1
dm"log;clear;output;clear";
2
3 options ps=61
ls=78
nocenter nonumber nodate;
4 **EXAMPLE
7********************************************;
5 *** Example of
a
Factorial Design
***;
6 *** From
Snedecor &
Cochran, 1980 (pg 305)
***;
7
*******************************************************;
8 OPTIONS PS=256
LS=78
NOCENTER NODATE PAGENO=1;
9 DATA RATS
(KEEP=LEVEL
SOURCE REP TREATMNT GAIN); INFILE CARDS MISSOVER;
10
ARRAY G GAIN1-GAIN10;
11
INPUT LEVEL $ SOURCE
$ TREATMNT $ 1-11 GAIN1-GAIN10;
12 DO
REP = 1 TO 10;
13
GAIN = G{REP};
OUTPUT; END;
14
TITLE1 'EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS';
15
TITLE2 'FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES';
16 CARDS;
NOTE: The data set WORK.RATS has 60 observations and 5 variables.
NOTE: DATA statement used:
real time
3.46 seconds
cpu time
0.07 seconds
16 !
RUN;
23 ;
24 PROC PRINT; TITLE3
'RAW
DATA LISTING'; RUN;
NOTE: There were 60 observations read from the data set WORK.RATS.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
real time
1.19 seconds
cpu time
0.03 seconds
EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS
FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES
RAW
DATA LISTING
Obs LEVEL SOURCE
TREATMNT REP GAIN
1 HIGH
BEEF HIGH BEEF
1
73
2 HIGH
BEEF HIGH BEEF
2
102
3 HIGH
BEEF HIGH BEEF
3
118
4 HIGH
BEEF HIGH BEEF
4
104
5 HIGH
BEEF HIGH BEEF
5
81
6 HIGH
BEEF HIGH BEEF
6
107
7 HIGH
BEEF HIGH BEEF
7
100
8 HIGH
BEEF HIGH BEEF
8
87
9 HIGH
BEEF HIGH BEEF
9
117
10 HIGH
BEEF HIGH BEEF
10
111
11 HIGH
CEREAL HIGH CEREAL 1
98
12 HIGH
CEREAL HIGH CEREAL 2
74
13 HIGH
CEREAL HIGH CEREAL 3
56
14 HIGH
CEREAL HIGH CEREAL 4
111
15 HIGH
CEREAL HIGH CEREAL 5
95
16 HIGH
CEREAL HIGH CEREAL
6
88
17 HIGH
CEREAL HIGH CEREAL 7
82
18 HIGH
CEREAL HIGH CEREAL 8
77
19 HIGH
CEREAL HIGH CEREAL 9
86
20 HIGH
CEREAL HIGH CEREAL 10
92
21
HIGH PORK
HIGH PORK 1
94
22 HIGH
PORK HIGH PORK
2
79
23 HIGH
PORK HIGH PORK
3
96
24 HIGH
PORK HIGH PORK
4
98
25 HIGH
PORK HIGH PORK
5
102
26 HIGH
PORK HIGH PORK
6
102
27 HIGH
PORK HIGH PORK
7
108
28 HIGH
PORK HIGH PORK
8
91
29 HIGH
PORK HIGH PORK
9
120
30 HIGH
PORK HIGH PORK
10
105
31 LOW
BEEF LOW BEEF
1 90
32 LOW
BEEF LOW BEEF
2 76
33 LOW
BEEF LOW BEEF
3 90
34 LOW
BEEF LOW BEEF
4 64
35 LOW
BEEF LOW BEEF
5 86
36 LOW
BEEF LOW BEEF
6 51
37 LOW
BEEF LOW BEEF
7 72
38 LOW
BEEF LOW BEEF
8 90
39 LOW
BEEF LOW BEEF
9 95
40 LOW
BEEF LOW
BEEF 10
78
41 LOW
CEREAL LOW CEREAL
1 107
42 LOW
CEREAL LOW CEREAL
2 95
43 LOW
CEREAL LOW CEREAL
3 97
44 LOW
CEREAL LOW CEREAL
4 80
45 LOW
CEREAL LOW
CEREAL 5 98
46 LOW
CEREAL LOW CEREAL
6 74
47 LOW
CEREAL LOW CEREAL
7 74
48 LOW
CEREAL LOW CEREAL
8 67
49 LOW
CEREAL LOW CEREAL
9 89
50 LOW
CEREAL LOW CEREAL
10 58
51 LOW
PORK LOW PORK
1 49
52 LOW
PORK LOW PORK
2 82
53 LOW
PORK LOW PORK
3 73
54 LOW
PORK LOW PORK
4 86
55 LOW
PORK LOW PORK
5 81
56 LOW
PORK LOW PORK
6 97
57 LOW
PORK LOW PORK
7 106
58 LOW
PORK LOW PORK
8 70
59 LOW
PORK LOW PORK
9 61
60 LOW
PORK LOW PORK
10 82
25 PROC SORT DATA=RATS;
BY LEVEL SOURCE;
RUN;
NOTE:
There were 60 observations read from the data set WORK.RATS.
NOTE:
The data set WORK.RATS has 60 observations and 5 variables.
