17.1 5.65
<.0001
treatment
SPERGON 8.2000
1.1679
17.1 7.02
<.0001
Differences of Least Squares Means
Standard
Effect treatment _treatment
Estimate Error DF
t Value Pr > |t| Adjustment
Adj P
treatment ARASAN
CHECK -4.6000
1.4711
16 -3.13 0.0065
Tukey-Kramer 0.0443
treatment ARASAN
FERMATE 0.4000
1.4711
16 0.27 0.7892
Tukey-Kramer 0.9987
treatment ARASAN
SEMESAN -0.4000
1.4711
16 -0.27 0.7892
Tukey-Kramer 0.9987
treatment ARASAN
SPERGON -2.0000
1.4711
16 -1.36 0.1928
Tukey-Kramer 0.6602
treatment CHECK
FERMATE 5.0000
1.4711
16 3.40 0.0037
Tukey-Kramer 0.0261
treatment CHECK
SEMESAN 4.2000
1.4711 16 2.86
0.0115 Tukey-Kramer 0.0740
treatment CHECK
SPERGON 2.6000
1.4711
16 1.77 0.0962
Tukey-Kramer 0.4242
treatment FERMATE
SEMESAN -0.8000
1.4711
16 -0.54 0.5941
Tukey-Kramer 0.9812
treatment FERMATE
SPERGON -2.4000
1.4711
16 -1.63 0.1223
Tukey-Kramer 0.4999
treatment SEMESAN
SPERGON -1.6000
1.4711
16 -1.09 0.2929
Tukey-Kramer 0.8102
186
proc univariate data=ResidDataP plot normal; var resid;
187
TITLE3 'Univariate analysis for PROC MIXED - RBD without reps';
188
run;
NOTE: The PROCEDURE UNIVARIATE printed page 20.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.03
seconds
cpu
time
0.03 seconds
FAILURES TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
Univariate analysis for PROC MIXED - RBD without
reps
The UNIVARIATE Procedure
Variable:
Resid
Moments
N
25 Sum Weights
25
Mean
0 Sum Observations
0
Std Deviation
1.99954014 Variance
3.99816078
Skewness
0.48805915 Kurtosis
-0.3291607
Uncorrected SS
95.9558587 Corrected SS
95.9558587
Coeff Variation
. Std Error Mean
0.39990803
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std Deviation
1.99954
Median
-0.24526 Variance
3.99816
Mode
. Range
7.40000
Interquartile Range 2.64205
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 0
Pr > |t| 1.0000
Sign
M -0.5 Pr >= |M|
1.0000
Signed Rank
S -8.5 Pr >= |S|
0.8244
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk W
0.963523 Pr < W
0.4890
Kolmogorov-Smirnov D
0.103754 Pr > D >0.1500
Cramer-von Mises W-Sq
0.033262 Pr > W-Sq >0.2500
Anderson-Darling A-Sq
0.249495 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile
Estimate
100% Max
4.512681
99%
4.512681
95%
3.736276
90%
2.336276
75% Q3
1.154735
50% Median
-0.245265
25% Q1
-1.487319
10%
-2.505778
5%
-2.887319
1%
-2.887319
0% Min
-2.887319
Extreme Observations
------Lowest-----
-----Highest-----
Value Obs
Value Obs
-2.88732
11 1.90209
18
-2.88732
6 2.09422
15
-2.50578
25 2.33628
19
-2.28732
16 3.73628
9
-1.86372
24 4.51268
21
Stem Leaf
# Boxplot
Normal Probability Plot
4 5
1 |
4.5+
*+++++
3 7
1 |
|
*+++++
2 13
2 |
|
*+*++
1 1289
4 +-----+ |
**+**+
0 3357
4 |
+ | |
+****+
-0 9832
4 *-----* |
++****
-1 96533
5 +-----+ |
+**+***
-2 9953
4 |
-2.5+ * *+*+*
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
189
PROC CHART DATA=SOYBEAN; OPTIONS PS=45 LS=88;
190
TITLE3 'Histogram of MIXED analysis - RBD without reps';
191
VBAR treatment / SUMVAR=FAILURES TYPE=MEAN; RUN;
NOTE: The PROCEDURE CHART printed page 21.
NOTE: PROCEDURE CHART used:
real
time 0.00
seconds
cpu
time
0.00 seconds
191
!
OPTIONS PS=256 LS=111;
FAILURES TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
Histogram of MIXED analysis - RBD without reps
FAILURES Mean
|
*****
|
*****
10 +
*****
|
*****
|
*****
|
*****
8 +
*****
*****
|
*****
*****
|
*****
*****
|
*****
***** *****
6 + *****
***** *****
***** *****
| *****
***** *****
***** *****
| *****
***** *****
*****
*****
| *****
***** *****
***** *****
4 + *****
***** *****
***** *****
| *****
***** *****
***** *****
| *****
***** *****
***** *****
| *****
***** *****
***** *****
2 + *****
***** *****
***** *****
| *****
***** *****
***** *****
| *****
***** *****
***** *****
| *****
***** *****
***** *****
--------------------------------------------------------------------
ARASAN CHECK
FERMATE SEMESAN
SPERGON
treatment
193
PROC GLM DATA=SOYBEAN; CLASSES treatment BLOCK;
194
TITLE3 'ANOVA with PROC GLM - RBD without reps';
195
MODEL FAILURES = treatment BLOCK;
196
RANDOM treatment BLOCK / TEST;
197
means treatment / tukey;
198
lsmeans treatment / pdiff stderr adjust=tukey;
199
RUN;
NOTE: TYPE I EMS not available without the E1
option.
NOTE: Means from the MEANS statement are not
adjusted for other terms in the model.
For adjusted means, use
the
LSMEANS statement.
199
! QUIT;
NOTE: The PROCEDURE GLM printed pages 22-27.
NOTE: PROCEDURE GLM used:
real
time 0.21
seconds
cpu
time
0.15 seconds
FAILURES TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
ANOVA with PROC GLM - RBD without reps
The GLM Procedure
Class Level Information
Class
Levels Values
treatment 5
ARASAN CHECK FERMATE SEMESAN SPERGON
BLOCK
5 1 2 3 4 5
Number of observations 25
FAILURES
TO GERMINATE OF SOYBEAN PLANTS
4 TREATMENTS AND A CONTROL, 5 BLOCKS
ANOVA with PROC GLM - RBD without reps
The GLM Procedure
Dependent Variable: FAILURES
Sum of
Source
DF Squares
Mean Square F Value Pr > F
Model
8 133.6800000
16.7100000 3.09
0.0262
Error
16 86.5600000
5.4100000
Corrected Total
24 220.2400000
R-Square Coeff Var
Root MSE FAILURES Mean
0.606974 30.93006
2.325941 7.520000
Source
DF Type I SS
Mean Square F Value
Pr > F
treatment
4 83.84000000
20.96000000 3.87
0.0219
BLOCK
4 49.84000000
12.46000000 2.30
0.1032
Source
DF Type III SS Mean
Square F Value
Pr > F
treatment
4 83.84000000
20.96000000 3.87
0.0219
BLOCK
4 49.84000000
12.46000000 2.30
0.1032
Source
Type III Expected Mean Square
treatment
Var(Error) + 5 Var(treatment)
BLOCK
Var(Error) + 5 Var(BLOCK)
FAILURES TO GERMINATE OF SOYBEAN
PLANTS
4 TREATMENTS AND A CONTROL, 5
BLOCKS
ANOVA with PROC GLM - RBD without
reps
The GLM Procedure
Tests of Hypotheses for Random
Model Analysis of Variance
Dependent Variable: FAILURES
Source
DF Type III SS Mean
Square F Value
Pr > F
treatment
4 83.840000
20.960000 3.87
0.0219
BLOCK
4 49.840000
12.460000 2.30
0.1032
Error: MS(Error)
16 86.560000
5.410000
Tukey's Studentized Range (HSD) Test for FAILURES
NOTE: This test controls the Type I
experimentwise error rate, but it generally has a higher Type II error
rate than REGWQ.
Alpha
0.05
Error Degrees of Freedom
16
Error Mean Square
5.41
Critical Value of Studentized Range 4.33269
Minimum Significant Difference
4.5068
Means with the same letter are not significantly
different.
