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Details of the FACTEX Procedure |

Confounding rules give the values of factors in terms of the values
of the *run-indexing factors* for a design. (See "Types of Factors"
for a discussion of run-indexing factors.) The
FACTEX procedure uses these rules to construct designs. The confounding
rules also determine the alias structure of the design. To display the
confounding rules for a design, use the CONFOUNDING option in the
EXAMINE statement.

For two-level factors, the rules are displayed in a multiplicative notation using the default values of -1 and +1 for the factors. For example, the confounding rule

means that the level of factor X8 is derived as the product of the levels
of factors X1 through X7 for each run in the design. X8 will always have
a value of +1 or -1 since these are the values of X1 through X7. For
factors with *q*>2 levels, confounding rules are printed in an additive
notation, and the arithmetic is performed in the Galois field of size
*q*. For example, in a design for three-level factors, the confounding
rule

means that the level of factor F is computed by adding the levels of B
and D and two times the levels of C and E, all modulo 3. Note that if *q*
is not a prime number, Galois field arithmetic is not equivalent
to arithmetic modulo *q*.

Blocks are introduced into designs by using *block pseudo-factors*.
The confounding rule for the *i*th block pseudo-factor has
`[B i]` on the left-hand side.

For details on how confounding rules are constructed, see "Suitable Confounding Rules" .

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