NOTE:
PROCEDURE SORT used:
real time
0.55 seconds
cpu time
0.05 seconds
26 PROC mixed DATA=RATS
CL METHOD=TYPE3;
CLASSES LEVEL SOURCE;
27
TITLE3 'FACTORIAL DONE AS 2 WAY
ANOVA IN PROC MIXED';
28 MODEL
GAIN = LEVEL SOURCE LEVEL*SOURCE /
htype=3 OUTP=ResidData;
29 RUN;
NOTE:
The data set WORK.RESIDDATA has 60 observations and 12 variables.
NOTE:
The PROCEDURE MIXED printed page 2.
NOTE:
PROCEDURE MIXED used:
real time
1.70 seconds
cpu time
0.17 seconds
EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS
FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES
FACTORIAL
DONE AS 2 WAY ANOVA IN PROC MIXED
The
Mixed Procedure
Model Information
Data
Set
WORK.RATS
Dependent
Variable
GAIN
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
LEVEL 2
HIGH LOW
SOURCE 3
BEEF CEREAL PORK
Dimensions
Covariance
Parameters
1
Columns
in X
12
Columns
in Z
0
Subjects
1
Max
Obs Per Subject
60
Observations
Used
60
Observations
Not Used
0
Total
Observations
60
Type
3 Analysis of Variance
Sum of
Source
DF Squares
Mean Square
LEVEL
1 3168.266667
3168.266667
SOURCE
2 266.533333
133.266667
LEVEL*SOURCE 2
1178.133333 589.066667
Residual 54
11586 214.555556
Type 3
Analysis of Variance
Source Expected Mean
Square
Error Term Error DF
LEVEL
Var(Residual)+Q(LEVEL,LEVEL*SOURCE)
MS(Residual)
54
SOURCE Var(Residual)+
Q(SOURCE,LEVEL*SOURCE) MS(Residual)
54
LEVEL*SOURCE
Var(Residual)+Q(LEVEL*SOURCE)
MS(Residual)
54
Residual Var(Residual)
.
.
Type
3 Analysis of Variance
Source F Value
Pr > F
LEVEL 14.77
0.0003
SOURCE 0.62
0.5411
LEVEL*SOURCE 2.75
0.0732
Residual .
.
Covariance Parameter Estimates
Cov
Parm Estimate Alpha
Lower Upper
Residual 214.56
0.05
152.06 325.57
Fit
Statistics
-2
Res Log Likelihood
457.0
AIC
(smaller is better)
459.0
AICC
(smaller is better) 459.0
BIC
(smaller is better)
461.0
Type 3 Tests of
Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
LEVEL
1 54
14.77 0.0003
SOURCE
2 54
0.62 0.5411
LEVEL*SOURCE 2
54 2.75 0.0732
30 PROC UNIVARIATE
DATA=ResidData NORMAL
PLOT; VAR RESID;
31
TITLE3 'PROC UNIVARIATE analysis of
residuals'; RUN;
NOTE:
The PROCEDURE UNIVARIATE printed page 3.
NOTE:
PROCEDURE UNIVARIATE used:
real time
0.09 seconds
cpu time
0.02 seconds
EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS
FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES
PROC
UNIVARIATE analysis of residuals
The
UNIVARIATE Procedure
Variable: Resid
Moments
N
60 Sum Weights
60
Mean
0 Sum Observations
0
Std
Deviation 14.0133109
Variance
196.372881
Skewness
-0.3576888 Kurtosis
-0.3451246
Uncorrected
SS 11586
Corrected SS
11586
Coeff
Variation
. Std Error Mean
1.80911065
Basic Statistical Measures
Location
Variability
Mean 0.00000 Std
Deviation
14.01331
Median 2.20000
Variance
196.37288
Mode 10.80000 Range
57.20000
Interquartile Range 19.60000
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t 0
Pr > |t| 1.0000
Sign M
3.5
Pr >= |M| 0.4350
Signed
Rank S 40.5
Pr >= |S| 0.7627
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk W
0.976634 Pr < W
0.3032
Kolmogorov-Smirnov D
0.090078 Pr > D >0.1500
Cramer-von
Mises W-Sq 0.052988
Pr > W-Sq >0.2500
Anderson-Darling A-Sq
0.361662 Pr > A-Sq >0.2500
Quantiles
(Definition 5)
Quantile Estimate
100%
Max 27.30
99%
27.30
95%
21.80
90%
17.50
75%
Q3 10.80
50%
Median 2.20
25%
Q1 -8.80
10%
-19.75
5%
-27.60
1%
-29.90
0%
Min -29.90
Extreme Observations
----Lowest---- ----Highest---
Value Obs
Value Obs
-29.9 13
18.3 56
-29.7 51
20.5 29
-28.2 36
23.1 41
-27.0 1
25.1 14
-25.9 50
27.3
57
Stem Leaf
# Boxplot
2 57
2 |
2 03
2 |
1 6788
4 |
1 11111234
8 +-----+
0 56677789
8
| |
0 0022222334
10 *--+--*
-0 444321
6 | |
-0 998766
6 +-----+
-1 3200
4 |
-1 9875
4 |
-2 0
1
|
-2 876
3 |
-3 00
2 |
----+----+----+----+
Multiply Stem.Leaf by 10**+1
Normal Probability Plot
27.5+
+*++ *
|
+**
|
****
|
******
|
****+
|
****+
-2.5+
***+
|
****+
|
+*+
| ++***
| +++ *
| * ++*+** *
-32.5+ +++
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
33
PROC MEANS DATA=RATS NOPRINT; BY LEVEL SOURCE; VAR GAIN;
34
OUTPUT OUT=RATMEANS N=N MEAN=MEAN
VAR=VAR; RUN;
NOTE: There were 60 observations read from
the data set WORK.RATS.