Tukey Grouping
Mean N treatment
A 10.800
5
CHECK
A
B A
8.200 5 SPERGON
B A
B A
6.600 5 SEMESAN
B
B
6.200 5
ARASAN
B
B
5.800 5
FERMATE
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
FAILURES Standard
LSMEAN
treatment
LSMEAN Error
Pr > |t| Number
ARASAN
6.2000000 1.0401923
<.0001 1
CHECK
10.8000000 1.0401923
<.0001 2
FERMATE
5.8000000 1.0401923
<.0001 3
SEMESAN
6.6000000 1.0401923
<.0001 4
SPERGON
8.2000000 1.0401923
<.0001 5
Least Squares Means for effect treatment
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable:
FAILURES
i/j
1
2
3
4
5
1
0.0443
0.9987 0.9987
0.6602
2 0.0443
0.0261 0.0740
0.4242
3 0.9987
0.0261
0.9812 0.4999
4 0.9987
0.0740 0.9812
0.8102
5 0.6602
0.4242 0.4999
0.8102
203
**EXAMPLE 5********************************************;
204
*** Example of RBD with sampling error
***;
205
*** From Snedecor & Cochran, 1980 (pg 267)
***;
206
*******************************************************;
207
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
208
DATA FUMIGANT; INFILE CARDS MISSOVER;
209
INPUT FUMIGANT $ BLOCK $ W1 W2 W3 W4;
210
TITLE1 'Number of wire worms
found for 2 fumigants and a control';
211
TITLE2 'Fumigants are C and S, control is 0, 5 BLOCKS';
212
REP=1; WORMS=W1; LWORMS=LOG(WORMS+1);
OUTPUT;
213
REP=2; WORMS=W2; LWORMS=LOG(WORMS+1);
OUTPUT;
214
REP=3; WORMS=W3; LWORMS=LOG(WORMS+1);
OUTPUT;
215
REP=4; WORMS=W4; LWORMS=LOG(WORMS+1);
OUTPUT;
216
KEEP FUMIGANT BLOCK REP WORMS LWORMS;
217
CARDS;
NOTE: The data set WORK.FUMIGANT has 60
observations and 5 variables.
NOTE: DATA statement used:
real
time 0.04
seconds
cpu
time
0.04 seconds
217
! RUN;
233
;
234
PROC PRINT; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There were 60 observations read from the
data set WORK.FUMIGANT.
NOTE: The PROCEDURE PRINT printed page 28.
NOTE: PROCEDURE PRINT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
RAW DATA LISTING
Obs FUMIGANT
BLOCK REP WORMS
LWORMS
1 C
I 1
5 1.79176
2 C
I 2
4 1.60944
3 C
I 3
5 1.79176
4 C
I 4
2 1.09861
5 C
II 1
0 0.00000
6 C
II 2
9 2.30259
7 C
II 3
3 1.38629
8 C
II
4 3
1.38629
9 C
III 1
4 1.60944
10
C III
2
4 1.60944
11
C III
3
3 1.38629
12
C III
4
9 2.30259
13
C IV
1 7
2.07944
14
C IV
2
3 1.38629
15
C IV
3
5 1.79176
16
C IV
4
12 2.56495
17
C V
1
4 1.60944
18
C V
2
9 2.30259
19
C V
3
8 2.19722
20
C V
4
6 1.94591
21
S I
1
5 1.79176
22
S I
2
5 1.79176
23 S
I 3
1
0.69315
24
S I
4
2 1.09861
25
S II
1
6 1.94591
26
S II
2
4 1.60944
27
S II
3
5 1.79176
28
S II
4
4 1.60944
29
S III
1
2 1.09861
30
S III
2
9 2.30259
31
S III
3
3 1.38629
32
S III
4
7 2.07944
33
S IV
1
6 1.94591
34
S IV
2
4 1.60944
35
S IV
3
8 2.19722
36
S IV
4
4 1.60944
37
S V
1
2 1.09861
38
S V
2
9 2.30259
39
S V
3
7 2.07944
40
S V
4
3 1.38629
41
0 I
1
12 2.56495
42
0 I
2
20 3.04452
43
0 I
3
8 2.19722
44
0 I
4
8 2.19722
45
0 II
1
7 2.07944
46
0 II
2
4 1.60944
47
0 II
3
4 1.60944
48
0 II
4
5 1.79176
49
0 III
1
9 2.30259
50
0 III
2
6 1.94591
51
0 III
3
7 2.07944
52
0 III
4
11 2.48491
53
0 IV
1
12 2.56495
54
0 IV
2
22 3.13549
55
0 IV
3
17 2.89037
56
0 IV
4
13 2.63906
57
0 V
1
7 2.07944
58
0 V
2
8 2.19722
59
0 V
3
5 1.79176
60
0 V
4
9 2.30259
235
PROC mixed DATA=FUMIGANT cl COVTEST; CLASSES FUMIGANT BLOCK REP;
236
TITLE3 'ANOVA with PROC MIXED - RBD with reps';
237
MODEL WORMS = FUMIGANT / htype=3
DDFM=Satterthwaite outp=ResidDataP outpM=ResidDataPM;
238
RANDOM BLOCK FUMIGANT*BLOCK;
239
lsmeans fumigant / pdiff ADJUST=DUNNETT diff=controll('0');
240
lsmeans fumigant / pdiff ADJUST=tukey;
241
RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 60
observations and 12 variables.
NOTE: The data set WORK.RESIDDATAPM has 60
observations and 12 variables.
NOTE: The PROCEDURE MIXED printed page 29.
NOTE: PROCEDURE MIXED used:
real
time 0.22
seconds
cpu
time
0.22 seconds
241
! QUIT;
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
ANOVA with PROC MIXED - RBD with reps
The Mixed Procedure
Model Information
Data Set
WORK.FUMIGANT
Dependent Variable
WORMS
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
FUMIGANT
3 0 C S
BLOCK 5
I II III IV V
REP
4 1 2 3 4
Dimensions
Covariance Parameters
3
Columns in X
4
Columns in Z
20
Subjects
1
Max Obs Per Subject
60
Observations Used
60
Observations Not Used
0
Total Observations
60
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 318.17726625
1
1 310.27325992
0.00000000
Convergence criteria met.
Covariance
Parameter Estimates
Standard Z
Cov
Parm
Estimate Error
Value Pr Z
Alpha
Lower Upper
BLOCK
1.1052 2.4502
0.45
0.3260 0.05
0.1473
25730931
FUMIGANT*BLOCK 3.8559
3.1035 1.24
0.1070 0.05
1.2517
50.5437
Residual
9.1056 1.9196
4.74
<.0001 0.05
6.2643 14.4450
Fit Statistics
-2 Res Log Likelihood
310.3
AIC (smaller is better)
316.3
AICC (smaller is better) 316.7
BIC (smaller is better)
315.1
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF F Value
Pr > F
FUMIGANT
2 8
5.98
0.0258
Least Squares Means
Standard
Effect
FUMIGANT Estimate
Error DF
t Value Pr > |t|
FUMIGANT
0
9.7000 1.2031
11.5 8.06
<.0001
FUMIGANT
C
5.2500 1.2031
11.5 4.36
0.0010
FUMIGANT
S
4.8000 1.2031
11.5 3.99
0.0020
FUMIGANT
0
9.7000
1.2031
11.5 8.06
<.0001
FUMIGANT
C
5.2500 1.2031
11.5 4.36
0.0010
FUMIGANT
S
4.8000 1.2031
11.5 3.99
0.0020
Differences
of Least Squares Means
Standard
Effect FUMIGANT
_FUMIGANT Estimate Error
DF t Value Tails
Pr t Adjustment Adj P
FUMIGANT 0
C
4.4500 1.5662
8 2.84 Upper
0.0109 Dunnett-Hsu 0.0194
FUMIGANT 0
S
4.9000 1.5662
8 3.13 Upper
0.0070 Dunnett-Hsu 0.0126
FUMIGANT 0
C
4.4500 1.5662
8 2.84 Both
0.0218 Tukey-Kramer 0.0512
FUMIGANT 0
S 4.9000
1.5662
8 3.13 Both
0.0140 Tukey-Kramer 0.0336
FUMIGANT C
S
0.4500 1.5662
8 0.29 Both
0.7812 Tukey-Kramer 0.9558
242
proc print data=residdataP; TITLE4 'Output from the OUTP option'; run;
NOTE: There were 60 observations read from the
data set WORK.RESIDDATAP.
NOTE: The PROCEDURE PRINT printed page 30.
