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