NOTE: The data set WORK.RATMEANS has 6
observations and 7 variables.
NOTE: PROCEDURE MEANS used:
real time
0.92 seconds
cpu time
0.06 seconds
35
PROC PRINT DATA=RATMEANS; TITLE3
'LISTING OF MEANS'; RUN;
NOTE: There were 6 observations read from
the data set WORK.RATMEANS.
NOTE: The PROCEDURE PRINT printed page 4.
NOTE: PROCEDURE PRINT used:
real time
0.01 seconds
cpu time
0.01 seconds
EXST7015: WEIGHT GAIN IN RATS ON VARIOUS
DIETS
FACTORIAL DESIGN (2 POR 3) WITH REPLICATES
LISTING OF MEANS
Obs
LEVEL SOURCE _TYPE_
_FREQ_ N MEAN
VAR
1
HIGH BEEF
0 10
10 100.0 229.111
2
HIGH CEREAL
0
10 10 85.9
225.656
3 HIGH PORK
0 10
10 99.5 119.167
4
LOW BEEF
0 10
10 79.2 192.844
5
LOW CEREAL
0
10 10 83.9
246.767
6
LOW PORK
0 10
10 78.7 273.789
35
OPTIONS PS=35;
36
PROC PLOT DATA=RATMEANS; TITLE3 'PLOT OF MEANS'; PLOT
36
! MEAN*SOURCE=LEVEL; RUN;
NOTE: There were 6 observations read from
the data set WORK.RATMEANS.
NOTE: The PROCEDURE PLOT printed page 5.
NOTE: PROCEDURE PLOT used:
real time
0.01 seconds
cpu time
0.01 seconds
EXST7015: WEIGHT GAIN IN RATS ON VARIOUS
DIETS
FACTORIAL DESIGN (2 POR 3) WITH REPLICATES
PLOT OF MEANS
Plot of MEAN*SOURCE. Symbol is value of
LEVEL.
MEAN |
100 + H
H
|
|
|
|
|
|
90 +
|
|
|
H
|
L
|
|
80 +
| L
L
|
|
|
|
|
70 +
---+----------------------+----------------------+--
BEEF
CEREAL
PORK
SOURCE
37 PROC PLOT
DATA=RATMEANS; TITLE3
'VARIANCE ON MEANS PLOT'; PLOT
37 ! VAR*MEAN; RUN;
38 OPTIONS PS=256;
NOTE:
There were 6 observations read from the data set WORK.RATMEANS.
NOTE:
The PROCEDURE PLOT printed page 6.
NOTE:
PROCEDURE PLOT used:
real time
0.01 seconds
cpu time
0.01 seconds
EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS
FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES
VARIANCE
ON MEANS PLOT
Plot
of VAR*MEAN. Legend: A = 1 obs, B = 2 obs, etc.
VAR |
300 +
|
|
|
A
|
250
+
A
|
|
A
A
|
|
200 +
|
A
|
|
|
150 +
|
|
|
A
|
100 +
|
--+-------------+-------------+-------------+-------------+-------------
75
80 85
90 95
100
MEAN
40
PROC GLM DATA=RATS; CLASSES LEVEL SOURCE;
41
TITLE3 'FACTORIAL DONE AS 2 WAY ANOVA IN GLM';
42
TITLE4 'ALL TREATMENTS PROBABLY SHOULD BE
FIXED, RUN AS MIXED MODEL TO SHOW EMS';
43 MODEL
GAIN = LEVEL SOURCE
LEVEL*SOURCE;
44
RANDOM LEVEL SOURCE LEVEL*SOURCE
/ TEST;
45
RUN;
NOTE: TYPE I EMS not available without the
E1 option.
46
47
NOTE: The PROCEDURE GLM printed pages 7-10.