NOTE: PROCEDURE PRINT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
Number
of wire worms found for 2 fumigants and a control
Fumigants
are C and S, control is 0, 5 BLOCKS
ANOVA
with PROC MIXED - RBD with reps
Output
from the OUTP option
StdErr
Obs FUMIGANT
BLOCK REP WORMS
LWORMS Pred Pred
DF Alpha Lower
Upper Resid
1 C I
1 5 1.79176
4.4423 1.29594 49.6771
0.05 1.8389 7.0457
0.55770
2 C I
2 4 1.60944
4.4423 1.29594 49.6771
0.05 1.8389 7.0457 -0.44230
3 C I
3 5 1.79176
4.4423 1.29594 49.6771
0.05 1.8389 7.0457
0.55770
4 C I
4 2 1.09861
4.4423 1.29594 49.6771
0.05 1.8389 7.0457
-2.44230
5 C II
1 0 0.00000
4.0354 1.29594 49.6771
0.05 1.4320 6.6388
-4.03542
6 C II
2 9 2.30259
4.0354 1.29594 49.6771
0.05 1.4320 6.6388
4.96458
7 C II
3 3 1.38629
4.0354 1.29594 49.6771
0.05 1.4320 6.6388
-1.03542
8 C II
4 3 1.38629
4.0354 1.29594 49.6771
0.05 1.4320 6.6388
-1.03542
9 C III
1 4 1.60944
5.0385 1.29594 49.6771
0.05 2.4351 7.6419
-1.03852
10
C III 2
4 1.60944 5.0385
1.29594 49.6771 0.05
2.4351 7.6419 -1.03852
11
C III 3
3 1.38629 5.0385
1.29594 49.6771 0.05
2.4351 7.6419 -2.03852
12
C III 4
9 2.30259 5.0385
1.29594 49.6771 0.05
2.4351 7.6419 3.96148
13
C IV 1
7 2.07944 6.5623
1.29594 49.6771 0.05
3.9589 9.1657 0.43771
14
C IV 2
3 1.38629 6.5623
1.29594 49.6771 0.05
3.9589 9.1657 -3.56229
15
C IV 3
5 1.79176 6.5623
1.29594 49.6771 0.05
3.9589 9.1657 -1.56229
16
C IV 4
12 2.56495 6.5623
1.29594 49.6771 0.05
3.9589 9.1657 5.43771
17
C V 1
4 1.60944 6.1715
1.29594 49.6771 0.05
3.5681 8.7748 -2.17147
18
C V 2
9 2.30259 6.1715
1.29594 49.6771 0.05
3.5681 8.7748 2.82853
19
C V 3
8 2.19722 6.1715
1.29594 49.6771 0.05
3.5681 8.7748 1.82853
20
C V
4 6 1.94591
6.1715 1.29594 49.6771
0.05 3.5681 8.7748
-0.17147
21
S I 1
5 1.79176 3.8037
1.29594 49.6771 0.05
1.2003 6.4071 1.19633
22
S I 2
5 1.79176 3.8037
1.29594 49.6771 0.05
1.2003 6.4071 1.19633
23
S I 3
1 0.69315 3.8037
1.29594 49.6771 0.05
1.2003 6.4071 -2.80367
24
S I 4
2 1.09861 3.8037
1.29594 49.6771 0.05
1.2003 6.4071 -1.80367
25 S
II 1 6
1.94591 4.4972 1.29594
49.6771 0.05 1.8938
7.1005 1.50284
26
S II 2
4 1.60944 4.4972
1.29594 49.6771 0.05
1.8938 7.1005 -0.49716
27
S II 3
5 1.79176 4.4972
1.29594 49.6771 0.05
1.8938 7.1005 0.50284
28
S II 4
4 1.60944 4.4972
1.29594 49.6771 0.05
1.8938 7.1005 -0.49716
29
S III 1
2 1.09861 5.0287
1.29594 49.6771 0.05
2.4253 7.6321 -3.02867
30
S III 2
9 2.30259 5.0287
1.29594 49.6771 0.05
2.4253 7.6321 3.97133
31
S III 3
3 1.38629 5.0287
1.29594 49.6771 0.05
2.4253 7.6321 -2.02867
32
S III 4
7 2.07944 5.0287
1.29594 49.6771 0.05
2.4253 7.6321 1.97133
33
S IV 1
6 1.94591 5.6093
1.29594 49.6771 0.05
3.0059 8.2126 0.39074
34
S IV 2
4 1.60944 5.6093
1.29594 49.6771 0.05
3.0059 8.2126 -1.60926
35
S IV 3
8 2.19722 5.6093
1.29594 49.6771 0.05
3.0059 8.2126 2.39074
36
S IV 4
4 1.60944 5.6093
1.29594 49.6771 0.05
3.0059 8.2126 -1.60926
37
S V 1
2 1.09861 5.0612
1.29594 49.6771 0.05
2.4579 7.6646 -3.06124
38
S V 2
9 2.30259 5.0612
1.29594 49.6771 0.05
2.4579 7.6646 3.93876
39
S V 3
7 2.07944 5.0612
1.29594 49.6771 0.05
2.4579 7.6646
1.93876
40
S V 4
3 1.38629 5.0612
1.29594 49.6771 0.05
2.4579 7.6646 -2.06124
41
0 I 1
12 2.56495 11.1245
1.29594 49.6771 0.05
8.5211 13.7279 0.87550
42
0 I 2
20 3.04452 11.1245
1.29594 49.6771 0.05
8.5211 13.7279 8.87550
43
0 I 3
8 2.19722 11.1245
1.29594 49.6771 0.05
8.5211 13.7279 -3.12450
44
0 I 4
8 2.19722 11.1245
1.29594 49.6771 0.05
8.5211 13.7279 -3.12450
45
0 II 1
7 2.07944 6.4733
1.29594 49.6771 0.05
3.8699 9.0767 0.52670
46
0 II 2
4 1.60944 6.4733
1.29594 49.6771 0.05
3.8699 9.0767 -2.47330
47
0 II 3
4 1.60944 6.4733
1.29594 49.6771 0.05
3.8699 9.0767 -2.47330
48
0 II 4
5 1.79176 6.4733
1.29594 49.6771 0.05
3.8699 9.0767 -1.47330
49
0 III 1
9 2.30259 8.7340
1.29594 49.6771 0.05
6.1306 11.3374 0.26602
50
0 III 2
6 1.94591 8.7340
1.29594 49.6771 0.05
6.1306 11.3374 -2.73398
51
0 III 3
7 2.07944 8.7340
1.29594 49.6771 0.05
6.1306 11.3374 -1.73398
52
0 III
4 11 2.48491
8.7340 1.29594 49.6771
0.05 6.1306 11.3374
2.26602
53
0 IV 1
12 2.56495 14.0305
1.29594 49.6771 0.05
11.4271 16.6338 -2.03046
54
0 IV 2
22 3.13549 14.0305
1.29594 49.6771 0.05
11.4271 16.6338 7.96954
55
0 IV 3
17 2.89037 14.0305
1.29594 49.6771 0.05
11.4271 16.6338 2.96954
56
0 IV 4
13 2.63906 14.0305
1.29594 49.6771 0.05
11.4271 16.6338 -1.03046
57 0
V 1 7
2.07944 8.1378 1.29594
49.6771 0.05 5.5344
10.7411 -1.13776
58
0 V 2
8 2.19722 8.1378
1.29594 49.6771 0.05
5.5344 10.7411 -0.13776
59
0 V 3
5 1.79176 8.1378
1.29594 49.6771 0.05
5.5344 10.7411 -3.13776
60
0 V 4
9 2.30259 8.1378
1.29594 49.6771 0.05
5.5344 10.7411 0.86224
243
proc print data=residdataPM; TITLE4 'Output from the OUTPM option'; run;
NOTE: There were 60 observations read from the
data set WORK.RESIDDATAPM.
NOTE: The PROCEDURE PRINT printed page 31.
