![](../../../../common/62850/HTML/default/images/spacer.gif) |
![](../../../../common/62850/HTML/default/images/spacer.gif) |
Example 47.1 Analysis of Variance through PROC LATTICE
In the following example, from Cochran and Cox (1957, p. 406), the data are yields (Yield ) in bushels per acre of 25 varieties (Treatmnt ) of soybeans. The data are collected in two replications (Group ) of 25 varieties in five blocks (Block ) containing five varieties each. This is an example of a partially balanced square lattice design.
data Soy;
do Group = 1 to 2;
do Block = 1 to 5;
do Plot = 1 to 5;
input Treatmnt Yield @@;
output;
end;
end;
end;
drop Plot;
datalines;
1 6 2 7 3 5 4 8 5 6
6 16 7 12 8 12 9 13 10 8
11 17 12 7 13 7 14 9 15 14
16 18 17 16 18 13 19 13 20 14
21 14 22 15 23 11 24 14 25 14
1 24 6 13 11 24 16 11 21 8
2 21 7 11 12 14 17 11 22 23
3 16 8 4 13 12 18 12 23 12
4 17 9 10 14 30 19 9 24 23
5 15 10 15 15 22 20 16 25 19
;
proc print data=Soy;
id Treatmnt;
run;
proc lattice data=Soy;
run;
The results from these statements are shown in Output 47.1.1 and Output 47.1.2.
Output 47.1.1
Displayed Output from PROC PRINT
1 |
1 |
1 |
6 |
1 |
1 |
2 |
7 |
1 |
1 |
3 |
5 |
1 |
1 |
4 |
8 |
1 |
1 |
5 |
6 |
1 |
2 |
6 |
16 |
1 |
2 |
7 |
12 |
1 |
2 |
8 |
12 |
1 |
2 |
9 |
13 |
1 |
2 |
10 |
8 |
1 |
3 |
11 |
17 |
1 |
3 |
12 |
7 |
1 |
3 |
13 |
7 |
1 |
3 |
14 |
9 |
1 |
3 |
15 |
14 |
1 |
4 |
16 |
18 |
1 |
4 |
17 |
16 |
1 |
4 |
18 |
13 |
1 |
4 |
19 |
13 |
1 |
4 |
20 |
14 |
1 |
5 |
21 |
14 |
1 |
5 |
22 |
15 |
1 |
5 |
23 |
11 |
1 |
5 |
24 |
14 |
1 |
5 |
25 |
14 |
2 |
1 |
1 |
24 |
2 |
1 |
6 |
13 |
2 |
1 |
11 |
24 |
2 |
1 |
16 |
11 |
2 |
1 |
21 |
8 |
2 |
2 |
2 |
21 |
2 |
2 |
7 |
11 |
2 |
2 |
12 |
14 |
2 |
2 |
17 |
11 |
2 |
2 |
22 |
23 |
2 |
3 |
3 |
16 |
2 |
3 |
8 |
4 |
2 |
3 |
13 |
12 |
2 |
3 |
18 |
12 |
2 |
3 |
23 |
12 |
2 |
4 |
4 |
17 |
2 |
4 |
9 |
10 |
2 |
4 |
14 |
30 |
2 |
4 |
19 |
9 |
2 |
4 |
24 |
23 |
2 |
5 |
5 |
15 |
2 |
5 |
10 |
15 |
2 |
5 |
15 |
22 |
2 |
5 |
20 |
16 |
2 |
5 |
25 |
19 |
Output 47.1.2
Displayed Output from PROC LATTICE
1 |
212.18 |
212.18 |
8 |
501.84 |
62.7300 |
8 |
501.84 |
62.7300 |
24 |
559.28 |
23.3033 |
16 |
218.48 |
13.6550 |
24 |
720.32 |
30.0133 |
49 |
1491.78 |
30.4445 |
15.7915 |
17.9280 |
17.2159 |
12.1189 |
8.7959 |
174.34 |
19.0681 |
16.9728 |
14.6463 |
14.7687 |
12.8470 |
13.1701 |
9.0748 |
6.7483 |
8.3707 |
8.4489 |
23.5511 |
12.4558 |
12.6293 |
20.7517 |
19.3299 |
12.6224 |
10.5272 |
10.7007 |
7.3231 |
11.4013 |
11.6259 |
18.5306 |
12.2041 |
17.3265 |
15.4048 |
The efficiency of the experiment relative to a randomized complete block design is 174.34%. Precision is gained using the lattice design via the recovery of intra-block error information, enabling more accurate estimates of the treatment effects. Variety 8 of soybean had the lowest adjusted treatment mean (6.7483 bushels per acre), while variety 11 of soybean had the highest adjusted treatment mean (23.5511 bushels per acre).
Copyright
© 2009 by SAS Institute Inc., Cary, NC, USA. All
rights reserved.