1          *****************************************************************;
2          *** Example of a Repeated Measures Design                     ***;
3          *** From Snedecor & Cochran, 1960 (pg 379) with modifications ***;
4          *****************************************************************;
5          OPTIONS PS=256 LS=121 NOCENTER NODATE PAGENO=1 NONUMBER;
6          DATA HARVEST (KEEP=CUTTING BLOCK YEAR HARVEST); INFILE CARDS MISSOVER;
7             ARRAY C YIELD1-YIELD4;
8             INPUT BLOCK $ YEAR $ YIELD1-YIELD4;
9             DO I = 1 TO 4;
10               IF I = 1 THEN CUTTING = '6/1 ';
11               IF I = 2 THEN CUTTING = '6/15';
12               IF I = 3 THEN CUTTING = '7/1 ';
13               IF I = 4 THEN CUTTING = '7/15';
14               HARVEST = C{I}; OUTPUT;  END;
15               TITLE1 'EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)';
16               TITLE2 'Repeated measure is 4 years of the study';
17         CARDS;
NOTE: The data set WORK.HARVEST has 64 observations and 4 variables.
NOTE: DATA statement used:
      real time           0.07 seconds
      cpu time            0.07 seconds
17       !        RUN;
34         ;
35         PROC PRINT; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There were 64 observations read from the data set WORK.HARVEST.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
      real time           0.03 seconds
      cpu time            0.03 seconds
 
EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
RAW DATA LISTING
 

Obs    BLOCK    YEAR    CUTTING    HARVEST
  1      1       0       6/1         230 
  2      1       0       6/15        212 
  3      1       0       7/1         183 
  4      1       0       7/15        148 
  5      1       1       6/1         324 
  6      1       1       6/15        415 
  7      1       1       7/1         320 
  8      1       1       7/15        246 
  9      1       2       6/1         512  
 10      1       2       6/15        584 
 11      1       2       7/1         456 
 12      1       2       7/15        304 
 13      1       3       6/1         399 
 14      1       3       6/15        386 
 15      1       3       7/1         255 
 16      1       3       7/15        144 
 17      2       0       6/1         216 
 18      2       0       6/15        190 
 19      2       0       7/1         186 
 20      2       0       7/15        126 
 21      2       1       6/1         317 
 22      2       1       6/15        296 
 23      2       1       7/1         295 
 24      2       1       7/15        201 
 25      2       2       6/1         448 
 26      2       2       6/15        471 
 27      2       2       7/1         387 
 28      2       2       7/15        289 
 29      2       3       6/1         361 
 30      2       3       6/15        280 
 31      2       3       7/1         187 
 32      2       3       7/15         83 
 33      3       0       6/1         219 
 34      3       0       6/15        151 
 35      3       0       7/1         177 
 36      3       0       7/15        107 
 37      3       1       6/1         357 
 38      3       1       6/15        278 
 39      3       1       7/1         298 
 40      3       1       7/15        192 
 41      3       2       6/1         496 
 42      3       2       6/15        399 
 43      3       2       7/1         427 
 44      3       2       7/15        271 
 45      3       3       6/1         344 
 46      3       3       6/15        254 
 47      3       3       7/1         239 
 48      3       3       7/15         90 
 49      4       0       6/1         200 
 50      4       0       6/15        150 
 51      4       0       7/1         209 
 52      4       0       7/15        168 
 53      4       1       6/1         362 
 54      4       1       6/15        336 
 55      4       1       7/1         328 
 56      4       1       7/15        226 
 57      4       2       6/1         540 
 58      4       2       6/15        485 
 59      4       2       7/1         462 
 60      4       2       7/15        312 
 61      4       3       6/1         381 
 62      4       3       6/15        279 
 63      4       3       7/1         244 
 64      4       3       7/15        168 



36         PROC MIXED DATA=HARVEST CL; CLASSES BLOCK YEAR CUTTING;
37             TITLE3 'Split plot Analysis of Variance with PROC MIXED and AR(1) covariance';
38           MODEL HARVEST = CUTTING YEAR CUTTING*YEAR / htype=3 outp=ResidDataP;
39             RANDOM BLOCK BLOCK*CUTTING;
40             REPEATED YEAR / SUBJECT=BLOCK*CUTTING TYPE=AR(1);
41             lsmeans cutting*year / slice=year;
42             lsmeans cutting year cutting*year / pdiff adjust=tukey;
43         RUN;
NOTE: Convergence criteria met.
NOTE: The data set WORK.RESIDDATAP has 64 observations and 11 variables.
NOTE: The PROCEDURE MIXED printed pages 2-3.
NOTE: PROCEDURE MIXED used:
      real time           0.54 seconds
      cpu time            0.54 seconds
43       !      QUIT;OPTIONS PS=50 LS=80;
 
EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Split plot Analysis of Variance with PROC MIXED and AR(1) covariance
 
The Mixed Procedure
 
                  Model Information
 
Data Set                     WORK.HARVEST            
Dependent Variable           HARVEST                 
Covariance Structures        Variance Components,    
                             Autoregressive          
Subject Effect               BLOCK*CUTTING           
Estimation Method            REML                    
Residual Variance Method     Profile                 
Fixed Effects SE Method      Model-Based             
Degrees of Freedom Method    Containment             
 
Class Level Information
Class      Levels    Values
BLOCK           4    1 2 3 4                      
YEAR            4    0 1 2 3                      
CUTTING         4    6/1 6/15 7/1 7/15             
 
Dimensions
Covariance Parameters             4
Columns in X                     25
Columns in Z                     20
Subjects                          1
Max Obs Per Subject              64
Observations Used                64
Observations Not Used             0
Total Observations               64
 
Iteration History
Iteration    Evaluations    -2 Res Log Like       Criterion
        0              1       506.34762590               
        1              3       470.97346057      0.00021691
        2              2       470.94926182      0.00004073
        3              1       470.94074781      0.00000105
        4              1       470.94054268      0.00000000
                   Convergence criteria met.                   
 
 


Covariance Parameter Estimates
Cov Parm          Subject          Estimate     Alpha       Lower       Upper
BLOCK                                421.43      0.05      105.67       31077
BLOCK*CUTTING                        126.08      0.05     11.1978    9.021E30
AR(1)             BLOCK*CUTTING      0.5612      0.05    -0.03582      1.1582
Residual                             765.31      0.05      277.67     6046.99
 
Fit Statistics
-2 Res Log Likelihood           470.9
AIC (smaller is better)         478.9
AICC (smaller is better)        479.9
BIC (smaller is better)         476.5
 
Type 3 Tests of Fixed Effects
Effect        Num DF  Den DF    F Value    Pr > F
CUTTING            3       9      36.20    <.0001
YEAR               3      36     431.61    <.0001
YEAR*CUTTING       9      36       8.91    <.0001
 
Least Squares Means
                                               Standard
Effect          YEAR    CUTTING    Estimate       Error      DF    t Value    Pr > |t|
YEAR*CUTTING    0       6/1          216.25     18.1164      36      11.94      <.0001
YEAR*CUTTING    0       6/15         175.75     18.1164      36       9.70      <.0001
YEAR*CUTTING    0       7/1          188.75     18.1164      36      10.42      <.0001
YEAR*CUTTING    0       7/15         137.25     18.1164      36       7.58      <.0001
YEAR*CUTTING    1       6/1          340.00     18.1164      36      18.77      <.0001
YEAR*CUTTING    1       6/15         331.25     18.1164      36      18.28      <.0001
YEAR*CUTTING    1       7/1          310.25     18.1164      36      17.13      <.0001
YEAR*CUTTING    1       7/15         216.25     18.1164      36      11.94      <.0001
YEAR*CUTTING    2       6/1          499.00     18.1164      36      27.54      <.0001
YEAR*CUTTING    2       6/15         484.75     18.1164      36      26.76      <.0001
YEAR*CUTTING    2       7/1          433.00     18.1164      36      23.90      <.0001
YEAR*CUTTING    2       7/15         294.00     18.1164      36      16.23      <.0001
YEAR*CUTTING    3       6/1          371.25     18.1164      36      20.49      <.0001
YEAR*CUTTING    3       6/15         299.75     18.1164      36      16.55      <.0001
YEAR*CUTTING    3       7/1          231.25     18.1164      36      12.76      <.0001
YEAR*CUTTING    3       7/15         121.25     18.1164      36       6.69      <.0001
CUTTING                 6/1          356.63     15.6289       9      22.82      <.0001
CUTTING                 6/15         322.88     15.6289       9      20.66      <.0001
CUTTING                 7/1          290.81     15.6289       9      18.61      <.0001
CUTTING                 7/15         192.19     15.6289       9      12.30      <.0001
YEAR            0                    179.50     12.6913      36      14.14      <.0001
YEAR            1                    299.44     12.6913      36      23.59      <.0001
YEAR            2                    427.69     12.6913      36      33.70      <.0001
YEAR            3                    255.88     12.6913      36      20.16      <.0001
YEAR*CUTTING    0       6/1          216.25     18.1164      36      11.94      <.0001
YEAR*CUTTING    0       6/15         175.75     18.1164      36       9.70      <.0001
YEAR*CUTTING    0       7/1          188.75     18.1164      36      10.42      <.0001
YEAR*CUTTING    0       7/15         137.25     18.1164      36       7.58      <.0001
YEAR*CUTTING    1       6/1          340.00     18.1164      36      18.77      <.0001
YEAR*CUTTING    1       6/15         331.25     18.1164      36      18.28      <.0001
YEAR*CUTTING    1       7/1          310.25     18.1164      36      17.13      <.0001
YEAR*CUTTING    1       7/15         216.25     18.1164      36      11.94      <.0001
YEAR*CUTTING    2       6/1          499.00     18.1164      36      27.54      <.0001
YEAR*CUTTING    2       6/15         484.75     18.1164      36      26.76      <.0001
YEAR*CUTTING    2       7/1          433.00     18.1164      36      23.90      <.0001
YEAR*CUTTING    2       7/15         294.00     18.1164      36      16.23      <.0001
YEAR*CUTTING    3       6/1          371.25     18.1164      36      20.49      <.0001
YEAR*CUTTING    3       6/15         299.75     18.1164      36      16.55      <.0001
YEAR*CUTTING    3       7/1          231.25     18.1164      36      12.76      <.0001
YEAR*CUTTING    3       7/15         121.25     18.1164      36       6.69      <.0001
 