NOTE: PROCEDURE PRINT used:
real
time 0.02
seconds
cpu
time
0.02 seconds
Number
of wire worms found for 2 fumigants and a control
Fumigants
are C and S, control is 0, 5 BLOCKS
ANOVA
with PROC MIXED - RBD with reps
Output
from the OUTPM option
StdErr
Obs FUMIGANT
BLOCK REP WORMS
LWORMS Pred Pred
DF Alpha Lower
Upper Resid
1
C I
1
5 1.79176 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -0.25
2
C I
2
4 1.60944 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -1.25
3
C I
3
5 1.79176 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -0.25
4
C I
4
2 1.09861 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -3.25
5
C II
1 0
0.00000 5.25 1.20312
11.4653 0.05 2.61500
7.8850 -5.25
6
C II
2
9 2.30259 5.25
1.20312 11.4653 0.05
2.61500 7.8850 3.75
7
C II
3
3 1.38629 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -2.25
8
C II
4
3 1.38629 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -2.25
9
C III
1
4 1.60944 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -1.25
10
C III
2
4 1.60944 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -1.25
11
C III
3
3 1.38629 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -2.25
12
C III
4
9 2.30259 5.25
1.20312 11.4653 0.05
2.61500 7.8850 3.75
13
C IV
1
7 2.07944 5.25
1.20312 11.4653 0.05
2.61500 7.8850 1.75
14
C IV
2
3 1.38629 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -2.25
15
C IV
3
5 1.79176 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -0.25
16
C IV
4
12 2.56495 5.25
1.20312 11.4653 0.05
2.61500 7.8850 6.75
17
C V
1
4 1.60944 5.25
1.20312 11.4653 0.05
2.61500 7.8850 -1.25
18
C V
2
9 2.30259 5.25
1.20312 11.4653 0.05
2.61500 7.8850 3.75
19
C V
3
8 2.19722 5.25
1.20312 11.4653 0.05
2.61500 7.8850 2.75
20
C V
4
6 1.94591 5.25
1.20312 11.4653 0.05
2.61500 7.8850 0.75
21
S I
1
5 1.79176 4.80
1.20312 11.4653 0.05
2.16500 7.4350 0.20
22
S I
2
5 1.79176 4.80
1.20312 11.4653 0.05
2.16500 7.4350 0.20
23
S I
3
1 0.69315 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -3.80
24
S I
4
2 1.09861 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -2.80
25
S II
1
6 1.94591 4.80
1.20312 11.4653 0.05
2.16500 7.4350 1.20
26
S II
2
4 1.60944 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -0.80
27
S II
3
5 1.79176 4.80
1.20312 11.4653 0.05
2.16500 7.4350 0.20
28
S II
4
4 1.60944 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -0.80
29
S III
1
2 1.09861 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -2.80
30
S III
2
9 2.30259 4.80
1.20312 11.4653 0.05
2.16500 7.4350 4.20
31
S III
3
3 1.38629 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -1.80
32
S III
4
7 2.07944 4.80
1.20312 11.4653 0.05
2.16500 7.4350 2.20
33
S IV
1
6 1.94591 4.80
1.20312 11.4653 0.05
2.16500 7.4350 1.20
34
S IV
2
4 1.60944 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -0.80
35
S IV
3
8 2.19722 4.80
1.20312 11.4653 0.05
2.16500 7.4350 3.20
36
S IV
4
4 1.60944 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -0.80
37
S V
1
2 1.09861 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -2.80
38
S V
2
9 2.30259 4.80
1.20312 11.4653 0.05
2.16500 7.4350 4.20
39
S V
3
7 2.07944 4.80
1.20312 11.4653 0.05
2.16500 7.4350
2.20
40
S V
4
3 1.38629 4.80
1.20312 11.4653 0.05
2.16500 7.4350 -1.80
41
0 I
1
12 2.56495 9.70
1.20312 11.4653 0.05
7.06500 12.3350 2.30
42
0 I
2 20 3.04452
9.70 1.20312 11.4653
0.05 7.06500 12.3350
10.30
43
0 I
3
8 2.19722 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -1.70
44
0 I
4
8 2.19722 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -1.70
45
0 II
1
7 2.07944 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -2.70
46
0 II
2
4 1.60944 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -5.70
47
0 II
3
4 1.60944 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -5.70
48
0 II
4
5 1.79176 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -4.70
49 0
III 1 9
2.30259 9.70 1.20312
11.4653 0.05 7.06500
12.3350 -0.70
50
0 III
2
6 1.94591 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -3.70
51
0 III
3
7 2.07944 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -2.70
52
0 III
4
11 2.48491 9.70
1.20312 11.4653 0.05
7.06500 12.3350 1.30
53
0 IV
1
12 2.56495 9.70
1.20312 11.4653 0.05
7.06500 12.3350 2.30
54
0 IV
2
22 3.13549 9.70
1.20312 11.4653 0.05
7.06500 12.3350 12.30
55
0 IV
3
17 2.89037 9.70
1.20312 11.4653 0.05
7.06500 12.3350 7.30
56
0 IV
4
13 2.63906 9.70
1.20312 11.4653 0.05
7.06500 12.3350 3.30
57
0 V
1
7 2.07944 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -2.70
58
0 V
2
8 2.19722
9.70 1.20312 11.4653
0.05 7.06500 12.3350
-1.70
59
0 V
3
5 1.79176 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -4.70
60
0 V
4
9 2.30259 9.70
1.20312 11.4653 0.05
7.06500 12.3350 -0.70
244
proc univariate data=ResidDataP plot normal; var resid;
245
TITLE3 'Univariate analysis for PROC MIXED - RBD with reps';
246
run;
NOTE: The PROCEDURE UNIVARIATE printed page 32.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.02
seconds
cpu
time
0.02 seconds
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
Univariate analysis for PROC MIXED - RBD with reps
The UNIVARIATE Procedure
Variable:
Resid
Moments
N
60 Sum Weights
60
Mean
0 Sum Observations
0
Std Deviation
2.74808542 Variance
7.55197347
Skewness
1.14385572 Kurtosis
1.43592384
Uncorrected SS
445.566435 Corrected SS
445.566435
Coeff Variation
. Std Error Mean
0.3547763
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std Deviation
2.74809
Median
-0.49716 Variance
7.55197
Mode
-3.12450 Range
12.91092
Interquartile Range 3.38408
NOTE: The mode displayed is the smallest of 8
modes with a count of 2.
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 0
Pr > |t| 1.0000
Sign
M -4 Pr
>= |M| 0.3663
Signed Rank
S -110 Pr >= |S|
0.4227
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk W
0.918552 Pr < W
0.0007
Kolmogorov-Smirnov D
0.129494 Pr > D
0.0136
Cramer-von Mises W-Sq
0.185609 Pr > W-Sq 0.0080
Anderson-Darling A-Sq
1.226204 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile
Estimate
100% Max
8.875503
99%
8.875503
95%
5.201148
90%
3.950118
75% Q3
1.349586
50% Median
-0.497159
25% Q1
-2.034492
10%
-3.044958
5%
-3.131129
1%
-4.035419
0% Min
-4.035419
Extreme Observations
------Lowest-----
-----Highest-----
Value Obs
Value Obs
-4.03542
5 3.97133
30
-3.56229
14 4.96458
6
-3.13776
59 5.43771
16
-3.12450
44 7.96954
54
-3.12450
43 8.87550
42
Stem Leaf
# Boxplot
Normal Probability Plot
8 9
1 0
8.75+
*
8 0
1 0
|
7
|
*
7
|
6
|
++
6
|
++
5
|
+
5 04
2 |
|
* ++
4
| |
*++
4 00
2 |
|
++
3 9
1 |
|
***
3 0
1 |
|
++
2 8
1 |
|
+*
2 034
3 |
2.25+
+**
1 589
3 |
|
+***
1 22
2 +-----+ |
++*
0 556699
6 |
| |
+***
0 344
3 |
+ | |
++**
-0 421
3 |
| |
+**
-0 55
2 *-----* |
++
-1 100000
6 |
| |
++***
-1 876665
6 |
| |
++**
-2 421000
6 +-----+ |
*****
-2 8755
4 |
|
*+
-3 11110
5 |
| **
**+
-3 6
1 |
| *
++
-4 0
1 |
-4.25+ * ++
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
247
proc sort data=FUMIGANT; by BLOCK FUMIGANT; run;
NOTE: There were 60 observations read from the
data set WORK.FUMIGANT.
NOTE: The data set WORK.FUMIGANT has 60
observations and 5 variables.
NOTE: PROCEDURE SORT used:
real
time 0.04
seconds
cpu
time
0.04 seconds
247
!
OPTIONS PS=45 LS=88;
248
proc means data=FUMIGANT noprint; by BLOCK FUMIGANT; var WORMS;
249
output out=next4 n=n mean=mean var=var; run;
NOTE: There were 60 observations read from the
data set WORK.FUMIGANT.
NOTE: The data set WORK.NEXT4 has 15 observations
and 7 variables.
NOTE: PROCEDURE MEANS used:
real
time 0.04
seconds
cpu
time 0.04
seconds
250
proc plot data=next4; plot var*mean; run;
NOTE: There were 15 observations read from the
data set WORK.NEXT4.
NOTE: The PROCEDURE PLOT printed page 33.
NOTE: PROCEDURE PLOT used:
real
time 0.01
seconds
cpu time
0.01 seconds
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
Univariate analysis for PROC MIXED - RBD with
reps
Plot of var*mean. Legend: A = 1 obs, B = 2 obs, etc.
var |
|
40 +
|
|
|
|
|
A
30 +
|
|
|
|
|
20 +
A
|
|
|
A
A
|
|
B
10 +
|
|
A
|
A
A A
|
A A
|
A
A A
0 +
|
---+----------+----------+----------+----------+----------+----------+----------+-
2
4 6
8 10
12 14
16
mean
251
PROC CHART DATA=FUMIGANT; OPTIONS PS=45 LS=88;
252
TITLE3 'Histogram of means for PROC MIXED - RBD with reps';
253
VBAR FUMIGANT / SUMVAR=WORMS TYPE=MEAN;
RUN;
NOTE: The PROCEDURE CHART printed page 34.