NOTE: PROCEDURE GLM used:
real time
0.73 seconds
cpu time
0.04 seconds
EXST7015:
WEIGHT GAIN IN RATS ON VARIOUS DIETS
FACTORIAL
DESIGN (2 POR 3) WITH REPLICATES
FACTORIAL
DONE AS 2 WAY ANOVA IN GLM
ALL
TREATMENTS PROBABLY SHOULD BE FIXED, RUN AS MIXED MODEL TO SHOW EMS
The
GLM Procedure
Class Level Information
Class Levels
Values
LEVEL
2 HIGH LOW
SOURCE
3 BEEF CEREAL PORK
Number
of observations 60
Dependent Variable: GAIN
Sum of
Source
DF Squares
Mean Square F Value
Pr > F
Model
5 4612.93333
922.58667 4.30
0.0023
Error
54 11586.00000 214.55556
Corrected Total
59 16198.93333
R-Square Coeff Var
Root MSE GAIN Mean
0.284768 16.67039
14.64772 87.86667
Source
DF Type I SS Mean Square
F Value
Pr > F
LEVEL
1
3168.266667 3168.266667 14.77
0.0003
SOURCE
2 266.533333 133.266667
0.62
0.5411
LEVEL*SOURCE
2 1178.133333 589.066667
2.75
0.0732
Source
DF Type III SS Mean Square
F Value
Pr > F
LEVEL
1 3168.266667 3168.266667
14.77
0.0003
SOURCE
2 266.533333 133.266667
0.62
0.5411
LEVEL*SOURCE
2 1178.133333 589.066667
2.75
0.0732
Source
Type III Expected Mean Square
LEVEL
Var(Error) + 10
Var(LEVEL*SOURCE) + 30 Var(LEVEL)
SOURCE
Var(Error) + 10
Var(LEVEL*SOURCE) + 20 Var(SOURCE)
LEVEL*SOURCE
Var(Error) + 10 Var(LEVEL*SOURCE)
Tests of Hypotheses for Random Model Analysis of Variance
Dependent Variable: GAIN
Source
DF Type III SS Mean Square
F Value
Pr > F
LEVEL
1 3168.266667 3168.266667
5.38
0.1462
SOURCE
2 266.533333 133.266667
0.23
0.8155
Error
2 1178.133333 589.066667
Error: MS(LEVEL*SOURCE)
Source
DF Type III SS Mean Square
F Value
Pr > F
LEVEL*SOURCE
2 1178.133333 589.066667
2.75
0.0732
Error: MS(Error)
54 11586
214.555556
48 data rats; set rats;
49
if level eq 'HIGH' then gainh =
gain;
50
if level eq 'LOW' then gainl =
gain;
51 run;
NOTE:
There were 60 observations read from the data set WORK.RATS.
NOTE:
The data set WORK.RATS has 60 observations and 7 variables.
NOTE:
DATA statement used:
real time
0.74 seconds
cpu time
0.02 seconds
52
53
GOPTIONS DEVICE=cgm GSFMODE=REPLACE GSFNAME=OUT1 NOPROMPT noROTATE;
54
FILENAME OUT1 'C:\Geaghan\EXST\EXST7015New\SAS\rats01.CGM';
55
PROC GPLOT DATA=rats;
56
TITLE3 F=SWISS H=1 'Plot with
standard 2x errors to examine interaction';
57
PLOT gainh*source=1 gainl*source=2 / OVERLAY HAXIS=AXIS1 VAXIS=AXIS2;
58
AXIS1 LABEL=(F=SWISS H=1
'Protein source') WIDTH=5 MINOR=(N=4)
59
VALUE=(F=SWISS H=1);
60
AXIS2 LABEL=(F=SWISS H=1
'Weight gain') WIDTH=6
61
VALUE=(F=SWISS H=1)
MINOR=(N=4) ORDER= 70 TO 110 BY 10;
62
SYMBOL1 C=RED L=1 V=NONE
I=STD1mjtp W=1 H=1mode=include;
63
SYMBOL2 C=BLUE L=1 V=NONE
I=STD1mjtp W=1 H=1mode=include;
64
**** V = dot would place a dot for each point;
65
**** I = requests STD (std dev) 1 (1 width, 2 or 3) M (of mean=std
65
! err)
66
J (join means of bars) t (add top
& bottom hash) p (use pooled
66
! variance);
67
**** Other options: omit M=std dev, use B to get bar for min/max;
68
* SYMBOL1 C=green L=1 V=dot
I=none W=1 H=1 mode=include;
69
* SYMBOL2 C=magenta L=1
V=dot I=none W=1 H=1 mode=include;
70
RUN;
WARNING: The axis frame outline was drawn
with line width 6 as specified on
the left vertical axis. Any other axis line widths were ignored.
NOTE: 30 observation(s) contained a MISSING
value for the gainh * SOURCE
request.
NOTE: 6 observation(s) outside the axis
range for the gainh * SOURCE request.
NOTE: 30 observation(s) contained a MISSING
value for the gainl * SOURCE
request.
NOTE: 6 observation(s) outside the axis
range for the gainl * SOURCE request.
NOTE:
24 RECORDS WRITTEN TO C:\Geaghan\EXST\EXST7015New\SAS\rats01.CGM
70
! QUIT;
NOTE: There were 60 observations read from
the data set WORK.RATS.
NOTE: PROCEDURE GPLOT used:
real time
4.13 seconds
cpu time
0.22 seconds
71
72
GOPTIONS GSFNAME=OUT2; FILENAME
OUT2
72
! 'C:\Geaghan\EXST\EXST7015New\SAS\RATS02.CGM';
73
PROC GCHART DATA=RATS; TITLE3 'BLOCK CHART TO EXAMINE INTERACTIONS'
73
! ;
74
BLOCK SOURCE / GROUP=LEVEL SUMVAR=GAIN TYPE=MEAN DISCRETE;
75
PATTERN C=RED V=S;RUN;
NOTE:
25 RECORDS WRITTEN TO C:\Geaghan\EXST\EXST7015New\SAS\RATS02.CGM
80 *EXAMPLE 8
********************************************;
81 *** Example of a
2*2*2
Factorial Design
***;
82 *** From Snedecor
&
Cochran, 1980 (pg 359)
***;
83
*******************************************************;
84 OPTIONS PS=256 LS=78
NOCENTER NODATE PAGENO=1;
NOTE: There were 60 observations read from the data set WORK.RATS.