 


Differences of Least Squares Means
                                                        Standard
Effect        YEAR  CUTTING  _YEAR  _CUTTING  Estimate     Error    DF  t Value  Pr > |t|  Adjustment     Adj P
CUTTING             6/1             6/15       33.7500   16.6677     9     2.02    0.0735  Tukey-Kramer  0.2482
CUTTING             6/1             7/1        65.8125   16.6677     9     3.95    0.0034  Tukey-Kramer  0.0146
CUTTING             6/1             7/15        164.44   16.6677     9     9.87    <.0001  Tukey-Kramer  <.0001
CUTTING             6/15            7/1        32.0625   16.6677     9     1.92    0.0866  Tukey-Kramer  0.2841
CUTTING             6/15            7/15        130.69   16.6677     9     7.84    <.0001  Tukey-Kramer  0.0001
CUTTING             7/1             7/15       98.6250   16.6677     9     5.92    0.0002  Tukey-Kramer  0.0010
YEAR          0              1                 -119.94    6.4790    36   -18.51    <.0001  Tukey-Kramer  <.0001
YEAR          0              2                 -248.19    8.0954    36   -30.66    <.0001  Tukey-Kramer  <.0001
YEAR          0              3                -76.3750    8.8744    36    -8.61    <.0001  Tukey-Kramer  <.0001
YEAR          1              2                 -128.25    6.4790    36   -19.79    <.0001  Tukey-Kramer  <.0001
YEAR          1              3                 43.5625    8.0954    36     5.38    <.0001  Tukey-Kramer  <.0001
YEAR          2              3                  171.81    6.4790    36    26.52    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      0      6/15       40.5000   21.1114    36     1.92    0.0630  Tukey-Kramer  0.8508
YEAR*CUTTING  0     6/1      0      7/1        27.5000   21.1114    36     1.30    0.2010  Tukey-Kramer  0.9932
YEAR*CUTTING  0     6/1      0      7/15       79.0000   21.1114    36     3.74    0.0006  Tukey-Kramer  0.0425
YEAR*CUTTING  0     6/1      1      6/1        -123.75   12.9580    36    -9.55    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      1      6/15       -115.00   21.1114    36    -5.45    <.0001  Tukey-Kramer  0.0004
YEAR*CUTTING  0     6/1      1      7/1       -94.0000   21.1114    36    -4.45    <.0001  Tukey-Kramer  0.0065
YEAR*CUTTING  0     6/1      1      7/15      -368E-15   21.1114    36    -0.00    1.0000  Tukey-Kramer  1.0000
YEAR*CUTTING  0     6/1      2      6/1        -282.75   16.1907    36   -17.46    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      2      6/15       -268.50   21.1114    36   -12.72    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      2      7/1        -216.75   21.1114    36   -10.27    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      2      7/15      -77.7500   21.1114    36    -3.68    0.0008  Tukey-Kramer  0.0492
YEAR*CUTTING  0     6/1      3      6/1        -155.00   17.7489    36    -8.73    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/1      3      6/15      -83.5000   21.1114    36    -3.96    0.0003  Tukey-Kramer  0.0248
YEAR*CUTTING  0     6/1      3      7/1       -15.0000   21.1114    36    -0.71    0.4820  Tukey-Kramer  1.0000
YEAR*CUTTING  0     6/1      3      7/15       95.0000   21.1114    36     4.50    <.0001  Tukey-Kramer  0.0057
YEAR*CUTTING  0     6/15     0      7/1       -13.0000   21.1114    36    -0.62    0.5419  Tukey-Kramer  1.0000
YEAR*CUTTING  0     6/15     0      7/15       38.5000   21.1114    36     1.82    0.0765  Tukey-Kramer  0.8916
YEAR*CUTTING  0     6/15     1      6/1        -164.25   21.1114    36    -7.78    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     1      6/15       -155.50   12.9580    36   -12.00    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     1      7/1        -134.50   21.1114    36    -6.37    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     1      7/15      -40.5000   21.1114    36    -1.92    0.0630  Tukey-Kramer  0.8508
YEAR*CUTTING  0     6/15     2      6/1        -323.25   21.1114    36   -15.31    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     2      6/15       -309.00   16.1907    36   -19.08    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     2      7/1        -257.25   21.1114    36   -12.19    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     2      7/15       -118.25   21.1114    36    -5.60    <.0001  Tukey-Kramer  0.0002
YEAR*CUTTING  0     6/15     3      6/1        -195.50   21.1114    36    -9.26    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     3      6/15       -124.00   17.7489    36    -6.99    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     6/15     3      7/1       -55.5000   21.1114    36    -2.63    0.0125  Tukey-Kramer  0.4112
YEAR*CUTTING  0     6/15     3      7/15       54.5000   21.1114    36     2.58    0.0141  Tukey-Kramer  0.4406
YEAR*CUTTING  0     7/1      0      7/15       51.5000   21.1114    36     2.44    0.0198  Tukey-Kramer  0.5329
YEAR*CUTTING  0     7/1      1      6/1        -151.25   21.1114    36    -7.16    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      1      6/15       -142.50   21.1114    36    -6.75    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      1      7/1        -121.50   12.9580    36    -9.38    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      1      7/15      -27.5000   21.1114    36    -1.30    0.2010  Tukey-Kramer  0.9932
YEAR*CUTTING  0     7/1      2      6/1        -310.25   21.1114    36   -14.70    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      2      6/15       -296.00   21.1114    36   -14.02    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      2      7/1        -244.25   16.1907    36   -15.09    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      2      7/15       -105.25   21.1114    36    -4.99    <.0001  Tukey-Kramer  0.0014
YEAR*CUTTING  0     7/1      3      6/1        -182.50   21.1114    36    -8.64    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/1      3      6/15       -111.00   21.1114    36    -5.26    <.0001  Tukey-Kramer  0.0006
YEAR*CUTTING  0     7/1      3      7/1       -42.5000   17.7489    36    -2.39    0.0220  Tukey-Kramer  0.5629
YEAR*CUTTING  0     7/1      3      7/15       67.5000   21.1114    36     3.20    0.0029  Tukey-Kramer  0.1478
YEAR*CUTTING  0     7/15     1      6/1        -202.75   21.1114    36    -9.60    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     1      6/15       -194.00   21.1114    36    -9.19    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     1      7/1        -173.00   21.1114    36    -8.19    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     1      7/15      -79.0000   12.9580    36    -6.10    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     2      6/1        -361.75   21.1114    36   -17.14    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     2      6/15       -347.50   21.1114    36   -16.46    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     2      7/1        -295.75   21.1114    36   -14.01    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     2      7/15       -156.75   16.1907    36    -9.68    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     3      6/1        -234.00   21.1114    36   -11.08    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     3      6/15       -162.50   21.1114    36    -7.70    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  0     7/15     3      7/1       -94.0000   21.1114    36    -4.45    <.0001  Tukey-Kramer  0.0065
YEAR*CUTTING  0     7/15     3      7/15       16.0000   17.7489    36     0.90    0.3733  Tukey-Kramer  0.9999
YEAR*CUTTING  1     6/1      1      6/15        8.7500   21.1114    36     0.41    0.6810  Tukey-Kramer  1.0000
YEAR*CUTTING  1     6/1      1      7/1        29.7500   21.1114    36     1.41    0.1674  Tukey-Kramer  0.9858
YEAR*CUTTING  1     6/1      1      7/15        123.75   21.1114    36     5.86    <.0001  Tukey-Kramer  0.0001
YEAR*CUTTING  1     6/1      2      6/1        -159.00   12.9580    36   -12.27    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     6/1      2      6/15       -144.75   21.1114    36    -6.86    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     6/1      2      7/1       -93.0000   21.1114    36    -4.41    <.0001  Tukey-Kramer  0.0074
YEAR*CUTTING  1     6/1      2      7/15       46.0000   21.1114    36     2.18    0.0360  Tukey-Kramer  0.7048
YEAR*CUTTING  1     6/1      3      6/1       -31.2500   16.1907    36    -1.93    0.0615  Tukey-Kramer  0.8452
YEAR*CUTTING  1     6/1      3      6/15       40.2500   21.1114    36     1.91    0.0646  Tukey-Kramer  0.8563
YEAR*CUTTING  1     6/1      3      7/1         108.75   21.1114    36     5.15    <.0001  Tukey-Kramer  0.0009
YEAR*CUTTING  1     6/1      3      7/15        218.75   21.1114    36    10.36    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     6/15     1      7/1        21.0000   21.1114    36     0.99    0.3265  Tukey-Kramer  0.9996
YEAR*CUTTING  1     6/15     1      7/15        115.00   21.1114    36     5.45    <.0001  Tukey-Kramer  0.0004
YEAR*CUTTING  1     6/15     2      6/1        -167.75   21.1114    36    -7.95    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     6/15     2      6/15       -153.50   12.9580    36   -11.85    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     6/15     2      7/1        -101.75   21.1114    36    -4.82    <.0001  Tukey-Kramer  0.0023
YEAR*CUTTING  1     6/15     2      7/15       37.2500   21.1114    36     1.76    0.0861  Tukey-Kramer  0.9133
YEAR*CUTTING  1     6/15     3      6/1       -40.0000   21.1114    36    -1.89    0.0662  Tukey-Kramer  0.8617
YEAR*CUTTING  1     6/15     3      6/15       31.5000   16.1907    36     1.95    0.0595  Tukey-Kramer  0.8377
YEAR*CUTTING  1     6/15     3      7/1         100.00   21.1114    36     4.74    <.0001  Tukey-Kramer  0.0029
YEAR*CUTTING  1     6/15     3      7/15        210.00   21.1114    36     9.95    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/1      1      7/15       94.0000   21.1114    36     4.45    <.0001  Tukey-Kramer  0.0065
YEAR*CUTTING  1     7/1      2      6/1        -188.75   21.1114    36    -8.94    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/1      2      6/15       -174.50   21.1114    36    -8.27    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/1      2      7/1        -122.75   12.9580    36    -9.47    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/1      2      7/15       16.2500   21.1114    36     0.77    0.4465  Tukey-Kramer  1.0000
YEAR*CUTTING  1     7/1      3      6/1       -61.0000   21.1114    36    -2.89    0.0065  Tukey-Kramer  0.2683
YEAR*CUTTING  1     7/1      3      6/15       10.5000   21.1114    36     0.50    0.6220  Tukey-Kramer  1.0000
YEAR*CUTTING  1     7/1      3      7/1        79.0000   16.1907    36     4.88    <.0001  Tukey-Kramer  0.0019
YEAR*CUTTING  1     7/1      3      7/15        189.00   21.1114    36     8.95    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     2      6/1        -282.75   21.1114    36   -13.39    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     2      6/15       -268.50   21.1114    36   -12.72    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     2      7/1        -216.75   21.1114    36   -10.27    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     2      7/15      -77.7500   12.9580    36    -6.00    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     3      6/1        -155.00   21.1114    36    -7.34    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  1     7/15     3      6/15      -83.5000   21.1114    36    -3.96    0.0003  Tukey-Kramer  0.0248
YEAR*CUTTING  1     7/15     3      7/1       -15.0000   21.1114    36    -0.71    0.4820  Tukey-Kramer  1.0000
YEAR*CUTTING  1     7/15     3      7/15       95.0000   16.1907    36     5.87    <.0001  Tukey-Kramer  0.0001
YEAR*CUTTING  2     6/1      2      6/15       14.2500   21.1114    36     0.67    0.5040  Tukey-Kramer  1.0000
YEAR*CUTTING  2     6/1      2      7/1        66.0000   21.1114    36     3.13    0.0035  Tukey-Kramer  0.1710
YEAR*CUTTING  2     6/1      2      7/15        205.00   21.1114    36     9.71    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/1      3      6/1         127.75   12.9580    36     9.86    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/1      3      6/15        199.25   21.1114    36     9.44    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/1      3      7/1         267.75   21.1114    36    12.68    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/1      3      7/15        377.75   21.1114    36    17.89    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/15     2      7/1        51.7500   21.1114    36     2.45    0.0192  Tukey-Kramer  0.5250
YEAR*CUTTING  2     6/15     2      7/15        190.75   21.1114    36     9.04    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/15     3      6/1         113.50   21.1114    36     5.38    <.0001  Tukey-Kramer  0.0005
YEAR*CUTTING  2     6/15     3      6/15        185.00   12.9580    36    14.28    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/15     3      7/1         253.50   21.1114    36    12.01    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     6/15     3      7/15        363.50   21.1114    36    17.22    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     7/1      2      7/15        139.00   21.1114    36     6.58    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     7/1      3      6/1        61.7500   21.1114    36     2.92    0.0059  Tukey-Kramer  0.2516
YEAR*CUTTING  2     7/1      3      6/15        133.25   21.1114    36     6.31    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     7/1      3      7/1         201.75   12.9580    36    15.57    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     7/1      3      7/15        311.75   21.1114    36    14.77    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  2     7/15     3      6/1       -77.2500   21.1114    36    -3.66    0.0008  Tukey-Kramer  0.0521
YEAR*CUTTING  2     7/15     3      6/15       -5.7500   21.1114    36    -0.27    0.7869  Tukey-Kramer  1.0000
YEAR*CUTTING  2     7/15     3      7/1        62.7500   21.1114    36     2.97    0.0052  Tukey-Kramer  0.2306
YEAR*CUTTING  2     7/15     3      7/15        172.75   12.9580    36    13.33    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  3     6/1      3      6/15       71.5000   21.1114    36     3.39    0.0017  Tukey-Kramer  0.0982
YEAR*CUTTING  3     6/1      3      7/1         140.00   21.1114    36     6.63    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  3     6/1      3      7/15        250.00   21.1114    36    11.84    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  3     6/15     3      7/1        68.5000   21.1114    36     3.24    0.0025  Tukey-Kramer  0.1338
YEAR*CUTTING  3     6/15     3      7/15        178.50   21.1114    36     8.46    <.0001  Tukey-Kramer  <.0001
YEAR*CUTTING  3     7/1      3      7/15        110.00   21.1114    36     5.21    <.0001  Tukey-Kramer  0.0007
 