NOTE: PROCEDURE CHART used:
real
time 0.00
seconds
cpu
time
0.00 seconds
254
OPTIONS PS=256 LS=111;
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
Histogram of means for PROC MIXED - RBD with reps
WORMS Mean
| *****
| *****
| *****
8 +
*****
| *****
| *****
| *****
6 +
*****
| *****
*****
| *****
***** *****
| *****
***** *****
4 +
***** *****
*****
| *****
***** *****
| *****
***** *****
| *****
***** *****
2 +
***** *****
*****
| *****
***** *****
| *****
***** *****
| *****
***** *****
--------------------------------------------
0 C
S
FUMIGANT
255
PROC mixed DATA=FUMIGANT cl COVTEST; CLASSES FUMIGANT BLOCK REP;
256
TITLE3 'ANOVA with PROC MIXED -
RBD with reps - using Logarithms';
257
MODEL LWORMS = FUMIGANT / htype=3
DDFM=Satterthwaite outp=ResidDataP;
258
RANDOM BLOCK FUMIGANT*BLOCK;
259
lsmeans fumigant / pdiff ADJUST=DUNNETT diff=controll('0');
260
lsmeans fumigant / pdiff ADJUST=tukey;
261
RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 60
observations and 12 variables.
NOTE: The PROCEDURE MIXED printed page 35.
NOTE: PROCEDURE MIXED used:
real
time 0.18
seconds
cpu
time
0.18 seconds
261
! QUIT;
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
ANOVA with PROC MIXED - RBD with reps - using
Logarithms
The Mixed Procedure
Model Information
Data Set
WORK.FUMIGANT
Dependent Variable
LWORMS
Covariance Structure
Variance Components
Estimation Method
REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
FUMIGANT
3 0 C S
BLOCK
5 I II III IV V
REP
4 1 2 3 4
Dimensions
Covariance Parameters
3
Columns in X
4
Columns in Z
20
Subjects
1
Max Obs Per Subject
60
Observations Used
60
Observations Not Used
0
Total Observations
60
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 88.06288591
1
1 84.95995798
0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Standard Z
Cov Parm Estimate
Error
Value Pr Z Alpha
Lower Upper
BLOCK
0.02554 0.03624
0.70
0.2405 0.05 0.005068
27.2141
FUMIGANT*BLOCK 0.02017
0.03609 0.56 0.2881
0.05 0.003244 1200.67
Residual
0.1959 0.04131
4.74
<.0001 0.05 0.1348
0.3108
Fit Statistics
-2 Res Log Likelihood
85.0
AIC (smaller is better)
91.0
AICC (smaller is better)
91.4
BIC (smaller is better)
89.8
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF F Value
Pr > F
FUMIGANT
2 8
8.30
0.0112
Least
Squares Means
Standard
Effect
FUMIGANT Estimate
Error DF
t Value Pr > |t|
FUMIGANT
0
2.2754 0.1376
10.5 16.53
<.0001
FUMIGANT
C
1.7076 0.1376
10.5 12.41
<.0001
FUMIGANT
S
1.6714 0.1376
10.5 12.14
<.0001
FUMIGANT
0
2.2754 0.1376
10.5 16.53
<.0001
FUMIGANT
C
1.7076 0.1376
10.5 12.41
<.0001
FUMIGANT
S
1.6714 0.1376
10.5 12.14
<.0001
Differences
of Least Squares Means
Standard
Effect FUMIGANT
_FUMIGANT Estimate Error
DF t Value Tails
Pr t Adjustment Adj P
FUMIGANT 0
C
0.5678 0.1663
8 3.41 Upper
0.0046 Dunnett-Hsu 0.0083
FUMIGANT 0
S
0.6040 0.1663
8 3.63 Upper
0.0033 Dunnett-Hsu 0.0061
FUMIGANT 0
C
0.5678 0.1663
8 3.41 Both
0.0092 Tukey-Kramer 0.0223
FUMIGANT 0
S
0.6040 0.1663
8 3.63 Both
0.0067 Tukey-Kramer 0.0163
FUMIGANT C
S 0.03622
0.1663 8 0.22
Both 0.8331 Tukey-Kramer
0.9743
262
proc univariate data=ResidDataP plot normal; var resid;
263
TITLE3 'Univariate analysis for
PROC MIXED on Logs - RBD with reps';
264
run;
NOTE: The PROCEDURE UNIVARIATE printed page 36.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.02
seconds
cpu
time
0.02 seconds
265
proc sort data=FUMIGANT; by BLOCK FUMIGANT; run;
NOTE: Input data set is already sorted, no
sorting done.
NOTE: PROCEDURE SORT used:
real
time 0.00
seconds
cpu
time
0.00 seconds
265
!
OPTIONS PS=45 LS=88;
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
Univariate analysis for PROC MIXED on Logs - RBD
with reps
The UNIVARIATE Procedure
Variable:
Resid
Moments
N
60 Sum Weights
60
Mean
0
Sum Observations
0
Std Deviation
0.41560217 Variance
0.17272516
Skewness
-0.5865127 Kurtosis
1.54273956
Uncorrected SS
10.1907847 Corrected SS
10.1907847
Coeff Variation
.
Std Error Mean 0.05365401
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std Deviation
0.41560
Median
0.02165 Variance
0.17273
Mode
-0.41081 Range
2.30259
Interquartile Range 0.47828
NOTE: The mode displayed is the smallest of 8
modes with a count of 2.
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 0
Pr > |t| 1.0000
Sign
M 1
Pr >= |M| 0.8974
Signed Rank
S 31 Pr
>= |S| 0.8217
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.971472
Pr < W 0.1722
Kolmogorov-Smirnov D
0.058041 Pr > D >0.1500
Cramer-von Mises W-Sq
0.025185 Pr > W-Sq >0.2500
Anderson-Darling A-Sq
0.239627 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile Estimate
100% Max
0.831431
99%
0.831431
95%
0.643056
90%
0.588689
75% Q3
0.249212
50% Median
0.021650
25% Q1
-0.229068
10%
-0.481377
5%
-0.596016
1%
-1.471154
0% Min
-1.471154
Extreme Observations
------Lowest------
------Highest-----
Value Obs
Value Obs
-1.471154
17 0.597013
58
-0.853315
11 0.618902
34
-0.606960
57 0.667211
44
-0.585071
33 0.732700
2
-0.540326
8 0.831431
18
Stem Leaf
# Boxplot
Normal Probability Plot
8 3
1 |
0.85+
++
*
7 3
1 |
|
++*
6 027
3 |
|
+**
5 99
2 |
|
***
4 08
2 |
|
+*+
3 46678
5 |
|
****
2 13555
5 +-----+ |
***
1 13558
5 |
| |
***
0 2335669
7 *--+--* |
***
-0 8853
4 |
| |
**
-1 7611100
7 |
| |
***
-2 3331
4 +-----+ |
****
-3 3210
4
| |
**
-4 5511
4 |
|
**+
-5 941
3 |
| * **
-6 1
1 |
| *++
-7
| |
+++
-8 5
1 |
|
++*
-9
|
+++
-10
|+
-11
|
-12
|
-13
|
-14 7
1 0
-1.45+ *
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by 10**-1
-2 -1
0 +1
+2
266
proc means data=FUMIGANT noprint; by BLOCK FUMIGANT; var LWORMS;
267
output out=next5 n=n mean=mean var=var; run;
NOTE: There were 60 observations read from the
data set WORK.FUMIGANT.
NOTE: The data set WORK.NEXT5 has 15 observations
and 7 variables.
NOTE: PROCEDURE MEANS used:
real
time 0.03
seconds
cpu
time
0.03 seconds
268
proc plot data=next5; plot var*mean;
269
TITLE3 'Variance/Mean plot for PROC MIXED on Logarithms - RBD with
reps';
270
run;
271
272
OPTIONS PS=256 LS=111;
NOTE: There were 15 observations read from the
data set WORK.NEXT5.
NOTE: The PROCEDURE PLOT printed page 37.
