SAS/STAT 9.1, Users Guide, Volume 3 (volume 3 ONLY)

Example 38.1. 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 38.1.1 and Output 38.1.2.

Output 38.1.1: 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 38.1.2: Displayed Output from PROC LATTICE

The Lattice Procedure Analysis of Variance for Yield Sum of Mean Source DF Squares 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 Description Value 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

The Lattice Procedure 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).