                 Tests of Effect Slices
Effect          YEAR  Num DF  Den DF    F Value    Pr > F
YEAR*CUTTING    0          3      36       4.84    0.0062
YEAR*CUTTING    1          3      36      14.50    <.0001
YEAR*CUTTING    2          3      36      39.25    <.0001
YEAR*CUTTING    3          3      36      50.81    <.0001
 
 
 
 
44         proc univariate data=ResidDataP plot normal; var resid;
45           TITLE3 'Univariate analysis for PROC MIXED - Nested Error'; run;
NOTE: The PROCEDURE UNIVARIATE printed pages 4-7.
NOTE: PROCEDURE UNIVARIATE used:
      real time           0.03 seconds
      cpu time            0.03 seconds
EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Univariate analysis for PROC MIXED - Nested Error
 


The UNIVARIATE Procedure
Variable:  Resid
                            Moments
N                          64    Sum Weights                 64
Mean                        0    Sum Observations             0
Std Deviation      22.0769009    Variance            487.389552
Skewness            0.3114769    Kurtosis             1.4598985
Uncorrected SS     30705.5418    Corrected SS        30705.5418
Coeff Variation             .    Std Error Mean      2.75961261
 
Basic Statistical Measures
    Location                    Variability
Mean     0.000000     Std Deviation           22.07690
Median   1.285035     Variance               487.38955
Mode      .           Range                  129.16819
                      Interquartile Range     20.82758
 
Tests for Location: Mu0=0
Test           -Statistic-    -----p Value------
Student's t    t         0    Pr > |t|    1.0000
Sign           M         2    Pr >= |M|   0.7080
Signed Rank    S        -9    Pr >= |S|   0.9526
 
Tests for Normality
Test                  --Statistic---    -----p Value------
Shapiro-Wilk          W     0.966233    Pr < W      0.0769
Kolmogorov-Smirnov    D     0.093618    Pr > D     >0.1500
Cramer-von Mises      W-Sq  0.135493    Pr > W-Sq   0.0380
Anderson-Darling      A-Sq  0.798106    Pr > A-Sq   0.0385
 
The UNIVARIATE Procedure
Variable:  Resid
Quantiles (Definition 5)
Quantile       Estimate
100% Max       66.37476
99%            66.37476
95%            33.43647
90%            26.63720
75% Q3          9.89557
50% Median      1.28503
25% Q1        -10.93201
10%           -28.06856
5%            -30.29342
1%            -62.79342
0% Min        -62.79342
 
Extreme Observations
------Lowest-----        -----Highest-----
   Value      Obs           Value      Obs
-62.7934       42         33.2337       57
-37.3201       25         33.4365       64
-35.7125        5         50.8748        6
-30.2934       38         53.3748       14
-29.8186       27         66.3748       10
 
 


EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Univariate analysis for PROC MIXED - Nested Error
 