NOTE: PROCEDURE PLOT used:
real
time 0.02
seconds
cpu
time
0.02 seconds
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
Variance/Mean plot for PROC MIXED on Logarithms -
RBD with reps
Plot of var*mean. Legend: A = 1 obs, B = 2 obs, etc.
var |
1.0 +
|
|
|
A
|
|
0.8 +
|
|
|
|
|
0.6 +
|
|
|
|
|
0.4 +
|
|
B
|
A
|
|
A
0.2 +
|
A
A
|
|
A
A
|
A
A
A
|
A A
A
0.0 +
|
--+---------+---------+---------+---------+---------+---------+---------+---------+-
1.2 1.4
1.6 1.8
2.0
2.2 2.4
2.6
2.8
mean
273
PROC GLM DATA=FUMIGANT; CLASSES FUMIGANT BLOCK REP;
274
TITLE3 'ANOVA with PROC GLM - RBD with reps';
275
MODEL WORMS = FUMIGANT BLOCK FUMIGANT*BLOCK;
276
TEST H=FUMIGANT BLOCK E=FUMIGANT*BLOCK;
277
RANDOM FUMIGANT BLOCK FUMIGANT*BLOCK;
278
LSMEANS FUMIGANT BLOCK / pdiff stderr adjust=tukey;
279
RUN;
NOTE: TYPE I EMS not available without the E1
option.
279
! QUIT;
NOTE: The PROCEDURE GLM printed pages 38-42.
NOTE: PROCEDURE GLM used:
real
time 0.13
seconds
cpu
time
0.12 seconds
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
ANOVA with PROC GLM - RBD with reps
The GLM Procedure
Class Level Information
Class
Levels Values
FUMIGANT
3 0 C S
BLOCK
5 I II III IV V
REP
4 1 2 3 4
Number of observations 60
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
ANOVA with PROC GLM - RBD with reps
The GLM Procedure
Dependent Variable: WORMS
Sum
of
Source
DF Squares
Mean Square F Value
Pr > F
Model
14 640.833333
45.773810 5.03
<.0001
Error
45 409.750000
9.105556
Corrected Total
59 1050.583333
R-Square Coeff Var
Root MSE WORMS Mean
0.609979 45.83607
3.017541 6.583333
Source
DF Type I SS
Mean Square F Value
Pr > F
FUMIGANT
2
293.4333333 146.7166667
16.11
<.0001
BLOCK
4 151.1666667
37.7916667 4.15
0.0060
FUMIGANT*BLOCK
8 196.2333333
24.5291667 2.69
0.0164
Source
DF
Type III SS Mean Square F
Value
Pr > F
FUMIGANT
2 293.4333333
146.7166667 16.11
<.0001
BLOCK
4 151.1666667
37.7916667 4.15
0.0060
FUMIGANT*BLOCK
8
196.2333333 24.5291667
2.69
0.0164
Tests of Hypotheses Using the Type III MS for FUMIGANT*BLOCK as an
Error
Term
Source
DF Type III SS Mean
Square F Value
Pr > F
FUMIGANT
2
293.4333333 146.7166667
5.98
0.0258
BLOCK
4 151.1666667
37.7916667 1.54
0.2790
Source
Type III Expected Mean Square
FUMIGANT
Var(Error) + 4
Var(FUMIGANT*BLOCK) + 20 Var(FUMIGANT)
BLOCK
Var(Error) + 4
Var(FUMIGANT*BLOCK) + 12 Var(BLOCK)
FUMIGANT*BLOCK
Var(Error) + 4 Var(FUMIGANT*BLOCK)
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
Standard
LSMEAN
FUMIGANT
WORMS LSMEAN
Error Pr > |t| Number
0
9.70000000 0.67474275
<.0001 1
C
5.25000000 0.67474275
<.0001 2
S
4.80000000 0.67474275
<.0001 3
Least
Squares Means for effect FUMIGANT
Pr
> |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable: WORMS
i/j
1
2
3
1
<.0001 <.0001
2 <.0001
0.8850
3 <.0001
0.8850
Number of wire worms found for 2 fumigants and a
control
Fumigants are C and S, control is 0, 5 BLOCKS
ANOVA with PROC GLM - RBD with reps
The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
Standard
LSMEAN
BLOCK
WORMS LSMEAN
Error Pr > |t| Number
I
6.41666667 0.87108914
<.0001 1
II
4.50000000 0.87108914
<.0001 2
III
6.16666667 0.87108914
<.0001 3
IV
9.41666667 0.87108914
<.0001 4
V
6.41666667 0.87108914
<.0001 5
Least Squares Means for effect BLOCK
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable:
WORMS
i/j
1
2
3
4
5
1
0.5327 0.9996
0.1246 1.0000
2 0.5327
0.6602 0.0021
0.5327
3 0.9996
0.6602
0.0803 0.9996
4 0.1246
0.0021 0.0803
0.1246
5 1.0000
0.5327 0.9996
0.1246
282
**EXAMPLE 6********************************************;
283
*** Example of Latin Square Design
***;
284
*** From Snedecor & Cochran, 1980 (pg 271)
***;
285 *******************************************************;
286
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
287
DATA MILLET; INFILE CARDS MISSOVER;
288
INPUT ROW COLUMN treatment $ YIELD;
289
TITLE1 'LATIN SQUARE WITH 5 ROWS, COLUMNS AND TREATMENTS';
290
TITLE2 'MILLET YIELDS (G) FOR
SPACINGS OF 2, 4, 6, 8 AND 10 INCHES';
291
CARDS;
NOTE: The data set WORK.MILLET has 25
observations and 4 variables.
NOTE: DATA statement used:
real
time 0.03
seconds
cpu
time
0.03 seconds
291
! RUN;
317
;
318
PROC SORT; BY ROW COLUMN;
NOTE: There were 25 observations read from the
data set WORK.MILLET.
NOTE: The data set WORK.MILLET has 25
observations and 4 variables.
NOTE: PROCEDURE SORT used:
real
time 0.04
seconds
cpu
time
0.04 seconds
319
PROC PRINT; VAR ROW COLUMN
treatment YIELD; RUN;
NOTE: There were 25 observations read from the
data set WORK.MILLET.
NOTE: The PROCEDURE PRINT printed page 43.
NOTE: PROCEDURE PRINT used:
real
time 0.02
seconds
cpu
time
0.02 seconds
LATIN SQUARE WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS (G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
Obs ROW
COLUMN treatment YIELD
1 1 1
B 257
2 1 2
E 230
3 1 3
A 279
4 1 4
C 287
5 1 5
D 202
6 2 1
D 245
7 2 2
A 283
8 2 3
E 245
9 2 4
B 280
10
2 5
C 260
11
3 1
E 182
12
3 2
B 252
13
3 3
C 280
14
3 4
D 246
15
3 5
A 250
16
4 1
A 203
17
4 2
C 204
18
4 3
D
227
19
4 4
E 193
20
4 5
B 259
21
5 1
C 231
22
5 2
D 271
23
5 3
B 266
24
5 4
A
334
25
5 5
E 338
320
PROC MIXED DATA=MILLET cl COVTEST; CLASSES ROW COLUMN treatment;
321
TITLE3 'ANOVA with PROC MIXED - Latin Square';
322
TITLE4 'Post-ANOVA tests will be done later with contrasts';
323
MODEL YIELD = treatment / htype=3
DDFM=Satterthwaite outp=ResidDataP;
324
RANDOM ROW COLUMN;
325
RUN;
NOTE:
Convergence criteria met.
NOTE: The data
set WORK.RESIDDATAP has 25
observations and 11 variables.
NOTE: The
PROCEDURE MIXED printed page 44.
NOTE:
PROCEDURE MIXED used:
real
time 0.15
seconds
cpu
time
0.15 seconds
325
! QUIT;
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC MIXED - Latin Square
Post-ANOVA
tests will be done later with
contrasts
The Mixed
Procedure
Model Information
Data
Set
WORK.MILLET
Dependent
Variable
YIELD
Covariance
Structure Variance
Components
Estimation
Method
REML
Residual
Variance Method Profile
Fixed Effects
SE Method Model-Based
Degrees of
Freedom Method Satterthwaite
Class Level Information
Class
Levels Values
ROW
5 1 2 3 4 5
COLUMN
5 1 2 3 4 5
treatment
5 A B C D E
Dimensions
Covariance
Parameters
3
Columns in
X
6
Columns in
Z
10
Subjects
1
Max Obs Per
Subject
25
Observations
Used
25
Observations
Not
Used
0
Total
Observations
25
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 212.61749317
1
1
210.22285841 0.00000000
Convergence criteria met.
Covariance
Parameter Estimates
Standard Z
Cov
Parm Estimate
Error
Value Pr
Z Alpha
Lower Upper
ROW
468.95
488.54 0.96
0.1686 0.05
122.70 24267
COLUMN
96.1867
233.77 0.41
0.3404 0.05
11.8899
7.401E10
Residual
1055.61
430.95 2.45
0.0072 0.05
542.81 2876.45
Fit Statistics
-2 Res Log
Likelihood
210.2
AIC (smaller
is better) 216.2
AICC (smaller
is better) 217.7
BIC (smaller
is better) 215.1
Type 3 Tests
of Fixed Effects
Num Den
Effect
DF DF F
Value
Pr > F
treatment
4 12
0.98
0.4523
326
proc univariate data=ResidDataP plot normal; var resid; run;
NOTE: The
PROCEDURE UNIVARIATE printed page 45.