NOTE: PROCEDURE GCHART used:
real time
0.28 seconds
cpu time
0.04 seconds
85 DATA PIGS
(KEEP=LYSINE
PROTEIN REP SEX GAIN); INFILE CARDS MISSOVER
85 ! ;
86
ARRAY G GAIN1-GAIN8;
87
INPUT LYSINE PROTEIN
SEX $ GAIN1-GAIN8;
88
FORMAT GAIN 5.1;
89 DO
REP = 1 TO 8;
90
GAIN = G{REP};
OUTPUT; END;
91
TITLE1 'EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS';
92
TITLE2 'FACTORIAL DESIGN (2x2x2)
WITH
REPLICATES';
93 CARDS;
NOTE: The data set WORK.PIGS has 64 observations and 5 variables.
NOTE: DATA statement used:
real time
0.29 seconds
cpu time
0.02 seconds
93 !
RUN;
102 ;
103 PROC PRINT; TITLE3 'RAW
DATA LISTING'; RUN;
NOTE: There were 64 observations read from the data set WORK.PIGS.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
real time
0.02 seconds
cpu time
0.01 seconds
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
RAW
DATA LISTING
Obs
LYSINE PROTEIN SEX
GAIN REP
1 0.0
12
M 1.1 1
2 0.0
12
M 1.0 2
3 0.0
12
M 1.1 3
4 0.0
12
M 1.0 4
5 0.0
12
M 0.9 5
6 0.0
12
M 1.2 6
7 0.0
12
M 1.3
7
8 0.0
12
M 1.0 8
9 0.0
12
F 1.0 1
10
0.0 12
F
1.0 2
11
0.0 12
F
1.0 3
12
0.0 12
F
1.0 4
13 0.0
12
F 1.0 5
14
0.0 12
F
1.2 6
15
0.0 12
F
1.2 7
16
0.0 12
F
1.2 8
17
0.0 14
M
1.5 1
18
0.0 14
M
1.5 2
19
0.0 14
M
1.3 3
20
0.0 14
M
1.2 4
21
0.0 14
M
1.7 5
22
0.0 14
M
1.2 6
23
0.0 14
M
1.3 7
24 0.0
14 M
1.3
8
25
0.0 14
F
1.5 1
26
0.0 14
F
1.2 2
27
0.0 14
F
1.5 3
28
0.0 14
F
1.2 4
29
0.0 14
F
1.2 5
30
0.0 14
F
1.6 6
31
0.0 14
F
1.1 7
32
0.0 14
F
1.4 8
33
0.6 12
M
1.2 1
34
0.6 12
M
1.1 2
35
0.6 12
M
1.3 3
36
0.6 12
M
1.4 4
37
0.6 12
M
1.3 5
38
0.6 12
M
1.2 6
39
0.6 12
M
1.3 7
40
0.6 12
M
1.3 8
41
0.6 12
F
0.9 1
42
0.6 12
F
1.0 2
43
0.6 12
F
1.2 3
44
0.6 12
F
1.3 4
45
0.6 12
F
1.0 5
46
0.6 12
F
1.1 6
47
0.6 12
F
1.4 7
48
0.6 12
F
1.3 8
49
0.6 14
M
1.4 1
50
0.6 14
M
1.1 2
51
0.6 14
M 1.4 3
52
0.6 14
M
1.2 4
53
0.6 14
M
1.5 5
54
0.6 14
M
1.4 6
55
0.6 14
M
1.2 7
56
0.6 14
M
1.2 8
57
0.6 14
F
1.1 1
58
0.6 14
F
1.1 2
59
0.6 14
F
1.5 3
60
0.6 14
F
1.4 4
61
0.6 14
F
1.2 5
62
0.6 14
F
1.2 6
63
0.6 14
F
1.0 7
64
0.6 14
F
1.1 8
104
PROC SORT DATA=PIGS; BY LYSINE PROTEIN
SEX; RUN;
NOTE:
There were 64 observations read from the data set WORK.PIGS.
NOTE:
The data set WORK.PIGS has 64 observations and 5 variables.
NOTE:
PROCEDURE SORT used:
real time
0.05 seconds
cpu
time
0.04 seconds
105
PROC MIXED DATA=PIGS CL METHOD=TYPE3;
CLASSES LYSINE PROTEIN SEX;
106
TITLE3 'ANALYSIS
OF VARIANCE WITH
MIXED';
107
MODEL GAIN = LYSINE|PROTEIN|SEX /
htype=3 OUTP=ResidData;
108
RUN;
NOTE:
The data set WORK.RESIDDATA has 64 observations and 12 variables.
NOTE:
The PROCEDURE MIXED printed page 2.
NOTE:
PROCEDURE MIXED used:
real time
0.53 seconds
cpu
time
0.13 seconds
108
!