The UNIVARIATE Procedure
Variable:  Resid
 
   Stem Leaf                     #  Boxplot
      6 6                        1     0
      6
      5
      5 13                       2     0
      4
      4
      3
      3 133                      3     |
      2 7                        1     |
      2 1                        1     |
      1 779                      3     |
      1 001334                   6  +-----+
      0 557789                   6  |     |
      0 11222223344             11  *--+--*
     -0 442210                   6  |     |
     -0 997765                   6  |     |
     -1 32110                    5  +-----+
     -1                                |
     -2 43333                    5     |
     -2 885                      3     |
     -3 00                       2     |
     -3 76                       2     |
     -4
     -4
     -5
     -5
     -6 3                        1     0
        ----+----+----+----+
    Multiply Stem.Leaf by 10**+1
 
 
                       Normal Probability Plot
    67.5+                                                *
        |
        |                                                  +
        |                                          *  *  ++
        |                                              ++
        |                                            ++
        |                                         +++
        |                                       ***
        |                                     +*
        |                                   ++*
        |                                +++**
        |                              ++***
        |                            ++***
     2.5+                        ******
        |                      ***
        |                   ****
        |                 ***+
        |                +++
        |             ****
        |          ***+
        |         *++
        |     * +*+
        |     ++
        |   ++
        | ++
        |+
   -62.5+  *
         +----+----+----+----+----+----+----+----+----+----+
             -2        -1         0        +1        +2
 


47         PROC GLM; CLASSES BLOCK YEAR CUTTING;
48           TITLE3 'Split plot Analysis of Variance with PROC GLM';
49           TITLE4 'The correct analysis : cutting and year (age) as fixed';
50           MODEL HARVEST = BLOCK CUTTING BLOCK*CUTTING YEAR CUTTING*YEAR;
51             TEST H=BLOCK CUTTING E=BLOCK*CUTTING;
52             RANDOM BLOCK BLOCK*CUTTING / TEST; RUN;
NOTE: TYPE I EMS not available without the E1 option.
53           TITLE3 'Model to show EMS with year as a random effect';
54             TEST H=YEAR E=CUTTING*YEAR;
55             RANDOM BLOCK BLOCK*CUTTING YEAR YEAR*CUTTING / TEST;
56         RUN;
NOTE: TYPE I EMS not available without the E1 option.
56       !      QUIT;
NOTE: The PROCEDURE GLM printed pages 8-14.
NOTE: PROCEDURE GLM used:
      real time           0.11 seconds
      cpu time            0.11 seconds
 
 
EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Split plot Analysis of Variance with PROC GLM
The correct analysis : cutting and year (age) as fixed
 
The GLM Procedure
         Class Level Information
Class         Levels    Values
BLOCK              4    1 2 3 4          
YEAR               4    0 1 2 3          
CUTTING            4    6/1 6/15 7/1 7/15
Number of observations    64
 
Dependent Variable: HARVEST  
                                      Sum of
Source                     DF        Squares    Mean Square   F Value   Pr > F
Model                      27    863306.3750     31974.3102     74.33   <.0001
Error                      36     15486.6250       430.1840                   
Corrected Total            63    878793.0000                                 
 
R-Square     Coeff Var      Root MSE    HARVEST Mean
0.982377      7.136646      20.74088        290.6250
 
Source                     DF      Type I SS    Mean Square   F Value   Pr > F
BLOCK                       3     30169.6250     10056.5417     23.38   <.0001
CUTTING                     3    241376.6250     80458.8750    187.03   <.0001
BLOCK*CUTTING               9     21860.7500      2428.9722      5.65   <.0001
YEAR                        3    518721.8750    172907.2917    401.94   <.0001
YEAR*CUTTING                9     51177.5000      5686.3889     13.22   <.0001
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3     30169.6250     10056.5417     23.38   <.0001
CUTTING                     3    241376.6250     80458.8750    187.03   <.0001
BLOCK*CUTTING               9     21860.7500      2428.9722      5.65   <.0001
YEAR                        3    518721.8750    172907.2917    401.94   <.0001
YEAR*CUTTING                9     51177.5000      5686.3889     13.22   <.0001
 
Tests of Hypotheses Using the Type III MS for BLOCK*CUTTING as an Error Term
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3     30169.6250     10056.5417      4.14   0.0423
CUTTING                     3    241376.6250     80458.8750     33.12   <.0001


EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Split plot Analysis of Variance with PROC GLM
The correct analysis : cutting and year (age) as fixed
 
The GLM Procedure
 
Source                Type III Expected Mean Square
BLOCK                 Var(Error) + 4 Var(BLOCK*CUTTING) + 16 Var(BLOCK)        
CUTTING               Var(Error) + 4 Var(BLOCK*CUTTING) + Q(CUTTING,YEAR*CUTTING)                                  
BLOCK*CUTTING         Var(Error) + 4 Var(BLOCK*CUTTING)                        
YEAR                  Var(Error) + Q(YEAR,YEAR*CUTTING)                        
YEAR*CUTTING          Var(Error) + Q(YEAR*CUTTING)                             
 
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: HARVEST  
   Source                    DF   Type III SS   Mean Square  F Value  Pr > F
   BLOCK                      3         30170         10057     4.14  0.0423
*  CUTTING                    3        241377         80459    33.12  <.0001
   Error                      9         21861   2428.972222                
Error: MS(BLOCK*CUTTING)
* This test assumes one or more other fixed effects are zero.
 
   Source                    DF   Type III SS   Mean Square  F Value  Pr > F
   BLOCK*CUTTING              9         21861   2428.972222     5.65  <.0001
*  YEAR                       3        518722        172907   401.94  <.0001
   YEAR*CUTTING               9         51178   5686.388889    13.22  <.0001
   Error: MS(Error)          36         15487    430.184028                
* This test assumes one or more other fixed effects are zero.
 
 
EXST7015: Total Asparagus weight harvested before 6/1 (measures vigor)
Repeated measure is 4 years of the study
Model to show EMS with year as a random effect
 
Source                Type III Expected Mean Square
BLOCK                 Var(Error) + 4 Var(BLOCK*CUTTING) + 16 Var(BLOCK)        
CUTTING               Var(Error) + 4 Var(YEAR*CUTTING) + 4 Var(BLOCK*CUTTING) + Q(CUTTING)
BLOCK*CUTTING         Var(Error) + 4 Var(BLOCK*CUTTING)                         
YEAR                  Var(Error) + 4 Var(YEAR*CUTTING) + 16 Var(YEAR)          
YEAR*CUTTING          Var(Error) + 4 Var(YEAR*CUTTING)                         
 
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: HARVEST  
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3          30170          10057      4.14   0.0423
Error                       9          21861    2428.972222                  
Error: MS(BLOCK*CUTTING)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
CUTTING                     3         241377          80459     10.47   0.0007
Error                  13.886         106713    7685.177083                  
Error: MS(BLOCK*CUTTING) + MS(YEAR*CUTTING) - MS(Error)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK*CUTTING               9          21861    2428.972222      5.65   <.0001
YEAR*CUTTING                9          51178    5686.388889     13.22   <.0001
Error: MS(Error)           36          15487     430.184028                  
 


Source                     DF    Type III SS    Mean Square   F Value   Pr > F
YEAR                        3         518722         172907     30.41   <.0001
Error                       9          51178    5686.388889                  
Error: MS(YEAR*CUTTING)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
YEAR                        3    518721.8750    172907.2917     30.41   <.0001
 
 
59         GOPTIONS DEVICE=CGMflwa GSFMODE=REPLACE GSFNAME=OUT NOPROMPT noROTATE
60            ftext='TimesRoman' ftitle='TimesRoman' htext=1 htitle=1
60       ! ctitle=black ctext=black;
61        
62         GOPTIONS GSFNAME=OUT3;  FILENAME OUT3
62       ! 'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-harvest
62       ! .CGM';
63         GOPTIONS VPOS=48 HPOS=90;
64         PROC GCHART DATA=HARVEST;
65            BLOCK YEAR / GROUP=CUTTING SUMVAR=HARVEST DISCRETE TYPE=MEAN; RUN;
NOTE: Foreground color BLACK same as background. Part of your graph may not be visible.
NOTE:  20 RECORDS WRITTEN TO
C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-harvest.CGM
66         quit;
NOTE: There were 64 observations read from the data set WORK.HARVEST.
NOTE: PROCEDURE GCHART used:
      real time           0.19 seconds
      cpu time            0.11 seconds
67        
68         GOPTIONS DEVICE=CGMflwa GSFMODE=REPLACE GSFNAME=OUT NOPROMPT noROTATE
69            ftext='TimesRoman' ftitle='TimesRoman' htext=1 htitle=1
69       ! ctitle=black ctext=black;
 
 


76         **EXAMPLE 10*******************************************;
77         *** Example of a Split - split Plot Design          ***;
78         *** From Snedecor & Cochran, 1960 (pg 374)          ***;
79         *************************************************************************;
80         ** Yield of Corn in bu/acre in a Split plot design. Main plot is a RBD,**;
81         ** Treatments are irrigation. Sub-plot treatment is stand density, and **;
82         ** Sub-sub plot is fertilizer level.  Stand (10, 13 and 16 thousand)   **;
83         ** and fertilizer (60, 120 and 180) are equally spaced treatments      **;
84         *************************************************************************;
85         OPTIONS PS=61 LS=121 NOCENTER NODATE PAGENO=1;
86         DATA SPLIT (KEEP=IRRIGATE BLOCK STAND YIELD FERT); INFILE CARDS MISSOVER;
87            ARRAY B {4} BLK1-BLK4;
88            INPUT IRRIGATE $ 1-8 STAND FERT BLK1-BLK4;
89            DO BLOCK = 1 TO 4;
90               YIELD = B{BLOCK}; OUTPUT; END;
91           TITLE1 'EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD';
92         CARDS;
NOTE: The data set WORK.SPLIT has 72 observations and 5 variables.
NOTE: DATA statement used:
      real time           0.04 seconds
      cpu time            0.04 seconds
92       !        RUN;
111        ;
112        PROC PRINT; TITLE2 'RAW DATA LISTING'; RUN;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: The PROCEDURE PRINT printed pages 1-2.
NOTE: PROCEDURE PRINT used:
      real time           0.02 seconds
      cpu time            0.02 seconds
 
EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD
RAW DATA LISTING
 

Obs    IRRIGATE    STAND    FERT    BLOCK    YIELD
  1    No Irrig      1        1       1        90
  2    No Irrig      1        1       2        83
  3    No Irrig      1        1       3        85
  4    No Irrig      1        1       4        86
  5    No Irrig      1        2       1        95
  6    No Irrig      1        2       2        80
  7    No Irrig      1        2       3        88
  8    No Irrig      1        2       4        78
  9    No Irrig      1        3       1       107
 10    No Irrig      1        3       2        95
 11    No Irrig      1        3       3        88
 12    No Irrig      1        3       4        89
 13    No Irrig      2        1       1        92
 14    No Irrig      2        1       2        98
 15    No Irrig      2        1       3       112
 16    No Irrig      2        1       4        79
 17    No Irrig      2        2       1        89
 18    No Irrig      2        2       2        98
 19    No Irrig      2        2       3       104
 20    No Irrig      2        2       4        86
 21    No Irrig      2        3       1        92
 22    No Irrig      2        3       2       106
 23    No Irrig      2        3       3        91
 24    No Irrig      2        3       4        87
 25    No Irrig      3        1       1        81
 26    No Irrig      3        1       2        74
 27    No Irrig      3        1       3        82
 28    No Irrig      3        1       4        85
 29    No Irrig      3        2       1        92
 30    No Irrig      3        2       2        81
 31    No Irrig      3        2       3        78
 32    No Irrig      3        2       4        89
 33    No Irrig      3        3       1        93
 34    No Irrig      3        3       2        74
 35    No Irrig      3        3       3        94
 36    No Irrig      3        3       4        83
 37    Irrigate      1        1       1        80
 38    Irrigate      1        1       2       102
 39    Irrigate      1        1       3        60
 40    Irrigate      1        1       4        73
 41    Irrigate      1        2       1        87
 42    Irrigate      1        2       2       109
 43    Irrigate      1        2       3       104
 44    Irrigate      1        2       4       114
 45    Irrigate      1        3       1       100
 46    Irrigate      1        3       2       105
 47    Irrigate      1        3       3       114
 48    Irrigate      1        3       4       114
 49    Irrigate      2        1       1       121
 50    Irrigate      2        1       2        99
 51    Irrigate      2        1       3        90
 52    Irrigate      2        1       4       109
 53    Irrigate      2        2       1       110
 54    Irrigate      2        2       2        94
 55    Irrigate      2        2       3       118
 56    Irrigate      2        2       4       131
 57    Irrigate      2        3       1       119
 58    Irrigate      2        3       2       123
 59    Irrigate      2        3       3       113
 60    Irrigate      2        3       4       126
 61    Irrigate      3        1       1        78
 62    Irrigate      3        1       2       136
 63    Irrigate      3        1       3       119
 64    Irrigate      3        1       4       116
 65    Irrigate      3        2       1        98
 66    Irrigate      3        2       2       133
 67    Irrigate      3        2       3       122
 68    Irrigate      3        2       4       136
 69    Irrigate      3        3       1       122
 70    Irrigate      3        3       2       132
 71    Irrigate      3        3       3       136
 72    Irrigate      3        3       4       133


 
 


113        PROC MIXED DATA=SPLIT CL; CLASSES BLOCK IRRIGATE STAND FERT;
114          TITLE2 'Split/Split plot Analysis of Variance with PROC MIXED';
115          MODEL YIELD = IRRIGATE STAND IRRIGATE*STAND
116              FERT FERT*IRRIGATE FERT*STAND FERT*IRRIGATE*STAND / htype=3;
117          RANDOM BLOCK BLOCK*IRRIGATE BLOCK*IRRIGATE*STAND;
118          REPEATED FERT / SUBJECT=BLOCK*IRRIGATE*stand TYPE=CS;
119            lsmeans IRRIGATE STAND FERT IRRIGATE*STAND IRRIGATE*FERT / pdiff adjust=tukey;
120            lsmeans IRRIGATE*FERT / slice=fert;
121            lsmeans IRRIGATE*FERT / slice=IRRIGATE;
122            lsmeans IRRIGATE*STAND / slice=stand;
123            lsmeans IRRIGATE*STAND / slice=IRRIGATE;
124        RUN;
NOTE: Convergence criteria met but final hessian is not positive definite.
NOTE: Estimated G matrix is not positive definite.
NOTE: The PROCEDURE MIXED printed pages 3-7.
NOTE: PROCEDURE MIXED used:
      real time           0.68 seconds
      cpu time            0.68 seconds
124      !      QUIT;
 
 
EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD
Split/Split plot Analysis of Variance with PROC MIXED
 
The Mixed Procedure
                  Model Information
Data Set                     WORK.SPLIT              
Dependent Variable           YIELD                   
Covariance Structures        Variance Components,    
                             Compound Symmetry       
Subject Effect               BLOCK*IRRIGATE*STAND    
Estimation Method            REML                    
Residual Variance Method     Profile                 
Fixed Effects SE Method      Model-Based             
Degrees of Freedom Method    Containment             
 
Class Level Information
Class       Levels    Values
BLOCK            4    1 2 3 4                      
IRRIGATE         2    Irrigate No Irrig            
STAND            3    1 2 3                        
FERT             3    1 2 3                        
 
Dimensions
Covariance Parameters             5
Columns in X                     48
Columns in Z                     36
Subjects                          1
Max Obs Per Subject              72
Observations Used                72
Observations Not Used             0
Total Observations               72
 
Iteration History
Iteration    Evaluations    -2 Res Log Like       Criterion
        0              1       444.63866543               
        1              4       437.70568840       .       
        2              1       437.62747377      0.00221086
        3              1       437.62125094      0.00001508
        4              1       437.62120219      0.00000000
   Convergence criteria met but final hessian is not positive definite.


Covariance Parameter Estimates
Cov Parm                 Subject                 Estimate     Alpha       Lower       Upper
BLOCK                                                   0         .           .           .
BLOCK*IRRIGATE                                     3.9295      0.05      0.3437    3.388E41
BLOCK*IRRIGATE*STAND                              48.6576      0.05     18.2912      334.20
CS                       BLOCK*IRRIGATE*STAND    -0.00008      0.05    -0.00011    -0.00004
Residual                                          86.3569      0.05     57.1088      145.71
 
Fit Statistics
-2 Res Log Likelihood           437.6
AIC (smaller is better)         445.6
AICC (smaller is better)        446.4
BIC (smaller is better)         443.2
 
Type 3 Tests of Fixed Effects
                        Num     Den
Effect                   DF      DF    F Value    Pr > F
IRRIGATE                  1       3      30.92    0.0115
STAND                     2      12       3.78    0.0532
IRRIGATE*STAND            2      12       5.91    0.0163
FERT                      2      36      11.45    0.0001
IRRIGATE*FERT             2      36       5.52    0.0081
STAND*FERT                4      36       0.88    0.4841
IRRIGATE*STAND*FERT       4      36       0.68    0.6107
 
Least Squares Means
                                                           Standard
Effect            IRRIGATE    STAND    FERT    Estimate       Error      DF    t Value    Pr > |t|
IRRIGATE          Irrigate                       110.44      2.7269       3      40.50      <.0001
IRRIGATE          No Irrig                      89.0000      2.7269       3      32.64      <.0001
STAND                         1                 92.7500      3.1893      12      29.08      <.0001
STAND                         2                  103.63      3.1893      12      32.49      <.0001
STAND                         3                  102.79      3.1893      12      32.23      <.0001
FERT                                   1        92.9167      2.4732      36      37.57      <.0001
FERT                                   2         100.58      2.4732      36      40.67      <.0001
FERT                                   3         105.67      2.4732      36      42.72      <.0001
IRRIGATE*STAND    Irrigate    1                 96.8333      4.5103      12      21.47      <.0001
IRRIGATE*STAND    Irrigate    2                  112.75      4.5103      12      25.00      <.0001
IRRIGATE*STAND    Irrigate    3                  121.75      4.5103      12      26.99      <.0001
IRRIGATE*STAND    No Irrig    1                 88.6667      4.5103      12      19.66      <.0001
IRRIGATE*STAND    No Irrig    2                 94.5000      4.5103      12      20.95      <.0001
IRRIGATE*STAND    No Irrig    3                 83.8333      4.5103      12      18.59      <.0001
IRRIGATE*FERT     Irrigate             1        98.5833      3.4977      36      28.19      <.0001
IRRIGATE*FERT     Irrigate             2         113.00      3.4977      36      32.31      <.0001
IRRIGATE*FERT     Irrigate             3         119.75      3.4977      36      34.24      <.0001
IRRIGATE*FERT     No Irrig             1        87.2500      3.4977      36      24.95      <.0001
IRRIGATE*FERT     No Irrig             2        88.1667      3.4977      36      25.21      <.0001
IRRIGATE*FERT     No Irrig             3        91.5833      3.4977      36      26.18      <.0001
IRRIGATE*FERT     Irrigate             1        98.5833      3.4977      36      28.19      <.0001
IRRIGATE*FERT     Irrigate             2         113.00      3.4977      36      32.31      <.0001
IRRIGATE*FERT     Irrigate             3         119.75      3.4977      36      34.24      <.0001
IRRIGATE*FERT     No Irrig             1        87.2500      3.4977      36      24.95      <.0001
IRRIGATE*FERT     No Irrig             2        88.1667      3.4977      36      25.21      <.0001
IRRIGATE*FERT     No Irrig             3        91.5833      3.4977      36      26.18      <.0001
 