NOTE:
PROCEDURE UNIVARIATE used:
real
time 0.02
seconds
cpu
time
0.02 seconds
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC MIXED - Latin Square
Post-ANOVA
tests will be done later with
contrasts
The UNIVARIATE
Procedure
Variable:
Resid
Moments
N
25 Sum
Weights
25
Mean
0 Sum Observations
0
Std
Deviation
26.519579
Variance
703.288072
Skewness
0.5867556
Kurtosis
0.94966715
Uncorrected
SS
16878.9137 Corrected
SS 16878.9137
Coeff
Variation
. Std Error Mean
5.30391581
Basic
Statistical Measures
Location
Variability
Mean
0.000000 Std
Deviation
26.51958
Median
3.939099
Variance
703.28807
Mode
.
Range
112.32380
Interquartile
Range 32.83900
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t
t 0
Pr > |t| 1.0000
Sign
M 0.5 Pr >=
|M| 1.0000
Signed
Rank
S 0.5 Pr >=
|S| 0.9896
Tests for
Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.942024 Pr < W
0.1648
Kolmogorov-Smirnov
D
0.14412 Pr > D >0.1500
Cramer-von
Mises W-Sq
0.071451 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq
0.461065 Pr > A-Sq 0.2428
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max
72.66893
99%
72.66893
95%
34.52834
90%
32.33981
75%
Q3
9.84803
50%
Median
3.93910
25%
Q1
-22.99096
10%
-37.17456
5%
-38.41741
1%
-39.65487
0%
Min
-39.65487
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-39.6549
11
17.2897 20
-38.4174
5
30.4420 4
-37.1746
21
32.3398 13
-33.7538
16
34.5283 24
-25.4509
19
72.6689 25
Stem
Leaf
# Boxplot
Normal
Probability Plot
6
3
1
0
70+
* +++
4
|
+++++++
2
025
3
|
|
+++*+*+*
0
457899017
9 +--+--+
10+
*******+**
-0
65322
5 |
|
|
++*****
-2
874543
6 +-----+
|
* *+*+*+** *
-4
0
1
|
-50+ +++++++
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by
10**+1
-2
-1
0
+1 +2
327
proc sort data=MILLET; by treatment; run; OPTIONS PS=45 LS=88;
NOTE: There
were 25 observations read from the
data set WORK.MILLET.
NOTE: The data
set WORK.MILLET has 25
observations and 4 variables.
NOTE:
PROCEDURE SORT used:
real
time 0.04
seconds cpu
time
0.04 seconds
328
proc means data=MILLET noprint; by treatment; var YIELD;
329
output out=next6 n=n mean=mean var=var; run;
NOTE: There
were 25 observations read from the
data set WORK.MILLET.
NOTE: The data
set WORK.NEXT6 has 5 observations
and 6 variables.
NOTE:
PROCEDURE MEANS used:
real
time 0.04
seconds cpu
time
0.04 seconds
330
proc plot data=next6; plot var*mean; run;
NOTE: There
were 5 observations read from the
data set WORK.NEXT6.
NOTE: The
PROCEDURE PLOT printed page 46.
NOTE:
PROCEDURE PLOT used:
real
time 0.01
seconds cpu
time
0.01 seconds
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC MIXED - Latin Square
Post-ANOVA
tests will be done later with
contrasts
Plot of var*mean. Legend: A = 1
obs, B = 2 obs, etc.
var |
|
4000 +
| A
|
|
|
|
|
3000 +
|
|
|
|
|
A
|
2000 +
|
|
|
|
|
|
A
1000 +
|
| A
|
|
|
|
A
0
+
|
---+----------+----------+----------+----------+----------+----------+----------+--
235
240
245
250
255
260
265 270
mean
331
PROC CHART DATA=MILLET; OPTIONS PS=45 LS=78;
332
TITLE3 'Histogram of mean number Millet yield by row spacing';
333
VBAR treatment / SUMVAR=YIELD TYPE=MEAN;
RUN;
NOTE: The
PROCEDURE CHART printed page 47.
NOTE:
PROCEDURE CHART used:
real
time 0.01
seconds
cpu
time
0.01 seconds
334
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
Histogram of
mean number Millet yield by row
spacing
YIELD Mean
| *****
|
***** *****
250
+
*****
*****
*****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
200
+
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
***** *****
*****
***** *****
|
*****
*****
*****
***** *****
150
+
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
| *****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
100
+
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
50 +
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
--------------------------------------------------------------------
A
B
C
D E
treatment
335
OPTIONS PS=256 LS=78;
336
PROC GLM DATA=MILLET; CLASSES ROW COLUMN treatment;
337
TITLE3 'ANOVA with PROC GLM - Latin Square';
338
MODEL YIELD = ROW COLUMN treatment;
339
RANDOM ROW COLUMN;
340
RUN;
NOTE: TYPE I
EMS not available without the E1
option.
340
! QUIT;
NOTE: The
PROCEDURE GLM printed pages 48-50.
NOTE:
PROCEDURE GLM used:
real
time 0.09
seconds
cpu
time
0.09 seconds
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC GLM - Latin Square
The GLM
Procedure
Class
Level Information
Class
Levels Values
ROW
5 1 2 3 4 5
COLUMN
5 1 2 3 4 5
treatment
5
A B C D E
Number of
observations 25
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC GLM - Latin Square
The GLM
Procedure
Dependent
Variable: YIELD
Sum of
Source
DF Squares
Mean Square F Value
Pr > F
Model
12 23904.08000
1992.00667 1.89
0.1426
Error
12 12667.28000 1055.60667
Corrected
Total
24 36571.36000
R-Square
Coeff Var Root MSE
YIELD Mean
0.653628
12.88472
32.49010 252.1600
Source
DF Type I SS Mean
Square F Value
Pr > F
ROW
4
13601.36000
3400.34000 3.22
0.0516
COLUMN
4 6146.16000
1536.54000 1.46
0.2758
treatment
4 4156.56000
1039.14000 0.98
0.4523
Source
DF Type III SS Mean
Square F Value
Pr > F
ROW
4 13601.36000
3400.34000 3.22
0.0516
COLUMN
4 6146.16000
1536.54000 1.46
0.2758
treatment
4 4156.56000
1039.14000 0.98
0.4523
LATIN SQUARE
WITH 5 ROWS, COLUMNS AND TREATMENTS
MILLET YIELDS
(G) FOR SPACINGS OF 2, 4, 6, 8 AND
10 INCHES
ANOVA with
PROC GLM - Latin Square
The GLM
Procedure
Source
Type III Expected Mean Square
ROW
Var(Error) + 5 Var(ROW)
COLUMN
Var(Error) + 5 Var(COLUMN)
treatment
Var(Error) + Q(treatment)
345
**EXAMPLE 7********************************************;
346
*** Example of a series of Latin
Squares
***;
347
*** From my
imagination
***;
348
*******************************************************;
349
OPTIONS PS=256 LS=111 NOCENTER NODATE NONUMBER;
350
351
data series;
352
Title1 'Example of a series of Latin Squares';
353
input square row col tmt $ y;
354
cards;
NOTE: The data
set WORK.SERIES has 18
observations and 5 variables.
NOTE: DATA
statement used:
real
time 0.02
seconds
cpu
time
0.02 seconds
373
;
374
proc print data=series; run;
NOTE: There
were 18 observations read from the
data set WORK.SERIES.
NOTE: The
PROCEDURE PRINT printed page 51.
NOTE:
PROCEDURE PRINT used:
real
time 0.01
seconds
cpu
time
0.01 seconds
Example of a
series of Latin Squares
Obs
square row col
tmt y
1
1
1 1
d
7
2
1
1 2
b
5
3
1
1 3
c
2
4
1
2 1
b
9
5
1
2 2
c
3
6
1
2 3
d
6
7
1
3 1
c
1
8
1
3 2
d
6
9
1
3 3
b
7
10
2
1 1
c
2
11
2
1 2
d
3
12
2
1 3
b
7
13
2
2 1
d
6
14
2
2 2
b
9
15
2
2 3
c
3
16
2
3 1
b
8
17
2
3 2
c 2
18
2
3 3
d
6
375
proc mixed data=series CL COVTEST; classes square row col tmt;
376
Title2 'ANOVA with PROC MIXED - Series of Latin Squares';
377
model y = tmt / outp=ResidDataP;
378
random square row(square) col(square) tmt*square;
379
LSMEANS tmt / pdiff adjust=tukey;
380
run;
NOTE:
Convergence criteria met.
NOTE:
Estimated G matrix is not positive
definite.