QUIT;
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
ANALYSIS
OF VARIANCE WITH MIXED
The
Mixed Procedure
Model Information
Data
Set
WORK.PIGS
Dependent
Variable
GAIN
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
LYSINE
2
0 0.6
PROTEIN
2
12 14
SEX
2 F M
Dimensions
Covariance
Parameters
1
Columns
in
X
27
Columns
in
Z
0
Subjects
1
Max
Obs Per
Subject
64
Observations
Used
64
Observations
Not
Used
0
Total
Observations
64
Type 3 Analysis of Variance
Sum of
Source
DF
Squares Mean Square
LYSINE
1
0.003164 0.003164
PROTEIN
1
0.430664 0.430664
LYSINE*PROTEIN
1
0.258827 0.258827
SEX
1
0.057002 0.057002
LYSINE*SEX
1
0.037539 0.037539
PROTEIN*SEX
1 0.000076562
0.000076562
LYSINE*PROTEIN*SEX
1
0.011289 0.011289
Residual
56
1.240538 0.022152
Type 3 Analysis of
Variance
Error
Source
Expected Mean
Square
Error Term DF
LYSINE
Var(Residual)
+
MS(Residual) 56
Q(LYSINE,LYSINE*PROTEIN,LYSINE*
SEX,LYSINE*PROTEIN*SEX)
PROTEIN
Var(Residual)
+
MS(Residual) 56
Q(PROTEIN,LYSINE*PROTEIN,PROTEIN*
SEX,LYSINE*PROTEIN*SEX)
LYSINE*PROTEIN
Var(Residual)
+
MS(Residual) 56
Q(LYSINE*PROTEIN,LYSINE*
PROTEIN*SEX)
SEX
Var(Residual)
+
MS(Residual) 56
Q(SEX,LYSINE*SEX,PROTEIN*
SEX,LYSINE*PROTEIN*SEX)
LYSINE*SEX
Var(Residual)
+
MS(Residual) 56
Q(LYSINE*SEX,LYSINE*PROTEIN*SEX)
PROTEIN*SEX
Var(Residual)
+
MS(Residual) 56
Q(PROTEIN*SEX,LYSINE*PROTEIN*SEX)
LYSINE*PROTEIN*SEX
Var(Residual)
+
MS(Residual) 56
Q(LYSINE*PROTEIN*SEX)
Residual
Var(Residual)
.
.
Type 3 Analysis of Variance
Source
F Value Pr > F
LYSINE
0.14
0.7069
PROTEIN
19.44 <.0001
LYSINE*PROTEIN
11.68
0.0012
SEX
2.57 0.1143
LYSINE*SEX
1.69 0.1983
PROTEIN*SEX
0.00 0.9533
LYSINE*PROTEIN*SEX
0.51
0.4783
Residual
. .
Covariance Parameter Estimates
Cov
Parm Estimate
Alpha
Lower Upper
Residual
0.02215 0.05
0.01579 0.03334
Fit Statistics
-2
Res Log
Likelihood
-37.8
AIC
(smaller is better)
-35.8
AICC
(smaller is better) -35.7
BIC
(smaller is better)
-33.8
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
LYSINE
1
56
0.14 0.7069
PROTEIN
1 56
19.44 <.0001
LYSINE*PROTEIN
1 56
11.68 0.0012
SEX
1 56
2.57 0.1143
LYSINE*SEX
1 56
1.69 0.1983
PROTEIN*SEX
1 56
0.00 0.9533
LYSINE*PROTEIN*SEX
1
56 0.51 0.4783
110
PROC UNIVARIATE DATA=ResidData NORMAL
PLOT; VAR RESID;
111
TITLE3 'PROC UNIVARIATE analysis of
residuals'; RUN;
NOTE:
The PROCEDURE UNIVARIATE printed page 3.
NOTE:
PROCEDURE UNIVARIATE used:
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
PROC
UNIVARIATE analysis of residuals
The
UNIVARIATE Procedure
Variable:
Resid
Moments
N
64 Sum
Weights
64
Mean
0 Sum
Observations
0
Std
Deviation 0.14032488
Variance
0.01969107
Skewness
0.24838382
Kurtosis
-0.9998829
Uncorrected
SS 1.2405375 Corrected
SS 1.2405375
Coeff
Variation
. Std Error Mean
0.01754061
Basic Statistical Measures
Location
Variability
Mean
0.00000
Std
Deviation
0.14032
Median
-0.03625
Variance
0.01969
Mode
-0.08625
Range
0.56375
Interquartile Range 0.23500
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t
0
Pr > |t| 1.0000
Sign
M -3
Pr >= |M| 0.5323
Signed
Rank S
-9
Pr >= |S| 0.9526
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.959246 Pr < W
0.0334
Kolmogorov-Smirnov
D
0.12541 Pr > D 0.0137
Cramer-von
Mises W-Sq
0.193266
Pr > W-Sq 0.0064
Anderson-Darling
A-Sq
1.027144 Pr > A-Sq 0.0098
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max 0.29125
99%
0.29125
95%
0.23125
90%
0.19125
75%
Q3 0.12375
50%
Median -0.03625
25%
Q1 -0.11125
10%
-0.15875
5%
-0.20750
1%
-0.27250
0%
Min -0.27250
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-0.27250
33
0.22625 52
-0.20875
13
0.23125 15
-0.20875
23
0.23125 22
-0.20750
58
0.26625 51
-0.19375
55
0.29125 29
Stem
Leaf
# Boxplot
2
79
2 |
2
2333
4
|
1
556789
6 |
1
0113444
7 +-----+
0
566799
6 | |
0
2344
4 |
+ |
-0
4320
4 *-----*
-0 999988877665
12
| |
-1
44442211110
11
+-----+
-1
9865
4 |
-2
111
3 |
-2
7
1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Normal
Probability Plot
0.275+
++*+
*
|
****
|
****+
|
****+
|
***++
|
+***
|
++***
|
+******
|
*******
| ***++
|
* **+
-0.275+
* ++++
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
113
PROC MEANS DATA=PIGS NOPRINT; BY LYSINE
PROTEIN; VAR GAIN;
114
OUTPUT OUT=PIGMEANS N=N MEAN=MEAN
VAR=VAR; RUN;
NOTE:
There were 64 observations read from the data set WORK.PIGS.