Tests of Effect Slices
                                                Num     Den
Effect            IRRIGATE    STAND    FERT      DF      DF    F Value    Pr > F
IRRIGATE*FERT                          1          1      36       5.25    0.0279
IRRIGATE*FERT                          2          1      36      25.20    <.0001
IRRIGATE*FERT                          3          1      36      32.43    <.0001
IRRIGATE*FERT     Irrigate                        2      36      16.24    <.0001
IRRIGATE*FERT     No Irrig                        2      36       0.72    0.4914
IRRIGATE*STAND                1                   1      12       1.64    0.2246
IRRIGATE*STAND                2                   1      12       8.19    0.0143
IRRIGATE*STAND                3                   1      12      35.34    <.0001
IRRIGATE*STAND    Irrigate                        2      12       8.22    0.0056
IRRIGATE*STAND    No Irrig                        2      12       1.47    0.2678


Differences of Least Squares Means
                                                                                 Standard
Effect           IRRIGATE   STAND   FERT   _IRRIGATE   _STAND   _FERT   Estimate      Error     DF   t Value   Pr > |t|
 
IRRIGATE         Irrigate                  No Irrig                      21.4444     3.8564      3      5.56     0.0115
STAND                       1                          2                -10.8750     4.4001     12     -2.47     0.0294
STAND                       1                          3                -10.0417     4.4001     12     -2.28     0.0415
STAND                       2                          3                  0.8333     4.4001     12      0.19     0.8530
FERT                                1                           2        -7.6667     2.6826     36     -2.86     0.0070
FERT                                1                           3       -12.7500     2.6826     36     -4.75     <.0001
IRRIGATE*STAND   Irrigate   1              Irrigate    2                -15.9167     6.2227     12     -2.56     0.0251
IRRIGATE*STAND   Irrigate   1              Irrigate    3                -24.9167     6.2227     12     -4.00     0.0017
IRRIGATE*STAND   Irrigate   1              No Irrig    1                  8.1667     6.3786     12      1.28     0.2246
IRRIGATE*STAND   Irrigate   1              No Irrig    2                  2.3333     6.3786     12      0.37     0.7209
IRRIGATE*STAND   Irrigate   1              No Irrig    3                 13.0000     6.3786     12      2.04     0.0642
IRRIGATE*STAND   Irrigate   2              Irrigate    3                 -9.0000     6.2227     12     -1.45     0.1737
IRRIGATE*STAND   Irrigate   2              No Irrig    1                 24.0833     6.3786     12      3.78     0.0026
IRRIGATE*STAND   Irrigate   2              No Irrig    2                 18.2500     6.3786     12      2.86     0.0143
IRRIGATE*STAND   Irrigate   2              No Irrig    3                 28.9167     6.3786     12      4.53     0.0007
IRRIGATE*STAND   Irrigate   3              No Irrig    1                 33.0833     6.3786     12      5.19     0.0002
IRRIGATE*STAND   Irrigate   3              No Irrig    2                 27.2500     6.3786     12      4.27     0.0011
IRRIGATE*STAND   Irrigate   3              No Irrig    3                 37.9167     6.3786     12      5.94     <.0001
IRRIGATE*STAND   No Irrig   1              No Irrig    2                 -5.8333     6.2227     12     -0.94     0.3670
IRRIGATE*STAND   No Irrig   1              No Irrig    3                  4.8333     6.2227     12      0.78     0.4524
IRRIGATE*STAND   No Irrig   2              No Irrig    3                 10.6667     6.2227     12      1.71     0.1122
IRRIGATE*FERT    Irrigate           1      Irrigate             2       -14.4167     3.7938     36     -3.80     0.0005
IRRIGATE*FERT    Irrigate           1      Irrigate             3       -21.1667     3.7938     36     -5.58     <.0001
IRRIGATE*FERT    Irrigate           1      No Irrig             1        11.3333     4.9464     36      2.29     0.0279
IRRIGATE*FERT    Irrigate           1      No Irrig             2        10.4167     4.9464     36      2.11     0.0423
IRRIGATE*FERT    Irrigate           1      No Irrig             3         7.0000     4.9464     36      1.42     0.1656
IRRIGATE*FERT    Irrigate           2      Irrigate             3        -6.7500     3.7938     36     -1.78     0.0836
IRRIGATE*FERT    Irrigate           2      No Irrig             1        25.7500     4.9464     36      5.21     <.0001
IRRIGATE*FERT    Irrigate           2      No Irrig             2        24.8333     4.9464     36      5.02     <.0001
IRRIGATE*FERT    Irrigate           2      No Irrig             3        21.4167     4.9464     36      4.33     0.0001
IRRIGATE*FERT    Irrigate           3      No Irrig             1        32.5000     4.9464     36      6.57     <.0001
IRRIGATE*FERT    Irrigate           3      No Irrig             2        31.5833     4.9464     36      6.39     <.0001
IRRIGATE*FERT    Irrigate           3      No Irrig             3        28.1667     4.9464     36      5.69     <.0001
IRRIGATE*FERT    No Irrig           1      No Irrig             2        -0.9167     3.7938     36     -0.24     0.8104
IRRIGATE*FERT    No Irrig           1      No Irrig             3        -4.3333     3.7938     36     -1.14     0.2609
IRRIGATE*FERT    No Irrig           2      No Irrig             3        -3.4167     3.7938     36     -0.90     0.3738
 
Differences of Least Squares Means
 
Effect           IRRIGATE   STAND   FERT   _IRRIGATE   _STAND   _FERT   Adjustment       Adj P
IRRIGATE         Irrigate                  No Irrig                     Tukey           0.0115
STAND                       1                          2                Tukey-Kramer    0.0704
STAND                       1                          3                Tukey-Kramer    0.0972
STAND                       2                          3                Tukey-Kramer    0.9805
FERT                                1                           2       Tukey-Kramer    0.0189
FERT                                1                           3       Tukey-Kramer    <.0001
FERT                                2                           3       Tukey-Kramer    0.1548
IRRIGATE*STAND   Irrigate   1              Irrigate    2                Tukey-Kramer    0.1819
IRRIGATE*STAND   Irrigate   1              Irrigate    3                Tukey-Kramer    0.0168
IRRIGATE*STAND   Irrigate   1              No Irrig    1                Tukey-Kramer    0.7899
IRRIGATE*STAND   Irrigate   1              No Irrig    2                Tukey-Kramer    0.9989
IRRIGATE*STAND   Irrigate   1              No Irrig    3                Tukey-Kramer    0.3771
IRRIGATE*STAND   Irrigate   2              Irrigate    3                Tukey-Kramer    0.7011
IRRIGATE*STAND   Irrigate   2              No Irrig    1                Tukey-Kramer    0.0248
IRRIGATE*STAND   Irrigate   2              No Irrig    2                Tukey-Kramer    0.1133
IRRIGATE*STAND   Irrigate   2              No Irrig    3                Tukey-Kramer    0.0069
IRRIGATE*STAND   Irrigate   3              No Irrig    1                Tukey-Kramer    0.0024
IRRIGATE*STAND   Irrigate   3              No Irrig    2                Tukey-Kramer    0.0107
IRRIGATE*STAND   Irrigate   3              No Irrig    3                Tukey-Kramer    0.0007
IRRIGATE*STAND   No Irrig   1              No Irrig    2                Tukey-Kramer    0.9288
IRRIGATE*STAND   No Irrig   1              No Irrig    3                Tukey-Kramer    0.9665
IRRIGATE*STAND   No Irrig   2              No Irrig    3                Tukey-Kramer    0.5481
IRRIGATE*FERT    Irrigate           1      Irrigate             2       Tukey-Kramer    0.0066
IRRIGATE*FERT    Irrigate           1      Irrigate             3       Tukey-Kramer    <.0001
IRRIGATE*FERT    Irrigate           1      No Irrig             1       Tukey-Kramer    0.2240
IRRIGATE*FERT    Irrigate           1      No Irrig             2       Tukey-Kramer    0.3072
IRRIGATE*FERT    Irrigate           1      No Irrig             3       Tukey-Kramer    0.7178
IRRIGATE*FERT    Irrigate           2      Irrigate             3       Tukey-Kramer    0.4912
IRRIGATE*FERT    Irrigate           2      No Irrig             1       Tukey-Kramer    0.0001
IRRIGATE*FERT    Irrigate           2      No Irrig             2       Tukey-Kramer    0.0002
IRRIGATE*FERT    Irrigate           2      No Irrig             3       Tukey-Kramer    0.0015
IRRIGATE*FERT    Irrigate           3      No Irrig             1       Tukey-Kramer    <.0001
IRRIGATE*FERT    Irrigate           3      No Irrig             2       Tukey-Kramer    <.0001
IRRIGATE*FERT    Irrigate           3      No Irrig             3       Tukey-Kramer    <.0001
IRRIGATE*FERT    No Irrig           1      No Irrig             2       Tukey-Kramer    0.9999
IRRIGATE*FERT    No Irrig           1      No Irrig             3       Tukey-Kramer    0.8603
IRRIGATE*FERT    No Irrig           2      No Irrig             3       Tukey-Kramer    0.9438
 
