## Example 67.1 A Split-Plot Design

This plan is appropriate for a split-plot design with main plots forming a randomized complete block design. In this example, there are three blocks, four main plots per block, and two subplots per main plot. First, three random permutations (one for each of the blocks) of the integers 1, 2, 3, and 4 are produced. The four integers correspond to the four levels of the main plot factor a; the permutation determines how the levels of a are assigned to the main plots within a block. For each of these 12 numbers (four numbers per block for three blocks), a random permutation of the integers 1 and 2 is produced. Each two-integer permutation determines the assignment of the two levels of the subplot factor b within a main plot. The following statements produce Output 67.1.1:

```title 'Split Plot Design';
proc plan seed=37277;
factors Block=3 ordered a=4 b=2;
run;
```

Output 67.1.1 A Split-Plot Design
 Split Plot Design

The PLAN Procedure

Factor Select Levels Order
Block 3 3 Ordered
a 4 4 Random
b 2 2 Random

Block a b
1 4 2 1
3 2 1
1 2 1
2 2 1
2 4 1 2
3 1 2
1 2 1
2 1 2
3 4 2 1
2 2 1
3 2 1
1 2 1