NOTE:
The data set WORK.PIGMEANS has 4 observations and 7 variables.
NOTE:
PROCEDURE MEANS used:
real time
0.25 seconds
cpu
time
0.04 seconds
115
DATA PIGMEANS; SET PIGMEANS; PROT='H';
IF PROTEIN LE 12 THEN
115
! PROT='L'; RUN;
NOTE:
There were 4 observations read from the data set WORK.PIGMEANS.
NOTE:
The data set WORK.PIGMEANS has 4 observations and 8 variables.
NOTE:
DATA statement used:
real time
0.08 seconds
cpu
time
0.04 seconds
116
PROC PRINT DATA=PIGMEANS; TITLE3 'LISTING OF MEANS'; RUN;
NOTE:
There were 4 observations read from the data set WORK.PIGMEANS.
NOTE:
The PROCEDURE PRINT printed page 4.
NOTE:
PROCEDURE PRINT used:
real time
0.02 seconds
cpu
time
0.01 seconds
117
OPTIONS PS=35;
118
PROC PLOT DATA=PIGMEANS; TITLE3 'PLOT
OF MEANS';
119
PLOT MEAN*LYSINE=PROT; RUN;
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
LISTING
OF MEANS
Obs
LYSINE
PROTEIN _TYPE_ _FREQ_
N MEAN
VAR
PROT
1
0.0
12
0
16 16 1.1
0.016033 L
2
0.0
14
0
16 16 1.4
0.027172 H
3
0.6
12
0
16 16 1.2
0.023105 L
4
0.6
14
0
16 16 1.2
0.023453 H
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
PLOT
OF MEANS
Plot of MEAN*LYSINE. Symbol is value of PROT.
MEAN |
1.4 +
|
|
H
|
|
1.3 +
|
|
|
H
|
1.2
+
L
|
|
|
|
1.1 +
|
|
L
|
|
1.0 +
|
---+-----------------------------------------------+--
0.0
0.6
LYSINE
120
GOPTIONS GSFNAME=OUT2; FILENAME OUT2
120
!
'C:\Geaghan\EXST\EXST7015New\SAS\PIGS.CGM';
NOTE:
There were 4 observations read from the data set WORK.PIGMEANS.
NOTE:
The PROCEDURE PLOT printed page 5.
NOTE:
PROCEDURE PLOT used:
real time
0.03 seconds
cpu
time
0.01 seconds
121
PROC GCHART DATA=PIGS; TITLE3 'BLOCK
CHART TO EXAMINE INTERACTIONS'
121
! ;
122
BLOCK lysine / GROUP=PROTEIN
SUMVAR=GAIN TYPE=MEAN DISCRETE;
123
PATTERN C=RED V=S; RUN;
NOTE: 22
RECORDS WRITTEN TO
C:\Geaghan\EXST\EXST7015New\SAS\PIGS.CGM
124
OPTIONS PS=256 LS=78;
NOTE:
There were 64 observations read from the data set WORK.PIGS.
NOTE:
PROCEDURE GCHART used:
real time
0.26 seconds
cpu
time
0.06 seconds
126
PROC GLM DATA=PIGS; CLASSES LYSINE
PROTEIN SEX;
127
TITLE3 'ANALYSIS OF VARIANCE WITH
GLM';
128
TITLE4 'ALL TREATMENTS PROBABLY
SHOULD BE FIXED, RUN AS MIXED
128
! MODEL TO SHOW EMS';
129
MODEL GAIN = LYSINE|PROTEIN|SEX;
130
RANDOM LYSINE|PROTEIN LYSINE*SEX
PROTEIN*SEX LYSINE*PROTEIN*SEX /
130
!
TEST;
131
RUN;
NOTE:
TYPE I EMS not available without the E1 option.
131
!
QUIT;
NOTE:
The PROCEDURE GLM printed pages 6-9.
