The PLAN Procedure

## Specifying Factor Structures

By appropriately combining features of the PLAN procedure, you can construct an extensive set of designs. The basic tools are the factor-selections, which are used in the FACTORS and TREATMENTS statements. Table 50.1 summarizes how the procedure interprets various factor-selections (assuming that the ORDERED option is not specified in the PROC PLAN statement).

Table 50.1: Factor Selection Interpretation
 Form of Request Interpretation Example Results name=m produce a random permutation of the integers 1,2, ... ,m. `t=15` lists a random ordering of the numbers 1,2, ... ,15. name=m cyclic cyclically permute the integers 1,2, ... ,m. `t=5 cyclic` selects the integers 1 to 5. On the next iteration, selects 2,3,4,5,1; then 3,4,5,1,2; and so on. name=m of n choose a random sample of m integers (without replacement) from the set of integers 1,2, ... ,n. `t=5 of 15` lists a random selection of 5 numbers from 1 to 15. First, the procedure selects 5 numbers and then arranges them in random order. name=m of n ordered has the same effect as name=m ordered. `t=5 of 15` `ordered` lists the integers 1 to 5 in increasing order (same as t=5 ordered). name=m of n cyclic permute m of the n integers. `t=5 of 30` `cyclic` selects the integers 1 to 5. On the next iteration, selects 2,3,4,5,6; then 3,4,5,6,7; and so on. The 30th iteration 30,1,2,3,4; the 31st iteration produces 1,2,3,4,5; and so on. name=m perm produce a list of all permutations of m integers. `t=5 perm` lists the integers 1,2,3,4,5 on the first iteration; on the second lists 1,2,3,5,4; and on the 119th iteration lists 5,4,3,1,2; and on the last (120th) lists 5,4,3,2,1. name=m of n comb choose combinations of m integers from n integers. `t=3 of 5` `comb` lists all combinations of 5 choose 3 integers. The first iteration is 1,2,3; the second is 1,2,4; the third is 1,2,5; and so on until the last iteration 3,4,5. name=m of n cyclic (initial-block) permute m of the n integers, starting with the values specified in the initial-block. `t=4 of 30` `cyclic` `(2 10 15 18)` selects the integers 2,10,15,18. On the next iteration, selects 3,11,16,19; then 4,12,17,20; and so on. The thirteenth iteration is 14,22,27,30; the fourteenth iteration is 15,23,28,1; and so on. name=m of n cyclic (initial-block) increment permute m of the n integers. Start with the values specified in the initial-block, then add the increment to each value. `t=4 of 30` `cyclic` `(2 10 15 18)` `2` selects the integers 2,10,15,18. On the next iteration, selects 4,12,17,20; then 6,14,19,22; and so on. The wrap occurs at the eighth iteration. The eighth iteration is 16,24,29,2; and so on.

In Table 50.1, in order for more than one iteration to appear in the plan, another name=j factor selection (with j>1) must precede the example factor selection. For example, the following statements produce six of the iterations described in the last entry of Table 50.1.

```   proc plan;
factors c=6 ordered t=4 of 30 cyclic (2 10 15 18) 2;
run;
```

The following statements create a randomized complete block design and output the design to a data set.

```   proc plan ordered;
factors blocks=3 cell=5;
treatments t=5 random;
output out=rcdb;
run;
```

Table 50.2 lists other kinds of experiment designs that can be constructed by PROC PLAN, along with section and page references for them in this chapter.

Table 50.2: Experimental Design Examples