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 2-level factors, the rules are displayed in a multiplicative notation that uses the default values of –1 and +1 for the factors. For example, the confounding rule
X8 = X1*X2*X3*X4*X5*X6*X7
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 always has 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 3-level factors, the confounding rule
F = B + (2*C) + D + (2*E)
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 ith block pseudo-factor has [B i] on the left-hand side.
For details about how confounding rules are constructed, see Suitable Confounding Rules.