Specifying Factor Structures

factor-selections

Table 50.1

factor-selections

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

Design	Page Number
Completely randomized design	this page
Split-plot design	this page
Nested design	this page
Latin square design	this page
Generalized cyclic incomplete block design	this page