NOTE: The data
set WORK.RESIDDATAP has 18
observations and 12 variables.
NOTE: The
PROCEDURE MIXED printed page 52.
NOTE:
PROCEDURE MIXED used:
real
time 0.20
seconds
cpu
time
0.20 seconds
Example of a
series of Latin Squares
ANOVA with
PROC MIXED - Series of Latin Squares
The Mixed
Procedure
Model Information
Data
Set
WORK.SERIES
Dependent
Variable y
Covariance
Structure Variance
Components
Estimation
Method
REML
Residual
Variance Method Profile
Fixed Effects
SE Method Model-Based
Degrees of
Freedom Method Containment
Class Level Information
Class
Levels Values
square
2 1 2
row
3 1 2 3
col
3 1 2 3
tmt
3 b c d
Dimensions
Covariance
Parameters
5
Columns in
X
4
Columns in
Z
20
Subjects
1
Max Obs Per
Subject
18
Observations
Used
18
Observations
Not
Used
0
Total
Observations
18
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 54.78369521
1
2
54.53562480 0.00005865
2
1
54.53481396 0.00000009
3
1
54.53481275 0.00000000
Convergence criteria met.
Covariance
Parameter Estimates
Standard Z
Cov
Parm
Estimate
Error
Value Pr
Z Alpha
Lower Upper
square
0
.
.
.
.
. .
row(square)
0.2433
0.5129 0.47
0.3176 0.05
0.03387
1079099
col(square)
0
.
.
.
.
. .
square*tmt
0.1099
0.5327 0.21
0.4183 0.05
0.009602
3.445E35
Residual
1.2822
0.7115 1.80
0.0358 0.05
0.5468 5.7192
Fit Statistics
-2 Res Log
Likelihood
54.5
AIC (smaller
is better) 60.5
AICC (smaller
is better) 62.7
BIC (smaller
is better) 56.6
Type 3 Tests
of Fixed Effects
Effect
Num DF Den DF F Value
Pr > F
tmt
2 2
27.33
0.0353
Least Squares
Means
Effect
tmt Estimate Std
Error DF
t Value Pr > |t|
tmt
b
7.5000
0.5561
2
13.49 0.0055
tmt
c
2.1667
0.5561
2
3.90 0.0600
tmt
d
5.6667
0.5561
2
10.19 0.0095
Differences of
Least Squares
Means
Standard
Effect
tmt
_tmt Estimate
Error DF
t Value Pr > |t|
Adjustment Adj P
tmt
b
c
5.3333
0.7330
2
7.28 0.0184
Tukey-Kramer 0.0334
tmt
b
d
1.8333
0.7330
2
2.50 0.1295
Tukey-Kramer 0.2258
tmt
c
d
-3.5000
0.7330
2
-4.77 0.0412
Tukey-Kramer 0.0742
381
proc univariate data=ResidDataP plot normal; var resid;
382
TITLE3 'Univariate analysis for PROC MIXED - Series of Latin Squares';
383
run;
NOTE: The
PROCEDURE UNIVARIATE printed page 53.
NOTE:
PROCEDURE UNIVARIATE used:
real
time 0.03
seconds
cpu
time
0.03 seconds
Example of a
series of Latin Squares
ANOVA with
PROC MIXED - Series of Latin Squares
Univariate
analysis for PROC MIXED - Series of
Latin Squares
The UNIVARIATE
Procedure
Variable:
Resid
Moments
N
18 Sum
Weights
18
Mean
0 Sum Observations
0
Std
Deviation
0.97821613
Variance
0.9569068
Skewness
-1.0965374
Kurtosis
1.33159688
Uncorrected
SS
16.2674156 Corrected
SS 16.2674156
Coeff
Variation
. Std Error Mean
0.23056775
Basic
Statistical Measures
Location
Variability
Mean
0.000000 Std
Deviation
0.97822
Median
0.174784
Variance
0.95691
Mode
.
Range
3.59468
Interquartile
Range 0.71323
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t
t 0
Pr > |t| 1.0000
Sign
M 2
Pr >= |M| 0.4807
Signed
Rank
S 18.5 Pr >=
|S| 0.4423
Tests for
Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.884881 Pr < W
0.0316
Kolmogorov-Smirnov
D
0.220142 Pr > D
0.0211
Cramer-von
Mises W-Sq
0.130755 Pr > W-Sq 0.0405
Anderson-Darling
A-Sq
0.803675 Pr > A-Sq 0.0313
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max
1.358201
99%
1.358201
95%
1.358201
90%
1.279796
75%
Q3
0.476755
50% Median
0.174784
25%
Q1
-0.236477
10%
-2.127186
5%
-2.236477
1%
-2.236477
0%
Min
-2.236477
Extreme Observations
------Lowest------
------Highest-----
Value
Obs
Value Obs
-2.236477
2
0.476755 15
-2.127186
11
0.544942 5
-0.971331
7
1.075234 14
-0.281382
17
1.279796 4
-0.236477
9
1.358201 1
Stem
Leaf
#
Boxplot
Normal Probability Plot
1
134
3 |
1.25+
*+*++ *
0
55
2 +-----+
|
++*++
0
012344
6 *--+--*
|
**+**+** *
-0
3221
4 +-----+
|
** **+++
-0
|
|
*+++++
-1
0
1
|
| +++++
-1
| +++++
-2
21
2 0
-2.25++++++ * *
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
386
proc glm data=series; classes square row col tmt;
387
Title2 'ANOVA with PROC GLM - Series of Latin Squares with PROC GLM';
388
model y = square row(square) col(square) tmt tmt*square;
389
random square row(square) col(square) tmt*square / test;
390
run;
NOTE: TYPE I
EMS not available without the E1
option.
391
NOTE: The
PROCEDURE GLM printed pages 54-57.
NOTE:
PROCEDURE GLM used:
real
time 0.08
seconds
cpu
time
0.08 seconds
Example of a
series of Latin Squares
ANOVA with
PROC GLM - Series of Latin Squares
with PROC GLM
The GLM
Procedure
Class
Level Information
Class
Levels Values
square
2 1 2
row
3 1 2 3
col
3 1 2 3
tmt
3 b c d
Number of
observations 18
Dependent
Variable: y
Sum of
Source
DF
Squares Mean Square F
Value
Pr > F
Model
13
104.6666667
8.0512821 4.53
0.0780
Error
4
7.1111111 1.7777778
Corrected
Total
17 111.7777778
R-Square
Coeff Var Root
MSE y Mean
0.936382
26.08696
1.333333 5.111111
Source
DF Type I
SS Mean Square F
Value
Pr > F
square
1
0.00000000
0.00000000 0.00
1.0000
row(square)
4
9.77777778
2.44444444 1.38
0.3826
col(square)
4
2.44444444
0.61111111 0.34
0.8372
tmt
2 88.11111111
44.05555556 24.78
0.0056
square*tmt
2
4.33333333
2.16666667 1.22
0.3861
Source
DF Type III SS Mean
Square F Value
Pr > F
square
1
0.00000000
0.00000000 0.00
1.0000
row(square)
4
9.77777778
2.44444444 1.38
0.3826
col(square)
4
2.44444444
0.61111111 0.34
0.8372
tmt
2 88.11111111
44.05555556 24.78
0.0056
square*tmt
2
4.33333333
2.16666667 1.22
0.3861
Source
Type III Expected Mean Square
square
Var(Error) + 3 Var(square*tmt)
+ 3 Var(col(square))
+
3
Var(row(square)) + 9 Var(square)
row(square)
Var(Error) + 3 Var(row(square))
col(square)
Var(Error) + 3 Var(col(square))
tmt
Var(Error) + 3
Var(square*tmt) + Q(tmt)
square*tmt
Var(Error) + 3
Var(square*tmt)
Tests of
Hypotheses for Mixed Model Analysis of
Variance
Dependent
Variable: y
Source
DF Type III SS Mean
Square F Value
Pr > F
square
1 7.345736E-31
7.345736E-31 0.00
1.0000
Error
0.3915
0.652529 1.666667
Error:
MS(row(square)) +
MS(col(square)) + MS(square*tmt) - 2*MS(Error)
Source
DF Type III SS Mean
Square F Value
Pr > F
row(square)
4
9.777778
2.444444 1.38
0.3826
col(square)
4
2.444444
0.611111 0.34
0.8372
square*tmt
2
4.333333
2.166667 1.22
0.3861
Error:
MS(Error)
4
7.111111 1.777778
Source
DF Type III SS Mean
Square F Value
Pr > F
tmt
2
88.111111
44.055556 20.33
0.0469
Error
2
4.333333
2.166667
Error:
MS(square*tmt)
Modified: August 16, 2004
James P. Geaghan