 
 


125        OPTIONS PS=25 LS=80;
126        PROC SORT DATA=SPLIT; BY STAND IRRIGATE;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: The data set WORK.SPLIT has 72 observations and 5 variables.
NOTE: PROCEDURE SORT used:
      real time           0.04 seconds
      cpu time            0.04 seconds
127           PROC MEANS NOPRINT; BY STAND IRRIGATE; VAR YIELD; OUTPUT OUT=X1
127      ! MEAN=Y;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: The data set WORK.X1 has 6 observations and 5 variables.
NOTE: PROCEDURE MEANS used:
      real time           0.04 seconds
      cpu time            0.04 seconds
128           PROC PLOT DATA=X1;PLOT Y*STAND=IRRIGATE;
129              TITLE2 'Plot of stand by irrigation interaction';
130        RUN;
NOTE: There were 6 observations read from the data set WORK.X1.
NOTE: The PROCEDURE PLOT printed page 8.
NOTE: PROCEDURE PLOT used:
      real time           0.01 seconds
      cpu time            0.01 seconds
 
EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD
Plot of stand by irrigation interaction
 
                 Plot of Y*STAND.  Symbol is value of IRRIGATE.
  Y |
140 +
    |
    |
    |
120 +                                                                          I
    |                                     I
    |
    |
100 +
    |I                                    N
    |N
    |                                                                          N
 80 +
    -+------------------------------------+------------------------------------+
     1                                    2                                    3
                                        STAND
 
131        PROC SORT DATA=SPLIT; BY FERT IRRIGATE;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: The data set WORK.SPLIT has 72 observations and 5 variables.
NOTE: PROCEDURE SORT used:
      real time           0.03 seconds
      cpu time            0.03 seconds
132           PROC MEANS NOPRINT; BY FERT IRRIGATE; VAR YIELD; OUTPUT OUT=X2
132      ! MEAN=Y;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: The data set WORK.X2 has 6 observations and 5 variables.
NOTE: PROCEDURE MEANS used:
real time           0.03 seconds
      cpu time            0.03 seconds
133           PROC PLOT DATA=X2;  PLOT Y*FERT=IRRIGATE;
134              TITLE2 'Plot of fertilizer by irrigation interaction';
135        RUN;


136        OPTIONS PS=50 LS=80;
137       
NOTE: There were 6 observations read from the data set WORK.X2.
NOTE: The PROCEDURE PLOT printed page 9.
NOTE: PROCEDURE PLOT used:
      real time           0.01 seconds
      cpu time            0.01 seconds
 
EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD
Plot of fertilizer by irrigation interaction
 
                 Plot of Y*FERT.  Symbol is value of IRRIGATE.
 
  Y |
120 +                                                                          I
    |
    |                                     I
    |
    |
    |
100 +I
    |
    |
    |                                                                          N
    |N                                    N
    |
 80 +
    -+------------------------------------+------------------------------------+
     1                                    2                                    3
                                        FERT
 
 
 
138        PROC GLM DATA=SPLIT; CLASSES BLOCK IRRIGATE STAND FERT;
139          TITLE2 'Split/Split plot Analysis of Variance with PROC GLM';
140          TITLE3 'The correct analysis probably has all fixed effects';
141          MODEL YIELD = BLOCK IRRIGATE BLOCK*IRRIGATE STAND IRRIGATE*STAND
142                BLOCK*IRRIGATE*STAND FERT FERT*IRRIGATE FERT*STAND
142      ! FERT*IRRIGATE*STAND;
143          TEST H=BLOCK IRRIGATE E=BLOCK*IRRIGATE;
144          TEST H=BLOCK*IRRIGATE STAND STAND*IRRIGATE E=BLOCK*IRRIGATE*STAND;
145          RANDOM BLOCK BLOCK*IRRIGATE BLOCK*IRRIGATE*STAND / TEST; RUN;
NOTE: TYPE I EMS not available without the E1 option.
146          TITLE3 'Model to show EMS with random subplot effects';
147          RANDOM BLOCK BLOCK*IRRIGATE STAND IRRIGATE*STAND
147      ! BLOCK*IRRIGATE*STAND
148                 FERT FERT*IRRIGATE FERT*STAND FERT*IRRIGATE*STAND / TEST;
149        RUN;
NOTE: TYPE I EMS not available without the E1 option.
149      !      QUIT;
NOTE: The PROCEDURE GLM printed pages 10-17.
NOTE: PROCEDURE GLM used:
      real time           0.12 seconds
      cpu time            0.12 seconds
 


EXST7015: Yield of Corn in a Split-split plot design. Main plot is RBD
Split/Split plot Analysis of Variance with PROC GLM
The correct analysis probably has all fixed effects
 
The GLM Procedure
         Class Level Information
Class         Levels    Values
BLOCK              4    1 2 3 4
IRRIGATE           2    Irrigate No Irrig
STAND              3    1 2 3
FERT               3    1 2 3
Number of observations    72
 
Dependent Variable: YIELD
                                      Sum of
Source                     DF        Squares    Mean Square   F Value   Pr > F
Model                      35    20647.61111      589.93175      6.83   <.0001
Error                      36     3108.83333       86.35648
Corrected Total            71    23756.44444
 
R-Square     Coeff Var      Root MSE    YIELD Mean
0.869137      9.318704      9.292819      99.72222
 
Source                     DF      Type I SS    Mean Square   F Value   Pr > F
BLOCK                       3     194.444444      64.814815      0.75   0.5292
IRRIGATE                    1    8277.555556    8277.555556     95.85   <.0001
BLOCK*IRRIGATE              3    1411.777778     470.592593      5.45   0.0034
STAND                       2    1758.361111     879.180556     10.18   0.0003
IRRIGATE*STAND              2    2747.027778    1373.513889     15.91   <.0001
BLOCK*IRRIGATE*STAND       12    2787.944444     232.328704      2.69   0.0108
FERT                        2    1977.444444     988.722222     11.45   0.0001
IRRIGATE*FERT               2     953.444444     476.722222      5.52   0.0081
STAND*FERT                  4     304.888889      76.222222      0.88   0.4841
IRRIGATE*STAND*FERT         4     234.722222      58.680556      0.68   0.6107
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3     194.444444      64.814815      0.75   0.5292
IRRIGATE                    1    8277.555556    8277.555556     95.85   <.0001
BLOCK*IRRIGATE              3    1411.777778     470.592593      5.45   0.0034
STAND                       2    1758.361111     879.180556     10.18   0.0003
IRRIGATE*STAND              2    2747.027778    1373.513889     15.91   <.0001
BLOCK*IRRIGATE*STAND       12    2787.944444     232.328704      2.69   0.0108
FERT                        2    1977.444444     988.722222     11.45   0.0001
IRRIGATE*FERT               2     953.444444     476.722222      5.52   0.0081
STAND*FERT                  4     304.888889      76.222222      0.88   0.4841
IRRIGATE*STAND*FERT         4     234.722222      58.680556      0.68   0.6107
 
Dependent Variable: YIELD
Tests of Hypotheses Using the Type III MS for BLOCK*IRRIGATE as an Error Term
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3     194.444444      64.814815      0.14   0.9312
IRRIGATE                    1    8277.555556    8277.555556     17.59   0.0247
 
                  Tests of Hypotheses Using the Type III MS
                  for BLOCK*IRRIGATE*STAND as an Error Term
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK*IRRIGATE              3    1411.777778     470.592593      2.03   0.1641
STAND                       2    1758.361111     879.180556      3.78   0.0532
IRRIGATE*STAND              2    2747.027778    1373.513889      5.91   0.0163
 


Source                Type III Expected Mean Square
BLOCK                 Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + 9 Var(BLOCK*IRRIGATE) + 18 Var(BLOCK)
IRRIGATE              Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + 9 Var(BLOCK*IRRIGATE) +
                      Q(IRRIGATE,IRRIGATE*STAND,IRRIGATE*FERT,IRRIGATE*STAND*FERT)
BLOCK*IRRIGATE        Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + 9 Var(BLOCK*IRRIGATE)
STAND                 Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) +
                      Q(STAND,IRRIGATE*STAND,STAND*FERT,IRRIGATE*STAND*FERT)
IRRIGATE*STAND        Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + Q(IRRIGATE*STAND,IRRIGATE*STAND*FERT)
BLOCK*IRRIGATE*STAND  Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND)
FERT                  Var(Error) + Q(FERT,IRRIGATE*FERT,STAND*FERT,IRRIGATE*STAND*FERT)
IRRIGATE*FERT         Var(Error) + Q(IRRIGATE*FERT,IRRIGATE*STAND*FERT)
STAND*FERT            Var(Error) + Q(STAND*FERT,IRRIGATE*STAND*FERT)
IRRIGATE*STAND*FERT   Var(Error) + Q(IRRIGATE*STAND*FERT)
 
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: YIELD
   Source                    DF   Type III SS   Mean Square  F Value  Pr > F
   BLOCK                      3    194.444444     64.814815     0.14  0.9312
*  IRRIGATE                   1   8277.555556   8277.555556    17.59  0.0247
   Error                      3   1411.777778    470.592593
Error: MS(BLOCK*IRRIGATE)
* This test assumes one or more other fixed effects are zero.
 
