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(drop=plot);
  do Group = 1 to 2;
    do Block = 1 to 5;
      do Plot = 1 to 5;
         input Treatmnt Yield @@;
         output;
      end;
    end;
  end;
  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.

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).