Example 35.1: 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 35.1.1 and Output 35.1.2.
Output 35.1.1: Displayed Output from PROC PRINT
Treatmnt |
Group |
Block |
Yield |
1 |
1 |
1 |
6 |
2 |
1 |
1 |
7 |
3 |
1 |
1 |
5 |
4 |
1 |
1 |
8 |
5 |
1 |
1 |
6 |
6 |
1 |
2 |
16 |
7 |
1 |
2 |
12 |
8 |
1 |
2 |
12 |
9 |
1 |
2 |
13 |
10 |
1 |
2 |
8 |
11 |
1 |
3 |
17 |
12 |
1 |
3 |
7 |
13 |
1 |
3 |
7 |
14 |
1 |
3 |
9 |
15 |
1 |
3 |
14 |
16 |
1 |
4 |
18 |
17 |
1 |
4 |
16 |
18 |
1 |
4 |
13 |
19 |
1 |
4 |
13 |
20 |
1 |
4 |
14 |
21 |
1 |
5 |
14 |
22 |
1 |
5 |
15 |
23 |
1 |
5 |
11 |
24 |
1 |
5 |
14 |
25 |
1 |
5 |
14 |
1 |
2 |
1 |
24 |
6 |
2 |
1 |
13 |
11 |
2 |
1 |
24 |
16 |
2 |
1 |
11 |
21 |
2 |
1 |
8 |
2 |
2 |
2 |
21 |
7 |
2 |
2 |
11 |
12 |
2 |
2 |
14 |
17 |
2 |
2 |
11 |
22 |
2 |
2 |
23 |
3 |
2 |
3 |
16 |
8 |
2 |
3 |
4 |
13 |
2 |
3 |
12 |
18 |
2 |
3 |
12 |
23 |
2 |
3 |
12 |
4 |
2 |
4 |
17 |
9 |
2 |
4 |
10 |
14 |
2 |
4 |
30 |
19 |
2 |
4 |
9 |
24 |
2 |
4 |
23 |
5 |
2 |
5 |
15 |
10 |
2 |
5 |
15 |
15 |
2 |
5 |
22 |
20 |
2 |
5 |
16 |
25 |
2 |
5 |
19 |
|
Output 35.1.2: Displayed Output from PROC LATTICE
Analysis of Variance for Yield |
Source |
DF |
Sum of Squares |
Mean Square |
Replications |
1 |
212.18 |
212.18 |
Blocks within Replications (Adj.) |
8 |
501.84 |
62.7300 |
Component B |
8 |
501.84 |
62.7300 |
Treatments (Unadj.) |
24 |
559.28 |
23.3033 |
Intra Block Error |
16 |
218.48 |
13.6550 |
Randomized Complete Block Error |
24 |
720.32 |
30.0133 |
Total |
49 |
1491.78 |
30.4445 |
Additional Statistics for Yield |
Variance of Means in Same Block |
15.7915 |
Variance of Means in Different Bloc |
17.9280 |
Average of Variance |
17.2159 |
LSD at .01 Level |
12.1189 |
LSD at .05 Level |
8.7959 |
Efficiency Relative to RCBD |
174.34 |
|
Adjusted Treatment Means for Yield |
Treatment |
Mean |
1 |
19.0681 |
2 |
16.9728 |
3 |
14.6463 |
4 |
14.7687 |
5 |
12.8470 |
6 |
13.1701 |
7 |
9.0748 |
8 |
6.7483 |
9 |
8.3707 |
10 |
8.4489 |
11 |
23.5511 |
12 |
12.4558 |
13 |
12.6293 |
14 |
20.7517 |
15 |
19.3299 |
16 |
12.6224 |
17 |
10.5272 |
18 |
10.7007 |
19 |
7.3231 |
20 |
11.4013 |
21 |
11.6259 |
22 |
18.5306 |
23 |
12.2041 |
24 |
17.3265 |
25 |
15.4048 |
|
The efficiency of the experiment relative to a randomized complete
block design is 174.34 percent. Precision is gained using the lattice
design via the recovery of intrablock 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 © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.