   Source                    DF   Type III SS   Mean Square  F Value  Pr > F
   BLOCK*IRRIGATE             3   1411.777778    470.592593     2.03  0.1641
*  STAND                      2   1758.361111    879.180556     3.78  0.0532
*  IRRIGATE*STAND             2   2747.027778   1373.513889     5.91  0.0163
   Error                     12   2787.944444    232.328704
Error: MS(BLOCK*IRRIGATE*STAND)
* This test assumes one or more other fixed effects are zero.
   Source                    DF   Type III SS   Mean Square  F Value  Pr > F
   BLOCK*IRRIGATE*STAND      12   2787.944444    232.328704     2.69  0.0108
*  FERT                       2   1977.444444    988.722222    11.45  0.0001
*  IRRIGATE*FERT              2    953.444444    476.722222     5.52  0.0081
*  STAND*FERT                 4    304.888889     76.222222     0.88  0.4841
   IRRIGATE*STAND*FERT        4    234.722222     58.680556     0.68  0.6107
   Error: MS(Error)          36   3108.833333     86.356481
* This test assumes one or more other fixed effects are zero.
 
 
Source                Type III Expected Mean Square
BLOCK                 Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + 9
                      Var(BLOCK*IRRIGATE) + 18 Var(BLOCK)
IRRIGATE              Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 12
                      Var(IRRIGATE*FERT) + 3 Var(BLOCK*IRRIGATE*STAND) + 12
                      Var(IRRIGATE*STAND) +9 Var(BLOCK*IRRIGATE) +Q(IRRIGATE)
BLOCK*IRRIGATE        Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND) + 9
                      Var(BLOCK*IRRIGATE)
STAND                 Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 8
                      Var(STAND*FERT) + 3 Var(BLOCK*IRRIGATE*STAND) + 12
                      Var(IRRIGATE*STAND) + 24 Var(STAND)
IRRIGATE*STAND        Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 3
                      Var(BLOCK*IRRIGATE*STAND) + 12 Var(IRRIGATE*STAND)
BLOCK*IRRIGATE*STAND  Var(Error) + 3 Var(BLOCK*IRRIGATE*STAND)
FERT                  Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 8
                      Var(STAND*FERT) + 12 Var(IRRIGATE*FERT) + 24 Var(FERT)
IRRIGATE*FERT         Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 12
                      Var(IRRIGATE*FERT)
STAND*FERT            Var(Error) + 4 Var(IRRIGATE*STAND*FERT) + 8
                      Var(STAND*FERT)
IRRIGATE*STAND*FERT   Var(Error) + 4 Var(IRRIGATE*STAND*FERT)
 


Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: YIELD
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK                       3     194.444444      64.814815      0.14   0.9312
Error                       3    1411.777778     470.592593
Error: MS(BLOCK*IRRIGATE)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
IRRIGATE                    1    8277.555556    8277.555556      4.08   0.1208
Error                  3.6267    7361.447284    2029.819444
Error: MS(BLOCK*IRRIGATE) + MS(IRRIGATE*STAND) - MS(BLOCK*IRRIGATE*STAND)
+ MS(IRRIGATE*FERT) - MS(IRRIGATE*STAND*FERT) - 36E-16*MS(Error)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK*IRRIGATE              3    1411.777778     470.592593      2.03   0.1641
Error                      12    2787.944444     232.328704
Error: MS(BLOCK*IRRIGATE*STAND)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
STAND                       2    1758.361111     879.180556      0.63   0.6113
Error                  2.0464    2846.646473    1391.055556
Error: MS(IRRIGATE*STAND) + MS(STAND*FERT) -
MS(IRRIGATE*STAND*FERT) + 19E-16*MS(Error)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
IRRIGATE*STAND              2    2747.027778    1373.513889      6.71   0.0212
Error                  7.5247    1539.945731     204.652778
Error: MS(BLOCK*IRRIGATE*STAND) + MS(IRRIGATE*STAND*FERT) - MS(Error)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
BLOCK*IRRIGATE*STAND       12    2787.944444     232.328704      2.69   0.0108
IRRIGATE*STAND*FERT         4     234.722222      58.680556      0.68   0.6107
Error: MS(Error)           36    3108.833333      86.356481
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
FERT                        2    1977.444444     988.722222      2.00   0.3259
Error                   2.107    1041.413780     494.263889
Error: MS(IRRIGATE*FERT) + MS(STAND*FERT) -
MS(IRRIGATE*STAND*FERT) + 24E-16*MS(Error)
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
IRRIGATE*FERT               2     953.444444     476.722222      8.12   0.0390
STAND*FERT                  4     304.888889      76.222222      1.30   0.4030
Error                       4     234.722222      58.680556
Error: MS(IRRIGATE*STAND*FERT)
 
 
 
 
134        GOPTIONS GSFNAME=OUT4;  FILENAME OUT4
134      ! 'C:\Geaghan\EXST\EXST7015New\SAS\split1.CGM';
135        PROC GCHART DATA=SPLIT;
136             BLOCK FERT / GROUP=IRRIGATE SUMVAR=YIELD DISCRETE TYPE=MEAN;
137             PATTERN C=RED V=S; RUN;
NOTE:  31 RECORDS WRITTEN TO C:\Geaghan\EXST\EXST7015New\SAS\split1.CGM
138        GOPTIONS GSFNAME=OUT5;  FILENAME OUT5
138      ! 'C:\Geaghan\EXST\EXST7015New\SAS\split2.CGM';
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: PROCEDURE GCHART used:
      real time           0.11 seconds
      cpu time            0.05 seconds
139        PROC GCHART DATA=SPLIT;
140             BLOCK STAND / GROUP=IRRIGATE SUMVAR=YIELD DISCRETE TYPE=MEAN;
141             PATTERN C=RED V=S; RUN;
NOTE:  31 RECORDS WRITTEN TO C:\Geaghan\EXST\EXST7015New\SAS\split2.CGM
142        QUIT;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: PROCEDURE GCHART used:
      real time           0.09 seconds
      cpu time            0.05 seconds
 
 
 
151        GOPTIONS GSFNAME=OUT4;  FILENAME OUT4
151      ! 'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-Corn1.C
151      ! GM';
 The SAS System
152        PROC GCHART DATA=SPLIT;
153             BLOCK FERT / GROUP=IRRIGATE SUMVAR=YIELD DISCRETE TYPE=MEAN;
154             PATTERN C=RED V=S; RUN;
NOTE: Foreground color BLACK same as background. Part of your graph may not be
      visible.
NOTE:  9 RECORDS WRITTEN TO
      C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-Corn1.CGM
155        GOPTIONS GSFNAME=OUT5;  FILENAME OUT5
           'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-Corn2.CGM';
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: PROCEDURE GCHART used:
      real time           0.08 seconds
      cpu time            0.04 seconds
156        PROC GCHART DATA=SPLIT;
157             BLOCK STAND / GROUP=IRRIGATE SUMVAR=YIELD DISCRETE TYPE=MEAN;
158             PATTERN C=RED V=S; RUN;
NOTE: Foreground color BLACK same as background. Part of your graph may not be
      visible.
NOTE:  9 RECORDS WRITTEN TO
      C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\24s-Anova-SplitPlot-Corn2.CGM
159        QUIT;
NOTE: There were 72 observations read from the data set WORK.SPLIT.
NOTE: PROCEDURE GCHART used:
      real time           0.06 seconds
      cpu time            0.03 seconds
56         GOPTIONS DEVICE=cgm GSFMODE=REPLACE GSFNAME=OUT1 NOPROMPT noROTATE;
57         GOPTIONS GSFNAME=OUT3;  FILENAME OUT3
                   'C:\Geaghan\EXST\EXST7015New\SAS\harvest.CGM';
58         ***GOPTIONS VPOS=48 HPOS=90;
59         PROC GCHART DATA=HARVEST;
60            BLOCK YEAR / GROUP=CUTTING SUMVAR=HARVEST DISCRETE TYPE=MEAN; RUN;
NOTE:  51 RECORDS WRITTEN TO C:\Geaghan\EXST\EXST7015New\SAS\harvest.CGM
61         quit;
NOTE: There were 64 observations read from the data set WORK.HARVEST.
NOTE: PROCEDURE GCHART used:
      real time           1.13 seconds
      cpu time            0.20 seconds
 
 
 



 
 




 

Modified: August 16, 2004
James P. Geaghan