Confounding Rules

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 that uses the default values of and 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 or since these are the values of X1 through X7. For factors with levels, confounding rules are printed in an additive notation, and the arithmetic is performed in the Galois field of size . 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 is not a prime number, Galois field arithmetic is not equivalent to arithmetic modulo .

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

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