NOTE:
PROCEDURE GLM used:
real time
0.09 seconds
cpu
time
0.09 seconds
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
ANALYSIS
OF VARIANCE WITH GLM
ALL
TREATMENTS PROBABLY SHOULD BE FIXED, RUN AS MIXED MODEL TO SHOW EMS
The
GLM Procedure
Class Level Information
Class
Levels Values
LYSINE
2 0 0.6
PROTEIN
2
12 14
SEX
2 F M
Number
of observations 64
Dependent
Variable: GAIN
Sum
of
Source
DF Squares
Mean Square F Value
Pr > F
Model
7 0.79856094
0.11408013 5.15
0.0001
Error
56 1.24053750 0.02215246
Corrected
Total
63 2.03909844
R-Square
Coeff Var Root
MSE GAIN Mean
0.391625
12.19819
0.148837 1.220156
Source
DF Type I SS Mean
Square F Value
Pr > F
LYSINE
1 0.00316406
0.00316406 0.14
0.7069
PROTEIN
1 0.43066406
0.43066406 19.44
<.0001
LYSINE*PROTEIN
1 0.25882656
0.25882656 11.68
0.0012
SEX
1 0.05700156
0.05700156 2.57
0.1143
LYSINE*SEX
1 0.03753906
0.03753906 1.69
0.1983
PROTEIN*SEX
1 0.00007656
0.00007656 0.00
0.9533
LYSINE*PROTEIN*SEX
1 0.01128906
0.01128906 0.51
0.4783
Source
DF Type III SS Mean
Square F Value
Pr > F
LYSINE
1 0.00316406
0.00316406 0.14
0.7069
PROTEIN
1 0.43066406
0.43066406 19.44
<.0001
LYSINE*PROTEIN
1 0.25882656
0.25882656 11.68
0.0012
SEX
1 0.05700156
0.05700156 2.57
0.1143
LYSINE*SEX
1 0.03753906
0.03753906 1.69
0.1983
PROTEIN*SEX
1
0.00007656
0.00007656 0.00
0.9533
LYSINE*PROTEIN*SEX
1 0.01128906
0.01128906 0.51
0.4783
EXST7015:
PIG WEIGHT GAIN WITH DIET SUPPLEMENTS
FACTORIAL
DESIGN (2x2x2) WITH REPLICATES
ANALYSIS
OF VARIANCE WITH GLM
ALL
TREATMENTS PROBABLY SHOULD BE FIXED, RUN AS MIXED MODEL TO SHOW EMS
The
GLM Procedure
Source
Type III Expected Mean Square
LYSINE
Var(Error) + 8
Var(LYSINE*PROTEIN*SEX) + 16
Var(LYSINE*SEX) + 16
Var(LYSINE*PROTEIN) + 32
Var(LYSINE)
PROTEIN
Var(Error) + 8
Var(LYSINE*PROTEIN*SEX) + 16
Var(PROTEIN*SEX) + 16
Var(LYSINE*PROTEIN) + 32
Var(PROTEIN)
LYSINE*PROTEIN
Var(Error) + 8 Var(LYSINE*PROTEIN*SEX)
+ 16
Var(LYSINE*PROTEIN)
SEX
Var(Error) + 8
Var(LYSINE*PROTEIN*SEX) + 16
Var(PROTEIN*SEX) + 16
Var(LYSINE*SEX) + Q(SEX)
LYSINE*SEX
Var(Error) + 8 Var(LYSINE*PROTEIN*SEX)
+ 16
Var(LYSINE*SEX)
PROTEIN*SEX
Var(Error) + 8
Var(LYSINE*PROTEIN*SEX) + 16
Var(PROTEIN*SEX)
Tests of
Hypotheses for Mixed Model Analysis of Variance
Dependent
Variable: GAIN
Source
DF
Type III SS Mean Square F
Value
Pr > F
LYSINE
1
0.003164
0.003164 0.01
0.9310
Error
1.1859
0.338079 0.285077
Error:
MS(LYSINE*PROTEIN) + MS(LYSINE*SEX) - MS(LYSINE*PROTEIN*SEX)
Source
DF Type III SS Mean
Square F Value
Pr > F
PROTEIN
1
0.430664
0.430664 1.74
0.4279
Error
0.9135
0.226195 0.247614
Error:
MS(LYSINE*PROTEIN) + MS(PROTEIN*SEX) - MS(LYSINE*PROTEIN*SEX)
Source
DF Type III SS Mean
Square F Value
Pr > F
LYSINE*PROTEIN
1
0.258827
0.258827 22.93
0.1311
LYSINE*SEX
1
0.037539
0.037539 3.33
0.3193
PROTEIN*SEX
1 0.000076563
0.000076563 0.01
0.9477
Error
1
0.011289 0.011289
Error:
MS(LYSINE*PROTEIN*SEX)
Source
DF Type III SS Mean
Square F Value
Pr > F
SEX
1
0.057002
0.057002 2.17
0.5332
Error
0.451
0.011874 0.026327
Error:
MS(LYSINE*SEX) + MS(PROTEIN*SEX) - MS(LYSINE*PROTEIN*SEX)
Source
DF
Type III SS Mean Square F
Value
Pr > F
LYSINE*PROTEIN*SEX
1
0.011289
0.011289 0.51
0.4783
Error:
MS(Error)
56
1.240537 0.022152
Modified: August 16, 2004
James P. Geaghan