The LATTICE Procedure |
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.
Obs | Group | Block | Treatmnt | Yield |
---|---|---|---|---|
1 | 1 | 1 | 1 | 6 |
2 | 1 | 1 | 2 | 7 |
3 | 1 | 1 | 3 | 5 |
4 | 1 | 1 | 4 | 8 |
5 | 1 | 1 | 5 | 6 |
6 | 1 | 2 | 6 | 16 |
7 | 1 | 2 | 7 | 12 |
8 | 1 | 2 | 8 | 12 |
9 | 1 | 2 | 9 | 13 |
10 | 1 | 2 | 10 | 8 |
11 | 1 | 3 | 11 | 17 |
12 | 1 | 3 | 12 | 7 |
13 | 1 | 3 | 13 | 7 |
14 | 1 | 3 | 14 | 9 |
15 | 1 | 3 | 15 | 14 |
16 | 1 | 4 | 16 | 18 |
17 | 1 | 4 | 17 | 16 |
18 | 1 | 4 | 18 | 13 |
19 | 1 | 4 | 19 | 13 |
20 | 1 | 4 | 20 | 14 |
21 | 1 | 5 | 21 | 14 |
22 | 1 | 5 | 22 | 15 |
23 | 1 | 5 | 23 | 11 |
24 | 1 | 5 | 24 | 14 |
25 | 1 | 5 | 25 | 14 |
26 | 2 | 1 | 1 | 24 |
27 | 2 | 1 | 6 | 13 |
28 | 2 | 1 | 11 | 24 |
29 | 2 | 1 | 16 | 11 |
30 | 2 | 1 | 21 | 8 |
31 | 2 | 2 | 2 | 21 |
32 | 2 | 2 | 7 | 11 |
33 | 2 | 2 | 12 | 14 |
34 | 2 | 2 | 17 | 11 |
35 | 2 | 2 | 22 | 23 |
36 | 2 | 3 | 3 | 16 |
37 | 2 | 3 | 8 | 4 |
38 | 2 | 3 | 13 | 12 |
39 | 2 | 3 | 18 | 12 |
40 | 2 | 3 | 23 | 12 |
41 | 2 | 4 | 4 | 17 |
42 | 2 | 4 | 9 | 10 |
43 | 2 | 4 | 14 | 30 |
44 | 2 | 4 | 19 | 9 |
45 | 2 | 4 | 24 | 23 |
46 | 2 | 5 | 5 | 15 |
47 | 2 | 5 | 10 | 15 |
48 | 2 | 5 | 15 | 22 |
49 | 2 | 5 | 20 | 16 |
50 | 2 | 5 | 25 | 19 |
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%. 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.