SIZE Statement :: SAS/QC(R) 13.1 User's Guide

SIZE Statement

SIZE size-specification ;

You use the SIZE statement to specify the size of the design, which is the number of runs in the design. The SIZE statement is required for designs of less than a full replicate (for example, fractional factorial designs). By default, the design consists of one full replication of all possible combinations of the factors.

The two simplest explicit size-specifications that you can use are

DESIGN=n, which specifies the number of runs (n) in the design
FRACTION=h, which specifies $1/h$ of one full replicate

Use only one of these two options. In all, there are six mutually exclusive size-specifications that you can use, as described by the following list:

DESIGN=n: specifies the actual number of runs in the design. The number of runs must be a power of the number of levels q for the factors in the design. (See the NLEV= option.) If the last FACTORS statement does not contain the NLEV= option, then q = 2 by default, and as a result, n must be a power of 2. For an example, see Example 7.1.
FRACTION=h: specifies the fraction of one full replication of all possible combinations of the factors. For instance, FRACTION=2 specifies a half-fraction, FRACTION=4 specifies a quarter-fraction, and so on. In general, FRACTION=h specifies a design with $1/h$ of the runs in a full replicate. If the design has f factors, each with q levels, then the size of the design is $q^ f/h$ . If you use FRACTION=h, h must be a power of q. See Example 7.4.
NRUNFACS=m: specifies the number of run-indexing factors in the design. The design contains one run for each possible combination of the levels of the run-indexing factors. Run-indexing factors are the first m factors for a design in $q^ m$ runs. All possible combinations of the levels of the run-indexing factors occur in the design. As a result, if each factor has q levels, the number of runs in the design is $q^ m$ . For details about run-indexing factors, see Types of Factors and Structure of General Factorial Designs.
DESIGN=MINIMUM FRACTION=MAXIMUM NRUNFACS=MINIMUM: constructs a design with the minimum number of runs (no larger than one full replicate) given all of the other characteristics of the design. In other words, the design size is optimized. You cannot specify this option if you specify any of the block size optimization features in the BLOCKS statement (see NBLKFACS=MAXIMUM).

Equivalence of Specifications

The three explicit size-specifications are related to each other, as demonstrated by the following example. Suppose you want to construct a design for 11 two-level factors in 128 runs. Since $128=2^{11}/16=2^7$ , three equivalent size specifications for this design are

size design=128;
size fraction=16;
size nrunfacs=7;